Class encapsulating necesarry data to place conjugation matrices in amplitudes when treating Majorana fermions. More...

#include <fermionFlow.h>

Public Types
enum	Type { Undefined, External, Internal }
	Type of ConjugationInfo. More...

using	FieldList = std::vector< mty::QuantumField const * >
	Quick definition of the data structure for a field list in this file.

Public Member Functions
	ConjugationInfo ()
	Constructs an empty ConjugationInfo. Will do nothing. More...

	ConjugationInfo (csl::Index const &t_A, bool t_conjugated)
	Constructs a ConjugationInfo for an external leg. More...

	ConjugationInfo (csl::Index const &t_A, csl::Index const &t_B, csl::Index const &t_preA, csl::Index const &t_postB)
	Constructs a ConjugationInfo for a part of a fermion chain. More...

	~ConjugationInfo ()=default
	Default constructor.

	ConjugationInfo (ConjugationInfo const &)=default
	Default copy constructor. More...

	ConjugationInfo (ConjugationInfo &&)=default
	Default move constructor. More...

ConjugationInfo &	operator= (ConjugationInfo const &)=default
	Default copy assignement operator. More...

ConjugationInfo &	operator= (ConjugationInfo &&)=default
	Default move assignement operator. More...

Type	getType () const
	Returns the type.

csl::Index	getA () const
	Returns the first index of the ConjugationInfo.

csl::Index	getB () const
	Returns the second index of the ConjugationInfo, has a meaning only for Internal ConjugationInfo.

csl::Index	getPreA () const
	Returns the index before A in the chain, has a meaning only for Internal ConjugationInfo.

csl::Index	getPostB () const
	Returns the index after B in the chain, has a meaning only for Internal ConjugationInfo.

bool	getConjugated () const
	Returns the conjugation of the ConjugationInfo, has a meaning only for External ConjugationInfo.

void	setInfo (csl::Index const &t_A, bool t_conjugated)
	Sets info for an external ConjugationInfo. See the corresponding constructor for more info. More...

void	setInfo (csl::Index const &t_A, csl::Index const &t_B, csl::Index const &t_preA, csl::Index const &t_postB)
	Sets info for an internal ConjugationInfo. See the corresponding constructor for more info. More...

void	apply (csl::Expr &expr, bool ruleMode, std::vector< FermionLine > const &lines) const
	Applies the conjugation on the underlying expression. More...

Static Public Member Functions
static ConjugationList	resolveFermionLines (FieldList init, FieldList const &ruleOrder, bool ruleMode)
	Resolves all fermion lines in a set of fields. More...

static ConjugationList	resolveFermionLines (FieldList const &init, std::vector< QuantumField > const &ruleOrder, bool ruleMode)
	Resolves all fermion lines in a set of fields. More...

static void	simplify (ConjugationList &infoList, bool ruleMode)
	Simplifies a set of ConjugationInfo, merging the consecutive ones. More...

static void	applyConjugation (ConjugationList infoList, csl::Expr &expr, bool ruleMode)

Static Public Attributes
static constexpr size_t	maxFermionLines = 3
	Maximum number of fermion lines in a diagram. More...

Protected Member Functions
void	insertInChain (csl::Expr &expr) const

void	insertInChainForRule (csl::Expr &expr, std::vector< FermionLine > const &lines) const

void	insertExternal (csl::Expr &expr) const

Protected Attributes
Type	type
	Type of ConjugationInfo. Can be external (external leg) or internal (part of gamma-matrices chain).

csl::Index	A
	First (or only for External type) index of the chain.

csl::Index	B
	Second index of the chain, not valued for External ConjugationInfo.

csl::Index	preA
	Index before A in the chain, not valued for External ConjugationInfo.

csl::Index	postB
	Index after B in the chain, not valued for External ConjugationInfo.

bool	conjugated
	Boolean for External ConjugationInfo, tells if the external leg is complex conjugated.

Detailed Description

Class encapsulating necesarry data to place conjugation matrices in amplitudes when treating Majorana fermions.

Member Enumeration Documentation

◆ Type

enum mty::ConjugationInfo::Type

Type of ConjugationInfo.

Enumerator
Undefined	Undefined ConjugationInfo.
External	Conjugation of an external leg.
Internal	Conjugation of a part of a gamma-matrices chain.

Constructor & Destructor Documentation

◆ ConjugationInfo() [1/5]

mty::ConjugationInfo::ConjugationInfo ( )

Constructs an empty ConjugationInfo. Will do nothing.

See also: setInfo()

◆ ConjugationInfo() [2/5]

mty::ConjugationInfo::ConjugationInfo	(	csl::Index const &	t_A,
		bool	t_conjugated
	)

explicit

Constructs a ConjugationInfo for an external leg.

Parameters

t_A	Index of the external leg to conjugate.
t_conjugated	Boolean that must be true if the external leg is initially complex conjugated.

◆ ConjugationInfo() [3/5]

mty::ConjugationInfo::ConjugationInfo	(	csl::Index const &	t_A,
		csl::Index const &	t_B,
		csl::Index const &	t_preA,
		csl::Index const &	t_postB
	)

Constructs a ConjugationInfo for a part of a fermion chain.

Parameters

t_A	First index (to the left) of the fermion chain.
t_B	Second index (to the right) of the fermion chain.

◆ ConjugationInfo() [4/5]

mty::ConjugationInfo::ConjugationInfo ( ConjugationInfo const & )

default

Default copy constructor.

Parameters

ConjugationInfo to copy.

◆ ConjugationInfo() [5/5]

mty::ConjugationInfo::ConjugationInfo ( ConjugationInfo && )

default

Default move constructor.

Parameters

ConjugationInfo to move.

Member Function Documentation

◆ apply()

void mty::ConjugationInfo::apply	(	csl::Expr &	expr,
		bool	ruleMode,
		std::vector< FermionLine > const &	lines
	)		const

Applies the conjugation on the underlying expression.

Inserts in the fermion chain (replacing indices carefully) the conjugation matrix (or matrices) in the right place. After those insertions, the C-matrix simplification should leave a clean and ordered fermion chain.

Parameters

expr	Expression to modify.
ruleMode	Boolean, true if Feynman rule calculation.
lines	Fermion lines in the diagram.

◆ operator=() [1/2]

ConjugationInfo& mty::ConjugationInfo::operator= ( ConjugationInfo const & )

default

Default copy assignement operator.

Parameters

ConjugationInfo to copy.

Returns: A reference to the target of the copy.

◆ operator=() [2/2]

ConjugationInfo& mty::ConjugationInfo::operator= ( ConjugationInfo && )

default

Default move assignement operator.

Parameters

ConjugationInfo to move.

Returns: A reference to the target of the copy.

◆ resolveFermionLines() [1/2]

ConjugationList mty::ConjugationInfo::resolveFermionLines	(	FieldList	init,
		FieldList const &	ruleOrder,
		bool	ruleMode
	)

static

Resolves all fermion lines in a set of fields.

This function is usefull when Majorana fermions come in amplitudes. Fermion flows must be defined for each fermion line (arbitrarily, see https://cds.cern.ch/record/240381/files/CM-P00063014.pdf) to write down the amplitude. Each propagator and vertex must be matched from the beginning to the end, and rules must then be applied to ensure that the fermion chain is continuous (no transposed gamma- matrix in the middle).

Parameters

init	Initial set of fields in the Wick contraction.
ruleOrder	Order of fields in the Feynman rules.

Returns: A list of ConjugationInfo, telling where to apply the conjugation matrix to recover a clean fermion flow, and a sign coming from fermion ordering.

◆ resolveFermionLines() [2/2]

ConjugationList mty::ConjugationInfo::resolveFermionLines	(	FieldList const &	init,
		std::vector< QuantumField > const &	ruleOrder,
		bool	ruleMode
	)

static

Resolves all fermion lines in a set of fields.

This function is just an overload to convert a vector of QuantumField (given by the class Graph) to a FieldList.

Parameters

init	Initial set of fields in the Wick contraction.
ruleOrder	Order of fields in the Feynman rules.

Returns: A list of ConjugationInfo, telling where to apply the conjugation matrix to recover a clean fermion flow.

◆ setInfo() [1/2]

void mty::ConjugationInfo::setInfo	(	csl::Index const &	t_A,
		bool	t_conjugated
	)

Sets info for an external ConjugationInfo. See the corresponding constructor for more info.

Parameters

t_A	Index of the external leg
t_conjugated	Conjugation of the external leg

◆ setInfo() [2/2]

void mty::ConjugationInfo::setInfo	(	csl::Index const &	t_A,
		csl::Index const &	t_B,
		csl::Index const &	t_preA,
		csl::Index const &	t_postB
	)

Sets info for an internal ConjugationInfo. See the corresponding constructor for more info.

Parameters

t_A	First index of the chain
t_B	Second index of the chain

◆ simplify()

void mty::ConjugationInfo::simplify	(	ConjugationList &	infoList,
		bool	ruleMode
	)

static

Simplifies a set of ConjugationInfo, merging the consecutive ones.

This functions uses the fact that \( C^TC = 1. \) For a list of conjugation, consecutive ones are merged. For example,

\[ \left(C\Gamma _1 C^T\right)\cdot \left(C\Gamma _2C^T\right) = C\Gamma _1\Gamma _2C^T. \]

Parameters

info	Vector of ConjugationInfo to simplify.
ruleMode	Boolean, must be true if Feynman rule calculation.

Field Documentation

◆ maxFermionLines

constexpr size_t mty::ConjugationInfo::maxFermionLines = 3

static

Maximum number of fermion lines in a diagram.

This number is 3 because for now a diagram (that can be fully simplified in MARTY) cannot have 6 external legs (5 at most) and is at the 1-loop level. There can be two external fermionic lines, and one internal in the loop. If in the future MARTY is extended to more, this number may be incremented or left as it is, the consequence will only be an increase in execution time for the function followFermionLines (if not incremented). This number is the memory allocated the the return value. If there is more fermion lines, memory will have to be reallocated elsewhere with more space (implies deallocation, reallocation, copies etc).

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

include/fermionFlow.h
src/fermionFlow.cpp

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Member Enumeration Documentation

◆ Type

Constructor & Destructor Documentation

◆ ConjugationInfo() [1/5]

◆ ConjugationInfo() [2/5]

◆ ConjugationInfo() [3/5]

◆ ConjugationInfo() [4/5]

◆ ConjugationInfo() [5/5]

Member Function Documentation

◆ apply()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ resolveFermionLines() [1/2]

◆ resolveFermionLines() [2/2]

◆ setInfo() [1/2]

◆ setInfo() [2/2]

◆ simplify()

Field Documentation

◆ maxFermionLines