X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.h;h=81abd9f5c879c956da862f009fc5f24f6b7bcbc4;hp=4d771530386b842320ba846853a81fa5a005212a;hb=547db2f0380c03c7d013aa8bda36aa33ff5559e1;hpb=5a7178a44f067581d3acd8cff8c0801354d0c61f diff --git a/ginac/clifford.h b/ginac/clifford.h index 4d771530..81abd9f5 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) 1999-2004 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 @@ -25,6 +25,10 @@ #include "indexed.h" #include "tensor.h" +#include "symbol.h" +#include "idx.h" + +#include namespace GiNaC { @@ -33,7 +37,7 @@ namespace GiNaC { * 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 commute). */ + * algebras (objects with different labels commutate). */ class clifford : public indexed { GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed) @@ -41,27 +45,36 @@ class clifford : public indexed // other constructors public: clifford(const ex & b, unsigned char rl = 0); - clifford(const ex & b, const ex & mu, unsigned char rl = 0); + clifford(const ex & b, const ex & mu, const ex & metr, 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 + clifford(unsigned char rl, const ex & metr, const exvector & v, bool discardable = false); + clifford(unsigned char rl, const ex & metr, std::auto_ptr vp); // 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 + representation_label; } + ex eval_ncmul(const exvector & v) const; + bool match_same_type(const basic & other) const; + ex thiscontainer(const exvector & v) const; + ex thiscontainer(std::auto_ptr 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(void) const {return representation_label;} + unsigned char get_representation_label() const { return representation_label; } + ex get_metric() const { return metric; } + ex get_metric(const ex & i, const ex & j) const; + bool same_metric(const ex & other) const; + +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 */ + ex metric; }; @@ -70,48 +83,119 @@ class diracone : public tensor { GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor) - // functions overriding virtual functions from bases classes + // 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 Clifford algebra generators (units). */ +class cliffordunit : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(cliffordunit, tensor) + + // other constructors +protected: + cliffordunit(unsigned ti) : inherited(ti) {} + + // 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 gamma Lorentz vector. */ -class diracgamma : public tensor +class diracgamma : public cliffordunit { - GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor) + GINAC_DECLARE_REGISTERED_CLASS(diracgamma, cliffordunit) - // 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. */ +/** This class represents the Dirac gamma5 object which anticommutates with + * all other gammas. */ class diracgamma5 : public tensor { GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor) - // functions overriding virtual functions from bases classes -public: - void print(const print_context & c, unsigned level = 0) const; + // functions overriding virtual functions from base classes + ex conjugate() 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 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 + ex conjugate() 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 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 + ex conjugate() 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; }; // 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(unsigned char rl = 0); +/** Create a Clifford unit object. + * + * @param mu Index (must be of class varidx or a derived class) + * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix) + * @param rl Representation label + * @return newly constructed Clifford unit object */ +ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0); + /** Create a Dirac gamma object. * * @param mu Index (must be of class varidx or a derived class) @@ -125,12 +209,88 @@ ex dirac_gamma(const ex & mu, unsigned char rl = 0); * @return newly constructed object */ ex dirac_gamma5(unsigned char rl = 0); -/** Calculate the trace of an expression containing gamma objects with - * a specified representation label. +/** 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 e Original expression + * @param dim Dimension of index * @param rl Representation label */ -ex dirac_trace(const ex & e, unsigned char rl = 0); +ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0); + +/** Calculate dirac traces over the specified set of representation labels. + * 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 rls Set of representation labels + * @param trONE Expression to be returned as the trace of the unit matrix */ +ex dirac_trace(const ex & e, const std::set & rls, const ex & trONE = 4); + +/** Calculate dirac traces over the specified list of representation labels. + * 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 rll List of representation labels + * @param trONE Expression to be returned as the trace of the unit matrix */ +ex dirac_trace(const ex & e, const lst & rll, const ex & trONE = 4); + +/** 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); +/** Automorphism of the Clifford algebra, simply changes signs of all + * clifford units. */ +ex clifford_prime(const ex & e); + +/** Main anti-automorphism of the Clifford algebra: makes reversion + * and changes signs of all clifford units. */ +inline ex clifford_bar(const ex & e) { return clifford_prime(e.conjugate()); } + +/** Reversion of the Clifford algebra, coincides with the conjugate(). */ +inline ex clifford_star(const ex & e) { return e.conjugate(); } + +ex delete_ONE(const ex &e); + +/** Calculation of the norm in the Clifford algebra. */ +ex clifford_norm(const ex & e); + +/** Calculation of the inverse in the Clifford algebra. */ +ex clifford_inverse(const ex & e); + +/** List or vector conversion into the Clifford vector. + * + * @param v List or vector of coordinates + * @param mu Index (must be of class varidx or a derived class) + * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix) + * @param rl Representation label + * @return Clifford vector with given components */ +ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl = 0); } // namespace GiNaC