Weyl fermion, two-component Chiral particle. More...

#include <fermionicField.h>

Inheritance diagram for mty::WeylFermion:

Public Member Functions
	WeylFermion (WeylFermion const &other)=default

	WeylFermion (std::weak_ptr< DiracFermion > parent, Chirality chirality=Chirality::Left)

	WeylFermion (const std::string &t_name, Model const &t_model, Chirality chirality=Chirality::Left)

	WeylFermion (const std::string &t_name, Gauge *t_gauge, Chirality chirality=Chirality::Left)

	WeylFermion (const std::string &t_name, const GaugeIrrep &irrep, Chirality chirality=Chirality::Left)

	WeylFermion (const std::string &t_name, Gauge *t_gauge, bool t_isSelfConjugate, Chirality chirality=Chirality::Left)

	WeylFermion (const std::string &t_name, const GaugeIrrep &irrep, bool t_isSelfConjugate, Chirality chirality=Chirality::Left)

	WeylFermion (const std::string &t_name, const GaugeIrrep &irrep, const FlavorIrrep &flavorRep, Chirality chirality=Chirality::Left)

	WeylFermion (const std::string &t_name, const WeylFermion *other)

void	printDefinition (std::ostream &out=std::cout, int indentSize=4, bool header=false) const override

ParticleType	getParticleType () const override

bool	isChiral () const override
	Tells if the field is chiral. More...

bool	isSameSpecies (QuantumFieldParent const *other) const override

Chirality	getChirality () const override
	Returns the chirality of the particle. More...

Particle	generateSimilar (std::string const &t_name) const override
	Pure virtual function. Generates a partical similar to the current object, changing only the name. More...

csl::Expr	getEnergyDimension () const override
	Pure virtual function. Returns the energy dimension of the field. More...

int	getNDegreesOfFreedom () const override
	Pure virtual function. Returns the number of degrees of freedom in the particle. It does not count gauge and flavor multiplicity. The result depends on the type of the particle and if it is complex. More...

csl::Expr	getKineticTerm (csl::Tensor &X) override
	Returns the kinetic term in the Lagrangian for the field. More...

Particle	getChiralityCounterPart () const override
	For a WeylFermion embedded in a DiracFermion, returns the other part of the DiracFermion. More...

Particle	getDiracParent () const override
	For a WeylFermion embedded in a DiracFermion, returns the dirac fermion. More...

void	setDiracParent (Particle const &parent) override

void	breakParticle (mty::Group *brokenGroup, std::vector< std::string > const &newNames) override

void	breakParticle (mty::FlavorGroup brokenFlavor, std::vector< mty::FlavorGroup > const &subGroups, std::vector< std::string > const &names) override

Public Member Functions inherited from mty::QuantumFieldParent
	QuantumFieldParent ()=default
	Default constructor.

	QuantumFieldParent (QuantumFieldParent const &other)=default
	Copy constructor.

	QuantumFieldParent (const std::string &t_name, int t_spin, Gauge *t_gauge)
	Constructor with 3 parameters. More...

	QuantumFieldParent (const std::string &t_name, int t_spin, const GaugeIrrep &irrep)
	Constructor with 3 parameters. More...

	QuantumFieldParent (const std::string &t_name, int t_spin, Gauge *t_gauge, bool t_isSelfConjugate)
	Constructor with 4 parameters. More...

	QuantumFieldParent (const std::string &t_name, int t_spin, const GaugeIrrep &irrep, bool t_isSelfConjugate)
	Constructor with 4 parameters. More...

	QuantumFieldParent (const std::string &t_name, int t_spin, const GaugeIrrep &irrep, const FlavorIrrep &flavorRep)
	Constructor with 4 parameters. More...

	QuantumFieldParent (const std::string &t_name, const QuantumFieldParent *other)
	Builds a new particle identical to another, with a different name. More...

drawer::ParticleType	getDrawType () const
	Returns the drawing type of the particle. More...

virtual bool	contains (QuantumFieldParent const *other) const

void	setDrawType (drawer::ParticleType type)
	Sets the drawing type of the particle. More...

int	getNGaugeDegreesOfFreedom () const

virtual bool	hasSpecialContractionWith (QuantumField const &other) const
	Tells if the field has a special contraction property with other. More...

virtual Particle	getWeylFermion (Chirality chirality) const
	For a DiracFermion, returns the chiral WeylFermion it contains of chirality chirality if it has one. More...

virtual Particle	getGoldstone () const
	For a vector boson in a non abelian gauged group, returns the associated Goldstone boson. More...

virtual csl::Expr	getPropagator (QuantumField const &self, QuantumField const &other, csl::Tensor &P, bool external) const
	Returns the expression of the propagator between two fields. More...

virtual csl::Expr	getInvPropagator (QuantumField const &other, QuantumField const &self, csl::Tensor &P, bool external) const
	Returns the expression of the propagator between two fields. More...

virtual bool	isGaugeBoson () const
	Tells if the particle is a gauge boson. More...

virtual csl::Expr	getXiGauge () const
	For a GaugeBoson, returns the expression of \( \xi \) in the current gauge. More...

virtual Particle	getVectorBoson () const
	For a ghost or goldstone boson, returns the GaugeBoson associated with it. More...

virtual GaugedGroup const *	getGaugedGroup () const

virtual GaugedGroup *	getGaugedGroup ()

virtual Particle	getGoldstoneBoson () const
	For a GaugeBoson, returns the associated Golstone boson of there is one. More...

virtual Particle	getGhostBoson () const
	For a GoldstoneBoson, returns the associated Golstone boson of there is one. More...

virtual Particle	getConjugatedGhostBoson () const

virtual void	setGoldstoneBoson (Particle const &goldstone)
	For a GaugeBoson, sets the associated GoldstoneBoson. More...

virtual void	setGhostBoson (Particle const &ghost)
	For a GaugeBoson, sets the associated GhostBoson. More...

virtual void	setConjugatedGhostBoson (Particle const &ghost)

virtual bool	hasFieldStrength () const
	Tells if the particle has a FieldStrength. More...

virtual Particle	getFieldStrength () const
	For a VectorBoson, returns the associated FieldStrength if it exists. More...

virtual void	setFieldStrength (Particle const &fieldStrength)
	For a VectorBoson, sets the associated FieldStrength. More...

bool	isContractibleWith (QuantumFieldParent const *other) const
	Tells if the field may be contracted with another in Wick contrations. More...

bool	isBosonic () const
	Tells if the field is bosonic. More...

bool	isFermionic () const
	Tells if the field is fermionic. More...

virtual bool	isAntiCommuting () const
	Tells if the field is a grassman field. More...

bool	isSelfConjugate () const
	Tells if the field is self-conjugate (real). More...

bool	isReal () const

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

bool	isEnabledInDiagrams () const
	Tells if the field is enabled in diagrams. More...

bool	isIntegratedOut () const
	Tells if the field is integrated out. More...

int	getSpinDimension () const
	Returns twice the spin of the particle in an integer. More...

csl::Expr	getMass () const
	Returns the expression of the mass of the particle. More...

csl::Expr	getSquaredMass () const

csl::Expr	getWidth () const
	Returns the expression of the witdh of the particle. More...

virtual mty::gauge::Choice	getGaugeChoice () const

Irrep	getLorentzRep () const
	Returns the lorentz representation of the field. More...

Gauge *	getGauge () const
	Returns a pointer to the gauge the field is a representation of. More...

GaugeIrrep	getGaugeIrrep () const
	Returns the gauge representation containing all individual group representations of the field in the gauge. More...

Irrep	getGroupIrrep (const Group *group) const
	Returns the representation of the field in a particle group. More...

Flavor const *	getFlavor () const

void	setFlavor (Flavor const *flavor)

FlavorIrrep	getFlavorIrrep () const
	Returns the flavor representation containing all individual group representations of the field in the flavor. More...

Irrep	getFlavorIrrep (const FlavorGroup *group) const
	Returns the representation of the field in a particle flavor group. More...

std::vector< csl::Index >	getSpaceIndex (const std::string &nameIndex="") const
	Returns a set of free space indices corresponding to the field. More...

std::vector< csl::Index >	getGaugeIndex (std::vector< std::string > names=std::vector< std::string >()) const
	Returns a set of gauge indices corresponding to the field. More...

std::vector< csl::Index >	getFlavorIndex (std::vector< std::string > names=std::vector< std::string >()) const
	Returns a set of flavor indices corresponding to the field. More...

std::vector< csl::Index >	getFullSetOfIndices () const
	Returns a full set of indices for the field including flavor , gauge, and space-time indices. More...

QuantumNumber::Value	getQuantumNumber (QuantumNumber const *number) const
	Returns the quantum number of the field with respect to number. More...

QuantumNumber::Value	getQuantumNumber (QuantumField const instance, QuantumNumber const number) const
	Returns the quantum number of an instance of the field with respect to number. More...

csl::Expr	getInstance (csl::Tensor point=defaultSpaceTimePoint)
	Returns an instance of the quantum field as an expression. More...

void	integrateOut (bool value=true)
	Sets the integrated out property of the field. More...

void	setMass (const std::string &t_mass)
	Sets the mass of the particle. More...

void	setMass (const std::string &t_mass, long double value)
	Sets the mass of the particle. More...

void	setMass (const csl::Expr &t_mass)
	Sets the mass of the particle. More...

void	setWidth (const csl::Expr &t_width)
	Sets the width of the particle. More...

virtual void	setGaugeChoice (gauge::Type type)

void	setSelfConjugate (bool t_selfConjugate)
	Sets the complex conjugation property of the particle. More...

void	setPhysical (bool t_physical)
	Sets the physical property of the particle. More...

void	setEnabledInDiagrams (bool t_enabled)
	Enables or disables the particle in diagrams. More...

void	adjustFlavorRep (Flavor *t_flavor)
	Ajusts the flavor representation of the field to a new flavor group. More...

void	setGaugeIrrep (const GaugeIrrep &newRep)

void	setGroupRep (Group *group, const Irrep &newRep)
	Sets the representation of the field for a given group. More...

void	setGroupRep (std::string const &group, std::vector< int > const &highestWeight)
	Sets the representation of the field for a given group. More...

void	setGroupRep (std::string const &group, int charge)

void	setFlavorRep (const FlavorGroup *group, const Irrep &newRep)
	Sets the representation of the field for a given flavor group. More...

void	setFundamentalFlavorRep (std::string const &flavorGroup)

void	addQuantumNumber (QuantumNumber const &number, QuantumNumber::Value value)
	Adds a non trivial quantum number to the particle. More...

virtual void	setBrokenParts (const csl::Space *broken, const std::vector< Particle > &brokenParts)
	Sets broken parts (from gauge of flavor symmetry full breaking) containing the new particles. More...

std::vector< csl::Parent >	breakSpace (const csl::Space broken, const std::vector< const csl::Space > &newSpace, const std::vector< size_t > &pieces) const override
	Returns the set of new tensors after breaking the particle in parts. More...

QuantumFieldParent &	operator= (const QuantumFieldParent &other)=default
	Assignment operator (c++ default). More...

csl::Expr	operator() (const csl::Tensor &t_point) override
	Generates an instance of the field as a symbolic expression. More...

csl::Expr	operator() (csl::Index index, const csl::Tensor &t_point) override
	Generates an instance of the field as a symbolic expression. More...

csl::Expr	operator() (std::vector< int > const &indices, const csl::Tensor &t_point) override
	Generates an instance of the QuantumField as a symbolic expression. More...

csl::Expr	operator() (std::vector< csl::Index > indices, const csl::Tensor &t_point) override
	Generates an instance of the field as a symbolic expression. More...

csl::Expr	operator() (csl::Index polarization, std::vector< int > const &indices, const csl::Tensor &t_point)
	Generates an instance of the PolarizationField as a symbolic expression. More...

csl::Expr	operator() ()
	Generates an instance of the field as a symbolic expression. More...

csl::Expr	operator() (csl::Index index) override
	Generates an instance of the field as a symbolic expression. More...

csl::Expr	operator() (std::vector< csl::Index > indices) override
	Generates an instance of the field as a symbolic expression. More...

csl::Expr	operator() (csl::Index polarization, csl::Index index, const csl::Tensor &momentum)
	Generates an instance of the polarization field as a symbolic expression. More...

csl::Expr	operator() (csl::Index polarization, std::vector< csl::Index > indices, const csl::Tensor &momentum)
	Generates an instance of the polarization field as a symbolic expression. More...

	operator csl::Expr ()

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

cslParent::Type	getType () const override

Public Member Functions inherited from csl::TensorParent
	TensorParent (const std::string &t_name)

	TensorParent (const TensorParent &abstract)=default

	TensorParent (const std::string &t_name, const Space *t_space)

	TensorParent (const std::string &t_name, const std::vector< const Space * > &t_space)

	TensorParent (const std::string &t_name, const std::vector< const Space * > &t_space, const Expr &t_tensor)

	TensorParent (const std::string &t_name, const Space *t_space, const Expr &t_tensor)

cslParent::PrimaryType	getPrimaryType () const override

cslParent::Type	getType () const override

int	getDim (const Space *t_space) const override

std::vector< const Space *>	getSpace () const override

Symmetry	getSymmetry () const

bool	getFullySymmetric () const override

bool	getFullyAntiSymmetric () const override

std::vector< Permutation >	getPermutation () const override

Expr	getTensor () const override

Expr	getTrace () const override

bool	dependsOn (Expr_info expr) const override

bool	dependsExplicitlyOn (Expr_info expr) const override

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

void	setFullySymmetric () override

void	setFullyAntiSymmetric () override

void	addSpace (const Space *space) override

void	addSymmetry (int i1, int i2) override

void	addAntiSymmetry (int i1, int i2) override

void	setSymmetry (const Symmetry &t_symetry) override

void	setTensor (const Expr &t_tensor) override

void	setElementary (bool t_elementary)

bool	hasContractionProperty (const Abstract *self, Expr_info B) const override

Expr	contraction (const Abstract *self, Expr_info B) const override

void	addSelfContraction (const Expr &A, const Expr &B, const Expr &res, std::optional< std::function< bool(Expr_info, Expr_info)>> condition=std::nullopt) override

virtual bool	operator== (const TensorParent &other) const

virtual bool	operator!= (const TensorParent &other) const

Public Member Functions inherited from csl::AbstractParent
	AbstractParent (const std::string &t_name)

	AbstractParent (const AbstractParent &abstract)=default

std::string const &	getName () const

bool	getCommutable () const

virtual void	setName (std::string t_name)

void	setCommutable (bool t_commutable)

void	addProperty (Equation *prop)

void	removeProperty (Equation *prop)

virtual int	getDim () const

Protected Member Functions
void	initPropagator () override
	Initializes default propagators for the particle. This function is called automatically in the constructor of derived classes. More...

Protected Member Functions inherited from mty::QuantumFieldParent
void	addRelative (std::weak_ptr< mty::QuantumFieldParent > const &particle)

std::weak_ptr< mty::QuantumFieldParent >	removeRelative (QuantumFieldParent const *particle)

void	checkRelatives ()

template<class Func >
void	applyToRelatives (Func &&func)

void	printQuantumDefinition (std::ostream &out, int indentSize) const

void	initIndexSpaces ()
	Initializes firstGaugeIndex and firstSpaceIndex. Automatically called by the constructor. More...

void	initPolarizationSum ()
	Initializes the polarization sum for PolarizationField arising in amplitudes. More...

void	setPropagator (QuantumFieldParent const *other, Propagator_func prop)
	Changes the propagator of a particle with another. More...

Private Attributes
Chirality	chirality
	Chirality of the particle.

std::weak_ptr< DiracFermion >	diracParent
	Weak pointer to the dirac parent if the fermion is part of a Dirac fermion. More...

Friends
class	DiracFermion

Additional Inherited Members
Public Types inherited from mty::QuantumFieldParent
using	Propagator_func = std::function< csl::Expr(QuantumField const &, QuantumField const &, csl::Tensor &, bool)>
	Type definition. A Propagator_func is a function called to get the propagator result of the contraction of two fields. More...

Protected Attributes inherited from mty::QuantumFieldParent
bool	bosonic
	True if the field is bosonic.

bool	selfConjugate = false
	True if the field is real (real scalars, gauge bosons , majorana fermions). More...

bool	integratedOut = false
	Tells if the field is integrated out in the theory. If true, the propagator is modified assuming \( M \gg p \).

bool	physical = true
	Tells if the field is physical. If true, it may appear in external states. Otherwise it is forbidden.

bool	enabledInDiagrams = true
	Tells if the field is enabled in diagrams. If no, it is fully discarded in computations.

csl::Expr	mass = CSL_0
	Mass of the particle. Appears in the propagator.

csl::Expr	width = CSL_0
	Width of the particle. Appears in the propagator.

drawer::ParticleType	drawType = drawer::ParticleType::None
	Particle type in graphical diagrams (straight line, arrow, vector, gluon ...).

Group *	stGroup
	Pointer to the space-time group. For know it is the Lorentz group, \( D_2 \) algebra.

Irrep	spin
	Spin representation in stGroup. To have a number corresponding to the spin, see getSpinDimension().

Gauge *	gauge
	Pointer to the gauge the particle is a representation of.

GaugeIrrep	irrep
	Representation of the field in the gauge gauge.

bool	polarizationSumInitialized = false
	Boolean making sure that polarization sum (see PolarizationField) is initialized only onde.

size_t	firstGaugeIndex
	Position of the first gauge index, after flavor indices.

size_t	firstSpaceIndex
	Position of the first space index, after flavor and gauge indices.

const Flavor *	flavor
	Pointer to the flavor the particle is a representation of.

FlavorIrrep	flavorRep
	Representation of the field in the flavor flavor.

std::map< QuantumNumber::ID, QuantumNumber::Value >	qNumbers
	List of quantum numbers of the field. More...

std::map< QuantumFieldParent const *, Propagator_func >	propagator
	Contains all propagators for the field with other. More...

std::vector< std::weak_ptr< mty::QuantumFieldParent > >	relatives

Protected Attributes inherited from csl::TensorParent
std::vector< const Space *>	space

Symmetry	symmetry

bool	fullySymmetric

bool	fullyAntiSymmetric

std::vector< std::pair< SelfContraction, Expr > >	selfContraction

bool	valued

Expr	tensor

Expr	trace

Protected Attributes inherited from csl::AbstractParent
std::string	name

std::string	latexName

bool	commutable

std::vector< Equation *>	props

Detailed Description

Weyl fermion, two-component Chiral particle.

Building a Weyl fermion require to give its chirality (see Chirality) left or right. By default, if not given, chirality will always be set to Chirality::Left.

Member Function Documentation

◆ generateSimilar()

Particle mty::WeylFermion::generateSimilar ( std::string const & t_name ) const

overridevirtual

Pure virtual function. Generates a partical similar to the current object, changing only the name.

Parameters

t_name Name of the new particle, identical to the current object.

Returns: The new Particle.

Implements mty::QuantumFieldParent.

◆ getChirality()

Chirality mty::WeylFermion::getChirality ( ) const

overridevirtual

Returns the chirality of the particle.

A DiracFermion or boson will return Chirality::None. WeylFermion will return either Chirality::Left or Chirality::Right.

Returns: The chirality of the particle.

Reimplemented from mty::QuantumFieldParent.

◆ getChiralityCounterPart()

Particle mty::WeylFermion::getChiralityCounterPart ( ) const

overridevirtual

For a WeylFermion embedded in a DiracFermion, returns the other part of the DiracFermion.

Returns: The right WeylFermion for a left WeylFermion embedded in a DiracFermion.; The left WeylFermion for a right WeylFermion embedded in a DiracFermion.; nullptr otherwise.

Reimplemented from mty::QuantumFieldParent.

◆ getDiracParent()

Particle mty::WeylFermion::getDiracParent ( ) const

overridevirtual

For a WeylFermion embedded in a DiracFermion, returns the dirac fermion.

Returns: A the DiracFermion embedding the current WeylFermion.; nullptr otherwise.

Reimplemented from mty::QuantumFieldParent.

◆ getEnergyDimension()

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

overridevirtual

Pure virtual function. Returns the energy dimension of the field.

Returns: An expression (numerical) equal to the dimension of the field.

Implements mty::QuantumFieldParent.

◆ getKineticTerm()

csl::Expr mty::WeylFermion::getKineticTerm ( csl::Tensor & X )

overridevirtual

Returns the kinetic term in the Lagrangian for the field.

This function is overriden in derived classes. Each particle has a specific form for its kinetic term, including covariant derivatives and mass term. An example of kinetic term for a complex scalar field is

\[ \mathcal{L} \ni (D_\mu \phi)^\dagger D^\mu\phi - m_\phi^2\phi ^\dagger \phi, \]

where \( D_\mu \) stands for the covariant derivative of the field including interactions with gauge vector fields.

See also: mty::gauge::covariantDerivative().

Parameters

X	Space-time point for the kinetic term.

Returns: The mathematical expression in the Lagrangian for the field.

Reimplemented from mty::QuantumFieldParent.

◆ getNDegreesOfFreedom()

int mty::WeylFermion::getNDegreesOfFreedom ( ) const

overridevirtual

Pure virtual function. Returns the number of degrees of freedom in the particle. It does not count gauge and flavor multiplicity. The result depends on the type of the particle and if it is complex.

Returns: An integer, number of degrees of freedom of the particle.

Implements mty::QuantumFieldParent.

◆ initPropagator()

void mty::WeylFermion::initPropagator ( )

overrideprotectedvirtual

Initializes default propagators for the particle. This function is called automatically in the constructor of derived classes.

See also: Propagator_func, ScalarBoson, WeylFermion, DiracFermion, VectorBoson.

Reimplemented from mty::QuantumFieldParent.

◆ isChiral()

bool mty::WeylFermion::isChiral ( ) const

overridevirtual

Tells if the field is chiral.

Returns: True if the field is a WeylFermion.; False otherwise.

Reimplemented from mty::QuantumFieldParent.

Field Documentation

◆ diracParent

std::weak_ptr<DiracFermion> mty::WeylFermion::diracParent

private

Weak pointer to the dirac parent if the fermion is part of a Dirac fermion.

If the Weyl fermion is alone (left neutrinos in the standard model for example), this pointer is null.

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

include/fermionicField.h
src/fermionicField.cpp

Public Member Functions

Protected Member Functions

Private Attributes

Friends

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ generateSimilar()

◆ getChirality()

◆ getChiralityCounterPart()

◆ getDiracParent()

◆ getEnergyDimension()

◆ getKineticTerm()

◆ getNDegreesOfFreedom()

◆ initPropagator()

◆ isChiral()

Field Documentation

◆ diracParent