X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.h;h=af3cb7883568dea7fda15ade6d1abf191fd4ca99;hp=68a81a452e19b9ec1bcb8a44e930862807213599;hb=43e0a8f5ca5e1c48cef5daaf014acdbca4e44568;hpb=a8507b8af1c08d9b27d98d57f95c7ca1a8671e27 diff --git a/ginac/clifford.h b/ginac/clifford.h index 68a81a45..af3cb788 100644 --- a/ginac/clifford.h +++ b/ginac/clifford.h @@ -1,8 +1,9 @@ /** @file clifford.h * - * Interface to GiNaC's clifford objects. - * - * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany + * Interface to GiNaC's clifford algebra (Dirac gamma) objects. */ + +/* + * GiNaC Copyright (C) 1999-2001 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 @@ -22,67 +23,125 @@ #ifndef __GINAC_CLIFFORD_H__ #define __GINAC_CLIFFORD_H__ -#include +#include "indexed.h" +#include "tensor.h" + +namespace GiNaC { -/** Base class for clifford object */ + +/** 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. 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 { -// member functions + GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed) - // default constructor, destructor, copy constructor assignment operator and helpers + // other constructors public: - clifford(); - ~clifford(); - clifford(clifford const & other); - clifford const & operator=(clifford const & other); + 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 protected: - void copy(clifford const & other); - void destroy(bool call_parent); + 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; } - // other constructors + // non-virtual functions in this class public: - explicit clifford(string const & initname); + unsigned char get_representation_label(void) const {return representation_label;} + + // member variables +private: + unsigned char representation_label; /**< Representation label to distinguish independent spin lines */ +}; - // functions overriding virtual functions from base classes + +/** This class represents the Clifford algebra unity element. */ +class diracone : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor) + + // functions overriding virtual functions from bases classes public: - basic * duplicate() const; - void printraw(ostream & os) const; - void printtree(ostream & os, unsigned indent) const; - void print(ostream & os, unsigned upper_precedence=0) const; - void printcsrc(ostream & os, unsigned type, unsigned upper_precedence=0) const; - bool info(unsigned inf) const; -protected: - int compare_same_type(basic const & other) const; - ex simplify_ncmul(exvector const & v) const; - unsigned calchash(void) const; - - // new virtual functions which can be overridden by derived classes - // none - - // non-virtual functions in this class + 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 bases classes public: - void setname(string const & n); -private: - string & autoname_prefix(void); + void print(const print_context & c, unsigned level = 0) const; + bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const; +}; -// member variables -protected: - string name; - unsigned serial; // unique serial number for comparision -private: - static unsigned next_serial; +/** 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 bases classes +public: + void print(const print_context & c, unsigned level = 0) const; }; -// global constants -extern const clifford some_clifford; -extern type_info const & typeid_clifford; +// global functions +inline const clifford &ex_to_clifford(const ex &e) +{ + return static_cast(*e.bp); +} + + +/** Create a Clifford unity object. + * + * @param rl Representation label + * @return newly constructed object */ +ex dirac_ONE(unsigned char rl = 0); -// macros +/** 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); -#define ex_to_clifford(X) static_cast(*(X).bp) +/** Create a Dirac gamma5 object. + * + * @param rl Representation label + * @return newly constructed object */ +ex dirac_gamma5(unsigned char rl = 0); -#endif // ndef __GINAC_CLIFFORD_H__ +/** 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 rl Representation label */ +ex dirac_trace(const ex & e, unsigned char rl = 0); +} // namespace GiNaC + +#endif // ndef __GINAC_CLIFFORD_H__