X-Git-Url: https://ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=ginac%2Fclifford.h;h=eebe5e1f5ac34ba16811505606e791872b61b5d1;hb=3791fff10fec1552ac740a7690f7a7a4b59e82f5;hp=50893c8153eed49fb56e9ea34d18f49abec73e76;hpb=06eb6b761f4b9d9eed4decd8ed50d94b40b94a0e;p=ginac.git diff --git a/ginac/clifford.h b/ginac/clifford.h index 50893c81..eebe5e1f 100644 --- a/ginac/clifford.h +++ b/ginac/clifford.h @@ -3,7 +3,7 @@ * 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 @@ -31,27 +31,42 @@ 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 hidden. */ + * 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, indexed) // other constructors public: - clifford(const ex & b); - clifford(const ex & b, const ex & mu); + clifford(const ex & b, unsigned char rl = 0); + clifford(const ex & b, const ex & mu, unsigned char rl = 0); // internal constructors - clifford(const exvector & v, bool discardable = false); - clifford(exvector * vp); // vp will be deleted + 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 protected: - ex simplify_ncmul(const exvector & v) 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; } + ex eval_ncmul(const exvector & v) const; + bool match_same_type(const basic & other) const; + ex thiscontainer(const exvector & v) const; + ex thiscontainer(exvector * vp) const; + unsigned return_type() const { return return_types::noncommutative; } + unsigned return_type_tinfo() const { return TINFO_clifford + representation_label; } + + // non-virtual functions in this class +public: + unsigned char get_representation_label() const {return representation_label;} + +protected: + void do_print_dflt(const print_dflt & c, unsigned level) const; + void do_print_latex(const print_latex & c, unsigned level) const; + + // member variables +private: + unsigned char representation_label; /**< Representation label to distinguish independent spin lines */ }; @@ -60,9 +75,10 @@ class diracone : public tensor { GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor) - // functions overriding virtual functions from bases classes -public: - void print(const print_context & c, unsigned level = 0) const; + // non-virtual functions in this class +protected: + void do_print(const print_context & c, unsigned level) const; + void do_print_latex(const print_latex & c, unsigned level) const; }; @@ -71,31 +87,116 @@ class diracgamma : public tensor { GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor) - // functions overriding virtual functions from bases classes + // 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; + + // non-virtual functions in this class +protected: + void do_print(const print_context & c, unsigned level) const; + void do_print_latex(const print_latex & c, unsigned level) const; +}; + + +/** This class represents the Dirac gamma5 object which anticommutes with + * all other gammas. */ +class diracgamma5 : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor) + + // non-virtual functions in this class +protected: + void do_print(const print_context & c, unsigned level) const; + void do_print_latex(const print_latex & c, unsigned level) 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) + + // non-virtual functions in this class +protected: + void do_print(const print_context & c, unsigned level) const; + void do_print_latex(const print_latex & c, unsigned level) 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) + + // non-virtual functions in this class +protected: + void do_print(const print_context & c, unsigned level) const; + void do_print_latex(const print_latex & c, unsigned level) 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; } - /** Create a Clifford unity object. * + * @param rl Representation label * @return newly constructed object */ -ex dirac_one(void); +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); +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); + +/** 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); } // namespace GiNaC