clifford.h File Reference

Interface to GiNaC's clifford algebra (Dirac gamma) objects. More...

#include "indexed.h"
#include "tensor.h"
#include "symbol.h"
#include "idx.h"
#include <set>

Go to the source code of this file.

Classes
class	GiNaC::clifford
	This class holds an object representing an element of the Clifford algebra (the Dirac gamma matrices). More...
class	GiNaC::diracone
	This class represents the Clifford algebra unity element. More...
class	GiNaC::cliffordunit
	This class represents the Clifford algebra generators (units). More...
class	GiNaC::diracgamma
	This class represents the Dirac gamma Lorentz vector. More...
class	GiNaC::diracgamma5
	This class represents the Dirac gamma5 object which anticommutates with all other gammas. More...
class	GiNaC::diracgammaL
	This class represents the Dirac gammaL object which behaves like 1/2 (1-gamma5). More...
class	GiNaC::diracgammaR
	This class represents the Dirac gammaL object which behaves like 1/2 (1+gamma5). More...

Namespaces
namespace	GiNaC

Functions
	GiNaC::GINAC_DECLARE_UNARCHIVER (clifford)
	GiNaC::GINAC_DECLARE_UNARCHIVER (diracone)
	GiNaC::GINAC_DECLARE_UNARCHIVER (cliffordunit)
	GiNaC::GINAC_DECLARE_UNARCHIVER (diracgamma)
	GiNaC::GINAC_DECLARE_UNARCHIVER (diracgamma5)
	GiNaC::GINAC_DECLARE_UNARCHIVER (diracgammaL)
	GiNaC::GINAC_DECLARE_UNARCHIVER (diracgammaR)
bool	GiNaC::is_clifford_tinfo (const return_type_t &ti)
	Check whether a given return_type_t object (as returned by return_type_tinfo() is that of a clifford object (with an arbitrary representation label). More...
ex	GiNaC::dirac_ONE (unsigned char rl=0)
	Create a Clifford unity object. More...
ex	GiNaC::clifford_unit (const ex &mu, const ex &metr, unsigned char rl=0)
	Create a Clifford unit object. More...
ex	GiNaC::dirac_gamma (const ex &mu, unsigned char rl=0)
	Create a Dirac gamma object. More...
ex	GiNaC::dirac_gamma5 (unsigned char rl=0)
	Create a Dirac gamma5 object. More...
ex	GiNaC::dirac_gammaL (unsigned char rl=0)
	Create a Dirac gammaL object. More...
ex	GiNaC::dirac_gammaR (unsigned char rl=0)
	Create a Dirac gammaR object. More...
ex	GiNaC::dirac_slash (const ex &e, const ex &dim, unsigned char rl=0)
	Create a term of the form e_mu * gamma~mu with a unique index mu. More...
ex	GiNaC::dirac_trace (const ex &e, const std::set< unsigned char > &rls, const ex &trONE=4)
	Calculate dirac traces over the specified set of representation labels. More...
ex	GiNaC::dirac_trace (const ex &e, const lst &rll, const ex &trONE=4)
	Calculate dirac traces over the specified list of representation labels. More...
ex	GiNaC::dirac_trace (const ex &e, unsigned char rl=0, const ex &trONE=4)
	Calculate the trace of an expression containing gamma objects with a specified representation label. More...
ex	GiNaC::canonicalize_clifford (const ex &e)
	Bring all products of clifford objects in an expression into a canonical order. More...
ex	GiNaC::clifford_prime (const ex &e)
	Automorphism of the Clifford algebra, simply changes signs of all clifford units. More...
ex	GiNaC::clifford_star_bar (const ex &e, bool do_bar, unsigned options)
	An auxillary function performing clifford_star() and clifford_bar(). More...
ex	GiNaC::clifford_bar (const ex &e)
	Main anti-automorphism of the Clifford algebra: makes reversion and changes signs of all clifford units. More...
ex	GiNaC::clifford_star (const ex &e)
	Reversion of the Clifford algebra, reverse the order of all clifford units in ncmul. More...
ex	GiNaC::remove_dirac_ONE (const ex &e, unsigned char rl=0, unsigned options=0)
	Replaces dirac_ONE's (with a representation_label no less than rl) in e with 1. More...
int	GiNaC::clifford_max_label (const ex &e, bool ignore_ONE=false)
	Returns the maximal representation label of a clifford object if e contains at least one, otherwise returns -1. More...
ex	GiNaC::clifford_norm (const ex &e)
	Calculation of the norm in the Clifford algebra. More...
ex	GiNaC::clifford_inverse (const ex &e)
	Calculation of the inverse in the Clifford algebra. More...
ex	GiNaC::lst_to_clifford (const ex &v, const ex &mu, const ex &metr, unsigned char rl=0)
	List or vector conversion into the Clifford vector. More...
ex	GiNaC::lst_to_clifford (const ex &v, const ex &e)
	List or vector conversion into the Clifford vector. More...
lst	GiNaC::clifford_to_lst (const ex &e, const ex &c, bool algebraic=true)
	An inverse function to lst_to_clifford(). More...
ex	GiNaC::clifford_moebius_map (const ex &a, const ex &b, const ex &c, const ex &d, const ex &v, const ex &G, unsigned char rl=0)
	Calculations of Moebius transformations (conformal map) defined by a 2x2 Clifford matrix (a b\c d) in linear spaces with arbitrary signature. More...
ex	GiNaC::clifford_moebius_map (const ex &M, const ex &v, const ex &G, unsigned char rl=0)
	The second form of Moebius transformations defined by a 2x2 Clifford matrix M This function takes the transformation matrix M as a single entity. More...

Detailed Description

Interface to GiNaC's clifford algebra (Dirac gamma) objects.

Definition in file clifford.h.