Handles wick contractions. A graph contains Vertices, and is able to connect them in all possible ways returning the set of all possible Graph. More...

#include <graph.h>

Public Types
using	Expr_type = std::pair< csl::Expr, ConjugationList >

Public Member Functions
	Graph ()
	Default constructor. Empty Graph.

	Graph (const std::vector< mty::QuantumField > &field, std::map< csl::Tensor, size_t > &vertexIds, bool ruleMode)
	Constructor with one parameter. More...

	Graph (const csl::Expr &expr, std::map< csl::Tensor, size_t > &vertexIds, bool ruleMode)
	Constructor with one parameter. More...

	Graph (Graph const &other, std::vector< std::shared_ptr< Node >> const &init)

	~Graph ()
	Destructor.

	Graph (const Graph &other)=default
	Copy constructor = C++ default.

Graph &	operator= (const Graph &other)=default
	Overload of operator= : C++ default.

Graph	copy () const

int	getFactor () const

int	getTotalDegeneracyFactor () const

std::vector< Vertex > const &	getVertices () const

void	addFactor (int t_factor)

void	setFactor (int t_factor)

void	setSymmetrizeExternalLegs (bool t_symmetrize)

void	multiply (int t_factor)

void	multiply (csl::Expr const &t_factor)

bool	isFullyConnected () const

bool	isPhysical () const
	A Graph is considered physical if it is not (yet) fully connected or if it is composed of one unique connected component. More...

bool	isValid () const

int	getNLoops () const

int	getFieldDimension () const

std::vector< Expr_type >	getExpression () const
	For a fully connected Graph, return the associated csl csl::Expr, applying combinatorial factors and propagators of the contracted pairs of fields (see mty::QuantumField::getPropagator()). More...

std::vector< Expr_type >	getExpression (mty::FeynruleMomentum &witness) const

std::vector< const mty::QuantumField * >	getFields () const

std::vector< const mty::QuantumField * >	getConnectedFieldsInVertex (const mty::QuantumField *init) const

const mty::QuantumField *	getConnectedField (const mty::QuantumField *init) const

std::vector< std::shared_ptr< Node > > &	getNodes ()

std::vector< std::shared_ptr< Node > > const &	getNodes () const

bool	empty () const

std::vector< std::shared_ptr< Graph > >	contractionStep () const
	Performs one contraction step (the Graph must not be fully connected) and returns all possible new Graphs. More...

bool	compare (const Graph &other, std::map< csl::Tensor, csl::Tensor > &mapping, bool fieldBlind=false) const

bool	compare (const Graph &other, bool fieldBlind=false) const

void	contractHighMass (mty::QuantumFieldParent const *field)

bool	operator== (const Graph &other) const

Static Public Member Functions
static Vertex const *	getVertexOf (std::shared_ptr< Node > const &node, std::vector< Vertex > const &vertices)

static std::vector< std::shared_ptr< Node > >	nextNodes (std::shared_ptr< Node > const &node, std::vector< Vertex > const &vertices)

static int	countExternalLegs (std::vector< csl::Tensor >::iterator first, std::vector< csl::Tensor >::iterator last, std::vector< Vertex > const &vertices)

static int	walk (std::vector< csl::Tensor >::iterator first, std::vector< csl::Tensor >::iterator last, std::shared_ptr< Node > const &node, std::vector< Vertex > const &vertices)

Private Member Functions
void	isolateIndependantVertices ()
	Isolates at the Graph's creation independant Internal vertices. More...

void	removeIntVertex (int indexVertex)

void	initConnectedComponent ()
	Puts the first external vertex in the connected component and removes it from the set of external vertices for further contractions.

Expr_type	getPartialExpression (std::vector< std::shared_ptr< Node >> &nodes, const std::vector< mty::QuantumField > &initialOrder, mty::FeynruleMomentum &witnessMapping, csl::Expr const &globalFactor) const

csl::ObjectSymmetry< const mty::QuantumField * >	getSymmetry (const Vertex &vertex, const mty::QuantumField *field) const

std::vector< std::vector< std::shared_ptr< Node > > >	symmetrize () const

std::vector< int >	getContractibleExtVertices (const mty::QuantumField *field) const

std::vector< int >	getContractibleIntVertices (const mty::QuantumField *field) const

std::vector< int >	getContractibleConnectedVertices (const mty::QuantumField *field) const

bool	contractExternal (const mty::QuantumField *field, int indexVertex)
	Tries to contract the mty::QuantumField field between the ConnectedComponent and the external vertex at position indexVertex. More...

bool	contractInternal (const mty::QuantumField *field, int indexVertex)
	Tries to contract the mty::QuantumField field between the ConnectedComponent and the internal vertex at position indexVertex. More...

bool	contractConnected (const mty::QuantumField *field, int indexVertex)
	Tries to contract the mty::QuantumField field between the ConnectedComponent and the vertex at position indexVertex in connectedCompo. More...

Static Private Member Functions
static std::vector< std::shared_ptr< Node > >	copyNodes (const std::vector< std::shared_ptr< Node >> &toCopy)

static void	applySymmetry (std::vector< std::shared_ptr< Node >> &nodes, const csl::ObjectPermutation< const mty::QuantumField *> &permutation)

static void	addFoundNode (const std::shared_ptr< Node > &newNode, std::vector< csl::Tensor > &foundNodes)

static void	sortNodes (std::vector< std::shared_ptr< Node >> &nodes)

static bool	compareFieldsDummyPoint (const mty::QuantumField fieldA, const mty::QuantumField fieldB, std::map< csl::Tensor, csl::Tensor > &constraints, bool fieldBlind=false)

static bool	compareNodesWithConstraints (const std::shared_ptr< Node > &nodeA, const std::shared_ptr< Node > &nodeB, std::map< csl::Tensor, csl::Tensor > &constraints, bool fieldBlind=false)

Private Attributes
std::vector< std::shared_ptr< Node > >	sortedNodes

long long int	factor = 1
	Combinatorial factor of the Graph in its current state of contraction.

csl::Expr	exprFactor = CSL_1

bool	symmetrizeExternalLegs = false

bool	ruleMode

std::shared_ptr< std::vector< Vertex > >	init
	Initial order of vertices, in order to keep track of a possible sign of commutation between fields.

std::shared_ptr< std::vector< mty::QuantumField > >	initialOrder

ConnectedComponent	connectedCompo
	Connected component of the Graph (contains all its vertices).

std::vector< Vertex >	extVertex
	List of external vertices not already contracted.

std::vector< Vertex >	intVertex
	List of internal vertices not already contracted.

std::vector< int >	independentVertices
	Sets of integers spotting the independant internal vertices in intVertex.

csl::ObjectSymmetry< const mty::QuantumField * >	symmetry = Id_Sym(const mty::QuantumField*)

bool	fixedExpression = false

std::vector< Expr_type >	expression

Friends
std::ostream &	operator<< (std::ostream &fout, const Graph &g)
	Overload of operator<< for Graph. More...

Detailed Description

Handles wick contractions. A graph contains Vertices, and is able to connect them in all possible ways returning the set of all possible Graph.

Constructor & Destructor Documentation

◆ Graph() [1/2]

mty::wick::Graph::Graph	(	const std::vector< mty::QuantumField > &	field,
		std::map< csl::Tensor, size_t > &	vertexIds,
		bool	ruleMode
	)

explicit

Constructor with one parameter.

Parameters

field std::vector of mty::QuantumField on which apply contractions.

◆ Graph() [2/2]

mty::wick::Graph::Graph	(	const csl::Expr &	expr,
		std::map< csl::Tensor, size_t > &	vertexIds,
		bool	ruleMode
	)

explicit

Constructor with one parameter.

Parameters

expr	csl csl::Expr converted into fields (convertExprToFields()).

Member Function Documentation

◆ contractConnected()

bool mty::wick::Graph::contractConnected	(	const mty::QuantumField *	field,
		int	indexVertex
	)

private

Tries to contract the mty::QuantumField field between the ConnectedComponent and the vertex at position indexVertex in connectedCompo.

Parameters

field	mty::QuantumField being contracted.
indexVertex	Position of the second Vertex being contracted in connectedCompo.

Returns: True if the contraction is done.; False if it was not possible.

◆ contractExternal()

bool mty::wick::Graph::contractExternal	(	const mty::QuantumField *	field,
		int	indexVertex
	)

private

Tries to contract the mty::QuantumField field between the ConnectedComponent and the external vertex at position indexVertex.

Parameters

field	mty::QuantumField being contracted.
indexVertex	Position of the external Vertex to contract with connectedCompo.

Returns: True if the contraction is done.; False if it was not possible.

◆ contractInternal()

bool mty::wick::Graph::contractInternal	(	const mty::QuantumField *	field,
		int	indexVertex
	)

private

Tries to contract the mty::QuantumField field between the ConnectedComponent and the internal vertex at position indexVertex.

Parameters

field	mty::QuantumField being contracted.
indexVertex	Position of the internal Vertex to contract with connectedCompo.

Returns: True if the contraction is done.; False if it was not possible.

◆ contractionStep()

std::vector< std::shared_ptr< Graph > > mty::wick::Graph::contractionStep ( ) const

Performs one contraction step (the Graph must not be fully connected) and returns all possible new Graphs.

A contraction step consists in contracting the first contractible Node of the ConnectedComponent with every possible partner. Each partner gives a new Graph, and all these possible graphs are returned in a std::vector.

Returns: All possible graphs after one contraction step in a std::vector.

◆ empty()

bool mty::wick::Graph::empty ( ) const

Returns: True if the Graph is empty.; False else.

◆ getContractibleConnectedVertices()

vector< int > mty::wick::Graph::getContractibleConnectedVertices ( const mty::QuantumField * field ) const

private

Parameters

field mty::QuantumField to contract.

Returns: A std::vector of integers corresponding to the positions of vertices contractible with field in connectedCompo.

◆ getContractibleExtVertices()

vector< int > mty::wick::Graph::getContractibleExtVertices ( const mty::QuantumField * field ) const

private

Parameters

field mty::QuantumField to contract.

Returns: A std::vector of integers corresponding to the positions of external vertices contractible with field.

◆ getContractibleIntVertices()

vector< int > mty::wick::Graph::getContractibleIntVertices ( const mty::QuantumField * field ) const

private

Parameters

field mty::QuantumField to contract.

Returns: A std::vector of integers corresponding to the positions of internal vertices contractible with field.

◆ getExpression()

std::vector< Graph::Expr_type > mty::wick::Graph::getExpression ( ) const

For a fully connected Graph, return the associated csl csl::Expr, applying combinatorial factors and propagators of the contracted pairs of fields (see mty::QuantumField::getPropagator()).

Returns: The symbolic expression where contractions are replaced by propagators.

◆ getFactor()

int mty::wick::Graph::getFactor ( ) const

Returns: factor, the combiinatorial factor of the graph.

◆ getFieldDimension()

int mty::wick::Graph::getFieldDimension ( ) const

Returns: The total number of fields in the Graph (counting powers of fields).

◆ isFullyConnected()

bool mty::wick::Graph::isFullyConnected ( ) const

Returns: True if the Graph is fully connected (no free Node left).; False else.

◆ isolateIndependantVertices()

void mty::wick::Graph::isolateIndependantVertices ( )

private

Isolates at the Graph's creation independant Internal vertices.

It is important to avoid unnecessary calculations and keep the good combinatorial factors to recognize identical internal vertices. For example two vertices \( \phi(X)^3\quad \phi(Y)^3 \) are degenerate (see Vertex::isDegenerateWith()). Contractions will be performed considering the two vertices discernable (eg treating X before Y) and a factor 2 will be added in front the Graph's expression.

◆ isPhysical()

bool mty::wick::Graph::isPhysical ( ) const

A Graph is considered physical if it is not (yet) fully connected or if it is composed of one unique connected component.

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

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	fout,
		const Graph &	g
	)

friend

Overload of operator<< for Graph.

Parameters

fout	Output stream.
g	Graph to display.

Returns: The output flux.

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

include/graph.h
src/graph.cpp

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Graph() [1/2]

◆ Graph() [2/2]

Member Function Documentation

◆ contractConnected()

◆ contractExternal()

◆ contractInternal()

◆ contractionStep()

◆ empty()

◆ getContractibleConnectedVertices()

◆ getContractibleExtVertices()

◆ getContractibleIntVertices()

◆ getExpression()

◆ getFactor()

◆ getFieldDimension()

◆ isFullyConnected()

◆ isolateIndependantVertices()

◆ isPhysical()

Friends And Related Function Documentation

◆ operator<<