GiNaC 1.8.7
Classes | Namespaces | Functions
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.


This page is part of the GiNaC developer's reference. It was generated automatically by doxygen. For an introduction, see the tutorial.