X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.h;h=667d7befd9d400749188f8af6f28bcecee1ce83e;hp=0feef3f049b135c3984af3bfba8f52df5df70923;hb=bc6dacb50cc13691efc466d2cc1900048158ec8d;hpb=61b8ecb02c8212efbc15f59face8a9c620dc823c diff --git a/ginac/clifford.h b/ginac/clifford.h index 0feef3f0..667d7bef 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 @@ -25,33 +25,54 @@ #include "indexed.h" #include "tensor.h" +#include "symbol.h" +#include "idx.h" 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 commutate). */ 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, const ex & metr, 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 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; } + 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() 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; }; @@ -60,42 +81,194 @@ 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(std::ostream & os, unsigned upper_precedence=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(std::ostream & os, unsigned upper_precedence=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 anticommutates with + * all other gammas. */ +class diracgamma5 : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, 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 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(void); +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) + * @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 e Original expression + * @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); + +/** 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