X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.h;h=ce5d2acfd50a6b3430d5717c9aa125389d19f3fc;hp=2d02ebcb8df7a4c6bc3db1d12c0fb34ca00aeae2;hb=dbd9c306a74f1cb258c0d15a346b973b39deaad2;hpb=e5362a33f72613b324b3714524a8c2e5f7b7f46f diff --git a/ginac/clifford.h b/ginac/clifford.h index 2d02ebcb..ce5d2acf 100644 --- a/ginac/clifford.h +++ b/ginac/clifford.h @@ -1,9 +1,9 @@ /** @file clifford.h * - * Interface to GiNaC's clifford objects. */ + * Interface to GiNaC's clifford algebra (Dirac gamma) objects. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -23,66 +23,176 @@ #ifndef __GINAC_CLIFFORD_H__ #define __GINAC_CLIFFORD_H__ -#include -#include "lortensor.h" +#include "indexed.h" +#include "tensor.h" -#ifndef NO_NAMESPACE_GINAC namespace GiNaC { -#endif // ndef NO_NAMESPACE_GINAC /** 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 always hidden in our implementation. */ -class clifford : public lortensor + * 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 commute). */ +class clifford : public indexed { - GINAC_DECLARE_REGISTERED_CLASS(clifford, lortensor) - -// friends - - friend clifford clifford_gamma(const ex & mu); + GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed) // other constructors public: - clifford(const std::string & n, const ex & mu); - clifford(const std::string & n, const exvector & iv); - clifford(const std::string & n, exvector * ivp); + clifford(const ex & b, unsigned char rl = 0); + clifford(const ex & b, const ex & mu, unsigned char rl = 0); + + // internal constructors + clifford(unsigned char rl, const exvector & v, bool discardable = false); + clifford(unsigned char rl, exvector * vp); // vp will be deleted // functions overriding virtual functions from base classes public: - basic * duplicate() const; - void printraw(std::ostream & os) const; - void printtree(std::ostream & os, unsigned indent) const; - void print(std::ostream & os, unsigned upper_precedence=0) const; - bool info(unsigned inf) const; - // ex eval(int level=0) const; + void print(const print_context & c, unsigned level = 0) const; + protected: - int compare_same_type(const basic & other) const; - bool is_equal_same_type(const basic & other) const; ex simplify_ncmul(const exvector & v) const; + bool match_same_type(const basic & other) const; ex thisexprseq(const exvector & v) const; ex thisexprseq(exvector * vp) const; + unsigned return_type(void) const { return return_types::noncommutative; } + unsigned return_type_tinfo(void) const { return TINFO_clifford + representation_label; } - // new virtual functions which can be overridden by derived classes - // none - // non-virtual functions in this class - // none +public: + unsigned char get_representation_label(void) const {return representation_label;} // member variables - // none +private: + unsigned char representation_label; /**< Representation label to distinguish independent spin lines */ +}; + + +/** This class represents the Clifford algebra unity element. */ +class diracone : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor) + + // functions overriding virtual functions from base classes +public: + void print(const print_context & c, unsigned level = 0) const; +}; + + +/** This class represents the Dirac gamma Lorentz vector. */ +class diracgamma : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor) + + // functions overriding virtual functions from base classes +public: + void print(const print_context & c, unsigned level = 0) const; + bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const; +}; + + +/** This class represents the Dirac gamma5 object which anticommutes with + * all other gammas. */ +class diracgamma5 : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor) + + // functions overriding virtual functions from base classes +public: + void print(const print_context & c, unsigned level = 0) const; +}; + + +/** This class represents the Dirac gammaL object which behaves like + * 1/2 (1-gamma5). */ +class diracgammaL : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(diracgammaL, tensor) + + // functions overriding virtual functions from base classes +public: + void print(const print_context & c, unsigned level = 0) const; +}; + + +/** This class represents the Dirac gammaL object which behaves like + * 1/2 (1+gamma5). */ +class diracgammaR : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(diracgammaR, tensor) + + // functions overriding virtual functions from base classes +public: + void print(const print_context & c, unsigned level = 0) const; }; + // global functions -inline const clifford &ex_to_clifford(const ex &e) + +/** Specialization of is_exactly_a(obj) for clifford objects. */ +template<> inline bool is_exactly_a(const basic & obj) { - return static_cast(*e.bp); + return obj.tinfo()==TINFO_clifford; } -clifford clifford_gamma(const ex & mu); +/** Create a Clifford unity object. + * + * @param rl Representation label + * @return newly constructed object */ +ex dirac_ONE(unsigned char rl = 0); + +/** Create a Dirac gamma object. + * + * @param mu Index (must be of class varidx or a derived class) + * @param rl Representation label + * @return newly constructed gamma object */ +ex dirac_gamma(const ex & mu, unsigned char rl = 0); + +/** Create a Dirac gamma5 object. + * + * @param rl Representation label + * @return newly constructed object */ +ex dirac_gamma5(unsigned char rl = 0); + +/** Create a Dirac gammaL object. + * + * @param rl Representation label + * @return newly constructed object */ +ex dirac_gammaL(unsigned char rl = 0); + +/** Create a Dirac gammaR object. + * + * @param rl Representation label + * @return newly constructed object */ +ex dirac_gammaR(unsigned char rl = 0); + +// These functions are deprecated. Use dirac_gammaL/R() instead. +ex dirac_gamma6(unsigned char rl = 0); +ex dirac_gamma7(unsigned char rl = 0); + +/** Create a term of the form e_mu * gamma~mu with a unique index mu. + * + * @param dim Dimension of index + * @param rl Representation label */ +ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0); + +/** Calculate the trace of an expression containing gamma objects with + * a specified representation label. The computed trace is a linear + * functional that is equal to the usual trace only in D = 4 dimensions. + * In particular, the functional is not always cyclic in D != 4 dimensions + * when gamma5 is involved. + * + * @param e Expression to take the trace of + * @param rl Representation label + * @param trONE Expression to be returned as the trace of the unit matrix */ +ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4); + +/** Bring all products of clifford objects in an expression into a canonical + * order. This is not necessarily the most simple form but it will allow + * to check two expressions for equality. */ +ex canonicalize_clifford(const ex & e); -#ifndef NO_NAMESPACE_GINAC } // namespace GiNaC -#endif // ndef NO_NAMESPACE_GINAC #endif // ndef __GINAC_CLIFFORD_H__