Class deriving from csl::TensorFieldElement, may enter expressions. In contrary to QuantumFieldParent, it is not a inherited from any class. More...

#include <quantumField.h>

Inheritance diagram for mty::QuantumField:

[legend]

Public Member Functions
	QuantumField (const csl::Tensor &t_vector, const csl::Parent &t_parent)
	Constructor with two parameters. More...

	QuantumField (const csl::Tensor &t_vector, const csl::Parent &t_parent, const std::vector< csl::Index > &indices)
	Constructor with three parameters. More...

	QuantumField (const csl::Tensor &t_vector, const csl::Parent &t_parent, const csl::IndexStructure &indices)
	Constructor with three parameters. More...

	QuantumField ()
	Default constructor. Initializes no parent and no space-time point. More...

	QuantumField (QuantumField const &)=default
	Default Copy constructor.

	QuantumField (QuantumField &&)=default
	Default Move constructor.

QuantumField &	operator= (const QuantumField &other)=default
	Default copy assignement operator.

QuantumField &	operator= (QuantumField &&)=default
	Default move assignement operator.

QuantumFieldParent *	getQuantumParent () const
	Returns a pointer to the QuantumFieldParent of the field. More...

Particle	getParticle () const
	Returns a mty::Particle, pointer to the parent of the field. More...

auto	getGaugeIrrep () const

auto	getFlavorIrrep () const

template<class GroupType >
auto	getGroupIrrep (GroupType &&group) const

template<class FlavorGroupType >
auto	getFlavorIrrep (FlavorGroupType &&group) const

int	getSpinDimension () const
	See QuantumFieldParent::getSpinDimension(). More...

csl::Expr	getEnergyDimension () const
	See QuantumFieldParent::getEnergyDimension(). More...

csl::Expr	getMass () const
	See QuantumFieldParent::getMass(). More...

csl::Expr	getWidth () const
	See QuantumFieldParent::getWidth(). More...

PartnerShip	getPartnerShip () const

bool	isChiral () const
	See QuantumFieldParent::isChiral(). More...

Chirality	getChirality () const
	See QuantumFieldParent::getChirality(). More...

void	setChirality (Chirality chirality)
	Sets the chirality of the particle. More...

bool	isGaugeBoson () const
	See QuantumFieldParent::isGaugeBoson(). More...

csl::Expr	getXiGauge () const
	See QuantumFieldParent::getXiGauge(). More...

csl::Expr	getSquaredMass () const
	Returns the mass squared of the field. More...

bool	getConjugated () const
	Tells if the field is complex conjugated. More...

bool	isExternal () const
	Tells if the field is an external field. More...

bool	isOnShell () const

bool	isBosonic () const
	See QuantumFieldParent::isBosonic(). More...

bool	isFermionic () const
	See QuantumFieldParent::isFermionic(). More...

bool	isAntiCommuting () const
	See QuantumFieldParent::isAntiCommuting(). More...

bool	isSelfConjugate () const
	See QuantumFieldParent::isSelfConjugate(). More...

bool	isReal () const override

bool	isPhysical () const
	Tells if the field is physical, i.e. may appear in external legs. More...

bool	isContractibleWith (const QuantumField &other) const
	See QuantumFieldParent::isContractibleWith(). More...

bool	isExactlyContractiblewith (const QuantumField &other) const
	Tests if the the field is exactly contractible with the other one. More...

void	addDerivative (const csl::Index &index)
	Adds a derivative index to the the field. More...

bool	hasDerivative () const
	Tells if the field has derivative indices. More...

csl::IndexStructure	getDerivativeStructure () const
	Returns the derivative structure of the field. More...

csl::Expr	getPropagator (const QuantumField &other, csl::Tensor &vertex) const
	Returns the propagator with another QuantumField. More...

csl::Expr	getLSZInsertion (const csl::Tensor &momentum, bool ruleMode=false, bool lock=false) const
	Returns the expression of the LSZ insertion corresponding to the field. More...

QuantumField	getConjugatedField () const
	Copies the field in a new new one and conjugates it before returning it. More...

csl::Expr	contraction (csl::Expr_info other) const override

virtual csl::Expr	matrixChargeConjugation (csl::Expr_info other) const

std::optional< csl::Expr >	getComplexConjugate () const override
	Returns the complex conjugate expression of the field. More...

void	conjugate ()
	Conjugates the field and changes its particle number. More...

void	setExternal (bool t_external)
	Sets the external property of the particle. More...

void	setOnShell (bool t_onShell)

virtual void	setIncoming (bool t_incoming)
	Sets the incoming property of the particle. More...

virtual void	setParticle (bool t_particle)
	Sets the particle property of the particle. More...

void	setPartnerShip (PartnerShip const &t_partnerShip)

void	setDerivativeStructure (const csl::IndexStructure &structure)
	Sets the derivative structure of the field. More...

bool	getCommutable () const override
	Tells if the field is a commutable object in products. More...

bool	commutesWith (csl::Expr_info other, int sign=-1) const override
	Tells if the field commutes with another expression. More...

bool	hasContractionProperty (csl::Expr_info expr) const override
	Tells if the field has an indicial contraction property with another expression. More...

csl::unique_Expr	copy_unique () const override
	Returns a copy of the field in a std::unique_ptr. More...

bool	isIndexed () const override
	Tells if the field is indexed. More...

bool	operator== (csl::Expr_info other) const override
	Compares the field with another expression. More...

bool	compareWithDummy (csl::Expr_info other, std::map< csl::Index, csl::Index > &constraints, bool keepAllCosntraints=false) const override
	Compares the field with another expression. More...

bool	operator< (const QuantumField &other) const
	Compares the simplicity of the field with another. More...

bool	operator== (const QuantumField &other) const
	Compares the field with another. More...

bool	operator!= (const QuantumField &other) const
	Compares the field with another. More...

bool	isParticle () const
	Tells if the (external) field is a particle or anti particle. More...

bool	isIncoming () const
	Tells if the (external) field is incoming or outgoing. More...

bool	isIncomingParticle () const
	Tells if the (external) field is an incoming particle. More...

bool	isOutgoingParticle () const
	Tells if the (external) field is an outgoing particle. More...

bool	isIncomingAntiParticle () const
	Tells if the (external) field is an incoming anti-particle. More...

bool	isOutgoingAntiParticle () const
	Tells if the (external) field is an outgoing an anti-particle. More...

Public Member Functions inherited from csl::TensorFieldElement
csl::PrimaryType	getPrimaryType () const override

csl::Type	getType () const override

void	print (int mode=0, std::ostream &out=std::cout, bool lib=false) const override

std::string	printLaTeX (int mode=0) const override

std::optional< Expr >	evaluate (csl::eval::mode user_mode=csl::eval::base) const override

bool	commutesWith (Expr_info expr, int sign=-1) const override

bool	dependsOn (Expr_info expr) const override

bool	dependsExplicitlyOn (Expr_info expr) const override

bool	compareWithDummy (Expr_info other, std::map< Index, Index > &constraints, bool keepAllCosntraints=false) const override

bool	operator== (Expr_info expr) const override

Public Member Functions inherited from csl::TensorElement
	TensorElement (const Index &t_index, const Parent &t_parent)

	TensorElement (const std::vector< Index > &indices, const Parent &t_parent)

	TensorElement (const IndexStructure &indices, const Parent &t_parent)

	TensorElement (const Abstract *&expression)

	TensorElement (const Expr &expression)

int	getNIndices () const override

IndexStructure	getIndexStructure () const override

Index	getIndex (int i) const override

bool	askTerm (Expr_info expr, bool exact=false) const override

const std::vector< Equation *> &	getProperties () const override

void	addProperty (Equation *property) override

void	removeProperty (Equation *property) override

bool	checkIndexStructure (const std::vector< Index > &t_index) const override

std::optional< Expr >	replaceIndex (const Index &indexToReplace, const Index &newIndex, bool refresh=true) const override

void	setIndexStructure (const IndexStructure &t_index) override

bool	hasContractionProperty (Expr_info B) const override

Expr	contraction (Expr_info B) const override

Expr	applyPermutation (const Permutation &permutations) const

csl::vector_expr	getPermutations (bool optimize=true) const override

csl::vector_expr	getAlternateForms () const override

std::optional< Expr >	derive (Expr_info expr) const override

Public Member Functions inherited from csl::AbstractElement
	AbstractElement (const std::shared_ptr< AbstractParent > &t_parent)

Parent	getParent () const override

std::string const &	getName () const override

void	setParent (const Parent &t_parent) override

void	setName (const std::string &t_name) override

void	setCommutable (bool t_commutable) override

int	isPolynomial (Expr_info variable) const override

std::optional< Expr >	getPolynomialTerm (Expr_info variable, int order) const override

Public Member Functions inherited from csl::Complexified
std::optional< Expr >	getRealPart () const override

Expr	getImaginaryPart () const override

Public Member Functions inherited from csl::AbstractBuildingBlock
bool	isBuildingBlock () const override

std::optional< Expr >	expand (bool full=false, bool inplace=false) const override

std::optional< Expr >	factor (bool full=false) const override

std::optional< Expr >	factor (Expr_info expr, bool full=false) const override

std::optional< Expr >	getTerm () const override

std::optional< Expr >	getComplexModulus () const override

std::optional< Expr >	findSubExpression (Expr_info subExpression, const Expr &newExpression) const override

Public Member Functions inherited from csl::Abstract
void	printExplicit (int mode=0) const

virtual int	getDim () const

virtual bool	isInteger () const

virtual bool	getValued () const

virtual long double	getValue () const

virtual long long int	getNum () const

virtual long long int	getDenom () const

virtual int	getNArgs (int axis=0) const

virtual csl::vector_expr::iterator	begin ()

virtual csl::vector_expr::iterator	end ()

virtual csl::vector_expr::const_iterator	begin () const

virtual csl::vector_expr::const_iterator	end () const

virtual Expr const &	getArgument (int iArg=0) const

virtual Expr const &	getArgument (const std::vector< int > &indices) const

virtual const csl::vector_expr &	getVectorArgument () const

virtual Expr	getVariable () const

virtual int	getOrder () const

virtual int	getSign () const

virtual bool	isAnOperator () const

virtual bool	isEmpty () const

virtual Expr	getOperand () const

virtual std::vector< int >	getShape () const

virtual IndexStructure	getFreeIndexStructure () const

virtual int	getNContractedPairs () const

virtual std::set< std::pair< int, int > >	getContractedPair () const

virtual void	setValue (long double t_value)

virtual void	setArgument (const Expr &expr, int iArg=0)

virtual void	setArgument (const Expr &expr, const std::vector< int > &indices)

virtual void	setOperand (const Expr &operand)

virtual void	setOperandPrivate (const Expr &operand, bool leaveEmpty)

virtual void	setVectorArgument (const csl::vector_expr &t_argument)

virtual void	insert (const Expr &expr, bool side=1)

virtual void	setFullySymmetric ()

virtual void	setFullyAntiSymmetric ()

virtual void	addSymmetry (int i1, int i2)

virtual void	addAntiSymmetry (int i1, int i2)

virtual int	permut (int i1, int i2)

virtual Expr	getNumericalFactor () const

virtual int	getNFactor () const

virtual csl::vector_expr	getFactors () const

virtual void	getExponents (std::vector< Expr > const &factors, std::vector< Expr > &exponents) const

virtual bool	checkIndexStructure (const std::initializer_list< Index > &index) const

virtual int	getParity (Expr_info t_variable) const

virtual bool	matchShape (Expr_info expr, bool exact=false) const

virtual long double	evaluateScalar () const

virtual std::optional< Expr >	collect (std::vector< Expr > const &factors, bool full=false) const

virtual Expr	suppressTerm (Expr_info expr) const

virtual std::optional< Expr >	suppressExponent (Expr const &factor, Expr const &exponent) const

virtual std::optional< Expr >	expand_if (std::function< bool(Expr const &)> const &f, bool full=false, bool inPlace=false) const

virtual std::optional< Expr >	getComplexArgument () const

virtual Expr	applyOperator (const Expr &operand, bool leaveEmpty=false) const

virtual Expr	addition_own (const Expr &expr) const

virtual Expr	multiplication_own (const Expr &expr, bool side=1) const

virtual Expr	division_own (const Expr &expr) const

virtual Expr	exponentiation_own (const Expr &expr) const

virtual Expr	getRegularExpression () const

virtual Expr	tensordot (const Expr &expr) const

virtual Expr	dot (const Expr &expr) const

virtual Expr	getSum () const

virtual Expr	getProduct () const

virtual Expr	getVectorialModulus () const

virtual Expr	getSubVectorial (int iExcept) const

virtual Expr	getSubVectorial (int iExcept, int jExcept) const

virtual Expr	getSubVectorial (const std::vector< int > &exceptions) const

virtual Expr	determinant () const

virtual Expr	trace () const

virtual Expr	trace (int axis1, int axis2) const

virtual Expr	transpose () const

virtual Expr	symmetrise () const

virtual Expr	antisymmetrise () const

virtual Expr	inverseMatrix () const

virtual void	operator= (double t_value)

virtual bool	operator== (int t_value) const

virtual bool	operator== (double t_value) const

virtual bool	operator!= (int t_value) const

virtual bool	operator!= (double t_value) const

bool	operator!= (const Expr_c &expr) const

virtual Expr const &	operator[] (int iArg) const

virtual Expr &	operator[] (int iArg)

virtual bool	operator< (Expr_info expr) const=0

bool	operator< (const Expr_c &expr) const

bool	operator> (Expr_info expr) const

bool	operator>= (Expr_info expr) const

bool	operator<= (const Expr_c &expr) const

Protected Attributes
bool	particle = true
	Tells if the QuantumField, if external, is a particle or an anti-particle. More...

bool	external = false
	Tells if the field is external (initial of final state in computations) or not. More...

bool	onShell = false

bool	incoming = true
	Tells if the QuantumField, if external, is a incoming or outgoing. More...

csl::IndexStructure	derivativeIndices {}
	csl::IndexStructure allowing to store derivative indices, to keep track of terms in \( \partial _\mu \) in computations while having only QuantumField objects. More...

PartnerShip	partnerShip {}
	Wanted partner for fermion ordering in amplitude results, together with the number defining the fermion. More...

Protected Attributes inherited from csl::TensorElement
IndexStructure	index

Protected Attributes inherited from csl::AbstractElement
std::shared_ptr< AbstractParent >	parent

Friends
template<typename ... Args>
csl::Expr	quantumfield_s (Args &&...args)
	Creates and returns an expression corresponding to a QuantumField. More...

Detailed Description

Class deriving from csl::TensorFieldElement, may enter expressions. In contrary to QuantumFieldParent, it is not a inherited from any class.

Any quantum field (boson, fermion, gauge ...) will have QuantumField instances. This simplifies the use of a generic instance, QuantumField, that will ask its parent to know its own properties (contractions, commutation, spin, mass, ...). All physical information is contained in QuantumFieldParent and its derived classes, except the few attributes of QuantumField that are instance-specific. QuantumField objects will not be in general directly created by the user. Giving a QuantumFieldParent or a Particle, one should used their operator()() to create a QuantumField instance, as an actual expression that may enter in mathematical expressions.

See also: QuantumFieldParent, Particle, csl::Expr, TensorFieldElement, Particle::operator()().

Constructor & Destructor Documentation

◆ QuantumField() [1/4]

mty::QuantumField::QuantumField	(	const csl::Tensor &	t_vector,
		const csl::Parent &	t_parent
	)

Constructor with two parameters.

This constructor takes no index and concerns then scalar fields.

Parameters

t_vector	Space_time point of the field.
t_parent	Parent (must be derived from QuantumFieldParent) of the field.

◆ QuantumField() [2/4]

mty::QuantumField::QuantumField	(	const csl::Tensor &	t_vector,
		const csl::Parent &	t_parent,
		const std::vector< csl::Index > &	indices
	)

Constructor with three parameters.

Parameters

t_vector	Space_time point of the field.
t_parent	Parent (must be derived from QuantumFieldParent) of the field.
indices	Set of indices of the tensor.

◆ QuantumField() [3/4]

mty::QuantumField::QuantumField	(	const csl::Tensor &	t_vector,
		const csl::Parent &	t_parent,
		const csl::IndexStructure &	indices
	)

Constructor with three parameters.

Parameters

t_vector	Space_time point of the field.
t_parent	Parent (must be derived from QuantumFieldParent) of the field.
indices	Set of indices of the tensor.

◆ QuantumField() [4/4]

mty::QuantumField::QuantumField ( )

Default constructor. Initializes no parent and no space-time point.

May be useful in some situations but keep in mind that a non initialized QuantumField is an invalid state and may cause problems.

Member Function Documentation

◆ addDerivative()

void mty::QuantumField::addDerivative ( const csl::Index & index )

Adds a derivative index to the the field.

Parameters

index Derivative index to add.

See also: derivativeIndices, hasDerivative(), getDerivativeStructure(), setDerivativeStructure().

◆ commutesWith()

bool mty::QuantumField::commutesWith	(	csl::Expr_info	other,
		int	sign = `-1`
	)		const

override

Tells if the field commutes with another expression.

This function assumes only that for two anti-commuting fields \( \psi _1 \) and \( \psi _2 \) we have \(\{\psi _1, \psi _2\}=0\). This function returns in this case true iif sign = +1 (anticommutation). For all other cases, this function returns true if sign = -1. In particular, beware that anti-commuting fields embedded in more complicated expressions are not taken into account for now. This means that \( \{\psi_ 1, \psi _2+\psi _3\}\neq 0 \)

Parameters

other	Expression with which we test the commutation.
sign	Sign of the commutation. +1 means anticommutation, -1 (default) means commutation.

Returns: True if the field commutes with other.; False else.

◆ compareWithDummy()

bool mty::QuantumField::compareWithDummy	(	csl::Expr_info	other,
		std::map< csl::Index, csl::Index > &	constraints,
		bool	keepAllCosntraints = `false`
	)		const

override

Compares the field with another expression.

Uses TensorFieldElement::compareWithDummy() and takes care of comparing the derivative structures of two fields if the other expression is another field (otherwise this function returns false). Dummy indices may compare succesfully with each other with different names. Only the abstract index structure is compared. Free indices must match exactly.

Parameters

other	Expression to compare.
constraints	Mapping constraints between already compared dummy indices.
keepAllCosntraints	Tell if constraints must be relaxed once pairs of indices are matched (default = false, the user should not need that).

Returns: True if the other expression is the same field, with the same structure (allowing different dummy indices) and space-time point.; False else.

See also: TensorFieldElement::compareWithDummy(), derivativeIndices.

◆ conjugate()

void mty::QuantumField::conjugate ( )

Conjugates the field and changes its particle number.

For example, a particle \( \phi (X) \) as insertion is an outgoing particle (otherwise it would be complex conjugated). Conjugating the particle, we get \( \phi ^*(X) \) an outgoing antiparticle.

See also: particle, getConjugatedField().

◆ copy_unique()

csl::unique_Expr mty::QuantumField::copy_unique ( ) const

override

Returns a copy of the field in a std::unique_ptr.

Returns: A std::unique_ptr<Abstract>, copy of the field.

◆ getChirality()

Chirality mty::QuantumField::getChirality ( ) const

See QuantumFieldParent::getChirality().

Returns: The chirality of the particle.

◆ getCommutable()

bool mty::QuantumField::getCommutable ( ) const

overridevirtual

Tells if the field is a commutable object in products.

Returns: True if the field is not anti commuting.; False else.

See also: #bosonic, isBosonic(), isFermionic(), isAntiCommuting().

Reimplemented from csl::AbstractElement.

◆ getComplexConjugate()

optional< csl::Expr > mty::QuantumField::getComplexConjugate ( ) const

overridevirtual

Returns the complex conjugate expression of the field.

Returns: The complex conjugate expression of the field.

See also: conjugate(), getConjugatedField().

Reimplemented from csl::TensorElement.

◆ getConjugated()

bool mty::QuantumField::getConjugated ( ) const

Tells if the field is complex conjugated.

Returns: True if the field is complex conjugated.; False else.

See also: Complexified::conjugated.

◆ getConjugatedField()

QuantumField mty::QuantumField::getConjugatedField ( ) const

Copies the field in a new new one and conjugates it before returning it.

Returns: The conjugated field.

See also: conjugate().

◆ getDerivativeStructure()

csl::IndexStructure mty::QuantumField::getDerivativeStructure ( ) const

Returns the derivative structure of the field.

Returns: The derivative structure of the field.

See also: derivativeIndices, addDerivative(), hasDerivative(), setDerivativeStructure().

◆ getEnergyDimension()

csl::Expr mty::QuantumField::getEnergyDimension ( ) const

See QuantumFieldParent::getEnergyDimension().

Returns: The energy dimension of the particle.

◆ getLSZInsertion()

csl::Expr mty::QuantumField::getLSZInsertion	(	const csl::Tensor &	momentum,
		bool	ruleMode = `false`,
		bool	lock = `false`
	)		const

Returns the expression of the LSZ insertion corresponding to the field.

Parameters

momentum	Momentum of the insertion.
ruleMode	Boolean that is true if we want to determine the feynman rule (in this case the insertion is not the same).

Returns: The expressoin of the LSZ insertion.

◆ getMass()

csl::Expr mty::QuantumField::getMass ( ) const

See QuantumFieldParent::getMass().

Returns: The mass of the particle.

◆ getParticle()

Particle mty::QuantumField::getParticle ( ) const

inline

Returns a mty::Particle, pointer to the parent of the field.

As QuantumField inherits from csl::TensorFieldElement, its parent is in the form of a csl::Parent. This function then makes a conversion to a mty::Particle before returning the pointer.

Returns: A shared pointer to the QuantumFieldParent (i.e. mty::Particle) of the field.

◆ getPropagator()

csl::Expr mty::QuantumField::getPropagator	(	const QuantumField &	other,
		csl::Tensor &	vertex
	)		const

Returns the propagator with another QuantumField.

This function checks if the propagator is non null with isExactlyContractiblewith(). Then, it ensure that if the field is not self-conjugate the conjugated field is on the right of the contraction (and adds a minus sign if the field is anti-commuting).

Parameters

other	Other field in the contraction.
vertex	Momentum integrated in the propagator.

Returns: The expression of the propagator.

See also: isExactlyContractiblewith(), isAntiCommuting(), isSelfConjugate(), QuantumFieldParent::getPropagator(), QuantumFieldParent::getInvPropagator(), , QuantumFieldParent::propagator, Propagator_func, quantumFieldTheory.h.

◆ getQuantumParent()

QuantumFieldParent* mty::QuantumField::getQuantumParent ( ) const

inline

Returns a pointer to the QuantumFieldParent of the field.

As QuantumField inherits from csl::TensorFieldElement, its parent is in the form of a csl::Parent. This function then makes a conversion to a mty::QuantumFieldParent before returning the pointer.

Returns: A pointer to the QuantumFieldParent of the field.

◆ getSpinDimension()

int mty::QuantumField::getSpinDimension ( ) const

See QuantumFieldParent::getSpinDimension().

Returns: Twice the spin of the particle.

◆ getSquaredMass()

csl::Expr mty::QuantumField::getSquaredMass ( ) const

Returns the mass squared of the field.

Equivalent to pow_s(getMass(), 2).

Returns: The squared mass of the particle.

◆ getWidth()

csl::Expr mty::QuantumField::getWidth ( ) const

See QuantumFieldParent::getWidth().

Returns: The width of the particle.

◆ getXiGauge()

csl::Expr mty::QuantumField::getXiGauge ( ) const

See QuantumFieldParent::getXiGauge().

Returns: The expression of the \( \xi \) parameter of a gauge boson.

◆ hasContractionProperty()

bool mty::QuantumField::hasContractionProperty ( csl::Expr_info expr ) const

override

Tells if the field has an indicial contraction property with another expression.

This functoin overrides the one of csl::TensorFieldElement and make sure to return false each time.

Parameters

expr	Other expression.

Returns: False.

◆ hasDerivative()

bool mty::QuantumField::hasDerivative ( ) const

Tells if the field has derivative indices.

Returns: True if the derivative structure derivativeIndices is not empty.; False else.

See also: derivativeIndices, addDerivative(), getDerivativeStructure(), setDerivativeStructure().

◆ isAntiCommuting()

bool mty::QuantumField::isAntiCommuting ( ) const

See QuantumFieldParent::isAntiCommuting().

Returns: True if the field is anti-commuting (fermion or ghost).; False else.

◆ isBosonic()

bool mty::QuantumField::isBosonic ( ) const

See QuantumFieldParent::isBosonic().

Returns: True if the field is bosonic.; False else.

◆ isChiral()

bool mty::QuantumField::isChiral ( ) const

See QuantumFieldParent::isChiral().

Returns: True if the particle is chiral.; False else.

◆ isContractibleWith()

bool mty::QuantumField::isContractibleWith ( const QuantumField & other ) const

See QuantumFieldParent::isContractibleWith().

Parameters

other Field to test if there is a contraction.

Returns: True if the field is contractible with the other field.; False else.

◆ isExactlyContractiblewith()

bool mty::QuantumField::isExactlyContractiblewith ( const QuantumField & other ) const

Tests if the the field is exactly contractible with the other one.

The condition that does not appear in isContractibleWith() is the complex conjugation of the field. In the first function, we test only that a propagator exists between the two abstract fields. Here, we test also if either the field is self-conjugate or one an only one of the two fields is complex conjugated. Other wise, even if a propagator exists, the contraction gives zero and this function returns false.

Parameters

other Field with which we test the contraction.

Returns: True if the actual contraction of the two fields is not zero.; False else.

◆ isExternal()

bool mty::QuantumField::isExternal ( ) const

Tells if the field is an external field.

Returns: True if the field is external.; False else.

See also: external, setExternal(), Insertion.

◆ isFermionic()

bool mty::QuantumField::isFermionic ( ) const

See QuantumFieldParent::isFermionic().

Returns: True if the field is fermionic.; False else.

◆ isGaugeBoson()

bool mty::QuantumField::isGaugeBoson ( ) const

See QuantumFieldParent::isGaugeBoson().

Returns: True if the particle is a gauge boson.; False else.

◆ isIncoming()

bool mty::QuantumField::isIncoming ( ) const

Tells if the (external) field is incoming or outgoing.

Returns: True if the field is incoming.; False else.

See also: incoming, setIncoming(), isIncoming(), isIncomingParticle(), isIncomingAntiParticle(), isOutgoingParticle(), isOutgoingAntiParticle().

◆ isIncomingAntiParticle()

bool mty::QuantumField::isIncomingAntiParticle ( ) const

Tells if the (external) field is an incoming anti-particle.

Returns: True if the field is incoming and is an anti-particle.; False else.

See also: isIncoming(), isParticle(), isIncomingParticle(), isOutgoingParticle(), isOutgoingAntiParticle().

◆ isIncomingParticle()

bool mty::QuantumField::isIncomingParticle ( ) const

Tells if the (external) field is an incoming particle.

Returns: True if the field is incoming and is a particle.; False else.

See also: isIncoming(), isParticle(), isIncomingAntiParticle(), isOutgoingParticle(), isOutgoingAntiParticle().

◆ isIndexed()

bool mty::QuantumField::isIndexed ( ) const

overridevirtual

Tells if the field is indexed.

Returns: True if the field has proper indices or derivative indices.; False else.

Reimplemented from csl::TensorFieldElement.

◆ isOutgoingAntiParticle()

bool mty::QuantumField::isOutgoingAntiParticle ( ) const

Tells if the (external) field is an outgoing an anti-particle.

Returns: True if the field is outgoing and is an anti-particle.; False else.

See also: isIncoming(), isParticle(), isIncomingAntiParticle(), isIncomingParticle(), isOutgoingParticle().

◆ isOutgoingParticle()

bool mty::QuantumField::isOutgoingParticle ( ) const

Tells if the (external) field is an outgoing particle.

Returns: True if the field is outgoing and is a particle.; False else.

See also: isIncoming(), isParticle(), isIncomingAntiParticle(), isIncomingParticle(), isOutgoingAntiParticle().

◆ isParticle()

bool mty::QuantumField::isParticle ( ) const

Tells if the (external) field is a particle or anti particle.

Returns: True if the field is a particle.; False else.

See also: particle, setParticle(), isIncoming(), isIncomingParticle(), isIncomingAntiParticle(), isOutgoingParticle(), isOutgoingAntiParticle().

◆ isPhysical()

bool mty::QuantumField::isPhysical ( ) const

Tells if the field is physical, i.e. may appear in external legs.

If the field is not physical, it will be forbidden in external legs. In particular, the function setExternal() will yield an error. For example, ghosts and goldstone bosons are not physical.

See also: #physical, isExternal(), setExternal(), setPhysical(), Insertion.

Returns: True if the field is physical.; False else.

◆ isSelfConjugate()

bool mty::QuantumField::isSelfConjugate ( ) const

See QuantumFieldParent::isSelfConjugate().

Returns: True if the field is real.; False else.

◆ operator!=()

bool mty::QuantumField::operator!= ( const QuantumField & other ) const

Compares the field with another.

Parameters

other Other field.

Returns: True if the field is equal to other.; False else.

See also: operator==(csl::Expr_info).

◆ operator<()

bool mty::QuantumField::operator< ( const QuantumField & other ) const

Compares the simplicity of the field with another.

Parameters

other Other field.

Returns: True if the field is simpler than other.; False else.

See also: TensorFieldElement::operator<().

◆ operator==() [1/2]

bool mty::QuantumField::operator== ( csl::Expr_info other ) const

override

Compares the field with another expression.

Uses TensorFieldElement::operator==() and takes care of comparing the derivative structures of two fields if the other expression is another field (otherwise this function returns false).

Parameters

other Expression to compare.

Returns: True if the other expression is the same field, with the same structure and space-time point.; False else.

See also: TensorFieldElement::operator==(), derivativeIndices.

◆ operator==() [2/2]

bool mty::QuantumField::operator== ( const QuantumField & other ) const

Compares the field with another.

Parameters

other Other field.

Returns: True if the field is equal to other.; False else.

See also: operator==(csl::Expr_info).

◆ setChirality()

void mty::QuantumField::setChirality ( Chirality chirality )

Sets the chirality of the particle.

This function should be called wisely. If the chirality is not consistent, it will raise an error. In particular, it should be used only for fermions that are linked (one DiracFermion and two WeylFermion). In this case, setting the chirality of the particle is equivalent to change its parent. chirality may be left or right (a WeylFermion takes the place of the parent) or none (a DiracFermion takes the place of the parent).

Parameters

chirality New chirality of the particle.

See also: QuantumFieldParent::getDiracParent(), QuantumFieldParent::getWeylFermion(), QuantumFieldParent::getChiralityCounterPart(), setParent().

◆ setDerivativeStructure()

void mty::QuantumField::setDerivativeStructure ( const csl::IndexStructure & structure )

Sets the derivative structure of the field.

Parameters

structure New derivative structure.

See also: derivativeIndices, getDerivativeStructure().

◆ setExternal()

void mty::QuantumField::setExternal ( bool t_external )

Sets the external property of the particle.

Parameters

t_external Must be true if the field is an external leg, false otherwise.

See also: external, isExternal().

◆ setIncoming()

void mty::QuantumField::setIncoming ( bool t_incoming )

virtual

Sets the incoming property of the particle.

Parameters

t_incoming Must be true if the field is incoming, false otherwise.

See also: incoming, isIncoming().

Reimplemented in mty::PolarizationField.

◆ setParticle()

void mty::QuantumField::setParticle ( bool t_particle )

virtual

Sets the particle property of the particle.

Parameters

t_particle Must be true if the field is a particle, false otherwise.

See also: particle, isParticle().

Reimplemented in mty::PolarizationField.

Friends And Related Function Documentation

◆ quantumfield_s

template<typename ... Args>

csl::Expr quantumfield_s ( Args &&... args )

friend

Creates and returns an expression corresponding to a QuantumField.

Template Parameters

Args	Variadic template parameters.

Parameters

args	Variadic function parameters, may be anything. Forwarded to csl::make_shared().

Returns: The expression of the field.

Field Documentation

◆ derivativeIndices

csl::IndexStructure mty::QuantumField::derivativeIndices {}

protected

csl::IndexStructure allowing to store derivative indices, to keep track of terms in \( \partial _\mu \) in computations while having only QuantumField objects.

This member allows to have an internal representation of the following definition for a field \( A_\mu ^I \):

\[ \partial _\mu A_\nu ^I \equiv A^I_{\nu,\mu}. \]

The derivative disappear and indices are transfered in the structure of the field.

See also: addDerivative(), hasDerivative(), getDerivativeStructure(), wick::Graph, wick::WickCalculator, Expander, AmplitudeCalculator.

◆ external

bool mty::QuantumField::external = false

protected

Tells if the field is external (initial of final state in computations) or not.

See also: isExternal(), setExternal(), isIncomingParticle(), isIncomingAntiParticle(), isOutgoingParticle(), isOutgoingAntiParticle(), setIncoming(), setExternal(), setParticle().

◆ incoming

bool mty::QuantumField::incoming = true

protected

Tells if the QuantumField, if external, is a incoming or outgoing.

As for the attribute particle, this boolean will determine if the field must be complex conjugated or not. Depending on its spin, if it is an incoming particle, outgoing anti-particle...

See also: isIncomingParticle(), isIncomingAntiParticle(), isOutgoingParticle(), isOutgoingAntiParticle(), setIncoming(), setExternal(), setParticle().

◆ particle

bool mty::QuantumField::particle = true

protected

Tells if the QuantumField, if external, is a particle or an anti-particle.

As for the attribute incoming, this boolean will determine if the field must be complex conjugated or not. Depending on its spin, if it is an incoming particle, outgoing anti-particle...

See also: isIncomingParticle(), isIncomingAntiParticle(), isOutgoingParticle(), isOutgoingAntiParticle(), setIncoming(), setExternal(), setParticle().

◆ partnerShip

PartnerShip mty::QuantumField::partnerShip {}

protected

Wanted partner for fermion ordering in amplitude results, together with the number defining the fermion.

Fermion ordering is determined outside (possibly by the user) and the information is stored in the quantum field itself to know what fermions must be paired together during simplifications. If fermions are not paired accordingly to the defined order (if there is one), Fierz identities are applied to correct the amplitude, like in the following with external fermions notes as 1,2,3,4 and \( \Gamma^A \) are chains of \( \gamma\)-matrices:

\[ \left(\Gamma^A\right)_{14}\left(\Gamma^B\right)_{32} = \sum _{C,D} C^{AB}_{CD}\left(\Gamma^C\right)_{12}\left(\Gamma^D\right)_{34}, \]

where \( C^{AB}_{CD} \) are scalar coefficients determined by the generalized Fierz identities.

The documentation for this class was generated from the following files:

include/quantumField.h
src/quantumField.cpp

Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ QuantumField() [1/4]

◆ QuantumField() [2/4]

◆ QuantumField() [3/4]

◆ QuantumField() [4/4]

Member Function Documentation

◆ addDerivative()

◆ commutesWith()

◆ compareWithDummy()

◆ conjugate()

◆ copy_unique()

◆ getChirality()

◆ getCommutable()

◆ getComplexConjugate()

◆ getConjugated()

◆ getConjugatedField()

◆ getDerivativeStructure()

◆ getEnergyDimension()

◆ getLSZInsertion()

◆ getMass()

◆ getParticle()

◆ getPropagator()

◆ getQuantumParent()

◆ getSpinDimension()

◆ getSquaredMass()

◆ getWidth()

◆ getXiGauge()

◆ hasContractionProperty()

◆ hasDerivative()

◆ isAntiCommuting()

◆ isBosonic()

◆ isChiral()

◆ isContractibleWith()

◆ isExactlyContractiblewith()

◆ isExternal()

◆ isFermionic()

◆ isGaugeBoson()

◆ isIncoming()

◆ isIncomingAntiParticle()

◆ isIncomingParticle()

◆ isIndexed()

◆ isOutgoingAntiParticle()

◆ isOutgoingParticle()

◆ isParticle()

◆ isPhysical()

◆ isSelfConjugate()

◆ operator!=()

◆ operator<()

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ setChirality()

◆ setDerivativeStructure()

◆ setExternal()

◆ setIncoming()

◆ setParticle()

Friends And Related Function Documentation

◆ quantumfield_s

Field Documentation

◆ derivativeIndices

◆ external

◆ incoming

◆ particle

◆ partnerShip