X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.h;h=667d7befd9d400749188f8af6f28bcecee1ce83e;hp=8dbc3767ddb94330fee5530ab7a90f7a0fb52489;hb=bc6dacb50cc13691efc466d2cc1900048158ec8d;hpb=68fdf425abf14d016d5f95ee7b9d06a19a3c5926 diff --git a/ginac/clifford.h b/ginac/clifford.h index 8dbc3767..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) 1999-2003 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 +25,8 @@ #include "indexed.h" #include "tensor.h" +#include "symbol.h" +#include "idx.h" namespace GiNaC { @@ -33,7 +35,7 @@ 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) @@ -41,31 +43,36 @@ 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 -public: - void print(const print_context & c, unsigned level = 0) const; - protected: 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; + 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;} + 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; }; @@ -74,33 +81,62 @@ class diracone : public tensor { GINAC_DECLARE_REGISTERED_CLASS(diracone, 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 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 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 +/** 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 -public: - void print(const print_context & c, unsigned level = 0) const; + 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; }; @@ -111,8 +147,12 @@ 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; + 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; }; @@ -123,8 +163,12 @@ 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; + 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; }; @@ -142,6 +186,14 @@ template<> inline bool is_exactly_a(const basic & obj) * @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) @@ -169,6 +221,7 @@ 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); @@ -189,6 +242,34 @@ ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4); * 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 #endif // ndef __GINAC_CLIFFORD_H__