This class holds an object representing an element of the Clifford algebra (the Dirac gamma matrices). More...

#include <clifford.h>

Inheritance diagram for GiNaC::clifford:

Public Member Functions
	clifford (const ex &b, unsigned char rl=0)
	Construct object without any indices.
	clifford (const ex &b, const ex &mu, const ex &metr, unsigned char rl=0, int comm_sign=-1)
	Construct object with one Lorentz index.
	clifford (unsigned char rl, const ex &metr, int comm_sign, const exvector &v, bool discardable=false)
	clifford (unsigned char rl, const ex &metr, int comm_sign, std::auto_ptr< exvector > vp)
unsigned	precedence () const
	Return relative operator precedence (for parenthezing output).
void	archive (archive_node &n) const
	Save (a.k.a.
void	read_archive (const archive_node &n, lst &sym_lst)
	Read (a.k.a.
unsigned char	get_representation_label () const
ex	get_metric () const
virtual ex	get_metric (const ex &i, const ex &j, bool symmetrised=false) const
bool	same_metric (const ex &other) const
int	get_commutator_sign () const
size_t	nops () const
	Number of operands/members.
ex	op (size_t i) const
	Return operand/member at position i.
ex &	let_op (size_t i)
	Return modifyable operand/member at position i.
ex	subs (const exmap &m, unsigned options=0) const
	Substitute a set of objects by arbitrary expressions.
Protected Member Functions
ex	eval_ncmul (const exvector &v) const
	Perform automatic simplification on noncommutative product of clifford objects.
bool	match_same_type (const basic &other) const
	Returns true if the attributes of two objects are similar enough for a match.
ex	thiscontainer (const exvector &v) const
ex	thiscontainer (std::auto_ptr< exvector > vp) const
unsigned	return_type () const
return_type_t	return_type_tinfo () const
void	do_print_dflt (const print_dflt &c, unsigned level) const
void	do_print_latex (const print_latex &c, unsigned level) const
Protected Attributes
unsigned char	representation_label
	Representation label to distinguish independent spin lines.
ex	metric
	Metric of the space, all constructors make it an indexed object.
int	commutator_sign
	It is the sign in the definition e~i e~j +/- e~j e~i = B(i, j) + B(j, i)

Detailed Description

This class holds an object representing an element of the Clifford algebra (the Dirac gamma matrices).

These objects only carry Lorentz indices. Spinor indices are hidden. A representation label (an unsigned 8-bit integer) is used to distinguish elements from different Clifford algebras (objects with different labels commutate).

Definition at line 40 of file clifford.h.

Constructor & Destructor Documentation

GiNaC::clifford::clifford	(	const ex &	b,
		unsigned char	rl = `0`
	)

Construct object without any indices.

This constructor is for internal use only. Use the dirac_ONE() function instead.

See also:: dirac_ONE

Definition at line 95 of file clifford.cpp.

GiNaC::clifford::clifford	(	const ex &	b,
		const ex &	mu,
		const ex &	metr,
		unsigned char	rl = `0`,
		int	comm_sign = `-1`
	)

Construct object with one Lorentz index.

This constructor is for internal use only. Use the clifford_unit() or dirac_gamma() functions instead.

See also:: clifford_unit; dirac_gamma

Definition at line 103 of file clifford.cpp.

References GINAC_ASSERT.

GiNaC::clifford::clifford	(	unsigned char	rl,
		const ex &	metr,
		int	comm_sign,
		const exvector &	v,
		bool	discardable = `false`
	)

Definition at line 108 of file clifford.cpp.

GiNaC::clifford::clifford	(	unsigned char	rl,
		const ex &	metr,
		int	comm_sign,
		std::auto_ptr< exvector >	vp
	)

Definition at line 112 of file clifford.cpp.

Member Function Documentation

unsigned GiNaC::clifford::precedence ( ) const [inline, virtual]

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::indexed.

Definition at line 54 of file clifford.h.

Referenced by do_print_dflt(), and do_print_latex().

void GiNaC::clifford::archive ( archive_node & n ) const [virtual]

Save (a.k.a.

serialize) indexed object into archive.

Reimplemented from GiNaC::indexed.

Definition at line 136 of file clifford.cpp.

References GiNaC::archive_node::add_ex(), GiNaC::archive_node::add_unsigned(), commutator_sign, metric, and representation_label.

void GiNaC::clifford::read_archive	(	const archive_node &	n,
		lst &	syms
	)		`[virtual]`

Read (a.k.a.

deserialize) indexed object from archive.

Reimplemented from GiNaC::indexed.

Definition at line 125 of file clifford.cpp.

References commutator_sign, GiNaC::archive_node::find_ex(), GiNaC::archive_node::find_unsigned(), metric, and representation_label.

ex GiNaC::clifford::eval_ncmul ( const exvector & v ) const [protected, virtual]

Perform automatic simplification on noncommutative product of clifford objects.

This removes superfluous ONEs, permutes gamma5/L/R's to the front and removes squares of gamma objects.

Reimplemented from GiNaC::basic.

Definition at line 516 of file clifford.cpp.

bool GiNaC::clifford::match_same_type ( const basic & other ) const [protected, virtual]

Returns true if the attributes of two objects are similar enough for a match.

This function must not match subexpressions (this is already done by basic::match()). Only attributes not accessible by op() should be compared. This is also the reason why this function doesn't take the wildcard replacement list from match() as an argument: only subexpressions are subject to wildcard matches. Also, this function only needs to be implemented for container classes because is_equal_same_type() is automatically used instead of match_same_type() if nops() == 0.