X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.h;h=b6c88d9efa79a0f4060264f102428af7dbb6b952;hp=79d714dc2e367f340ecc98f6f283ae1c67a68aa9;hb=c9ff42724b6c9b37cbb474b13826692c733fef84;hpb=383d5eb3b0f0506810d9105a268f939125bfc347 diff --git a/ginac/clifford.h b/ginac/clifford.h index 79d714dc..b6c88d9e 100644 --- a/ginac/clifford.h +++ b/ginac/clifford.h @@ -1,6 +1,6 @@ /** @file clifford.h * - * Interface to GiNaC's clifford objects. */ + * Interface to GiNaC's clifford algebra (Dirac gamma) objects. */ /* * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany @@ -23,77 +23,142 @@ #ifndef __GINAC_CLIFFORD_H__ #define __GINAC_CLIFFORD_H__ -#include #include "indexed.h" -#include "ex.h" +#include "tensor.h" -#ifndef NO_NAMESPACE_GINAC namespace GiNaC { -#endif // ndef NO_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 - - // default constructor, destructor, copy constructor assignment operator and helpers -public: - clifford(); - ~clifford(); - clifford(const clifford & other); - const clifford & operator=(const clifford & other); -protected: - void copy(const clifford & other); - void destroy(bool call_parent); + GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed) // other constructors public: - explicit clifford(const std::string & initname); + 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 public: - basic * duplicate() const; - void printraw(std::ostream & os) const; - void printtree(std::ostream & os, unsigned indent) const; - void print(std::ostream & os, unsigned upper_precedence=0) const; - void printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence=0) const; - bool info(unsigned inf) const; + void print(const print_context & c, unsigned level = 0) const; + protected: - int compare_same_type(const basic & other) const; + bool match_same_type(const basic & other) const; ex simplify_ncmul(const exvector & v) const; - unsigned calchash(void) 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; } - // new virtual functions which can be overridden by derived classes - // none - // non-virtual functions in this class public: - void setname(const std::string & n); + unsigned char get_representation_label(void) const {return representation_label;} + + // member variables private: - std::string & autoname_prefix(void); + unsigned char representation_label; /**< Representation label to distinguish independent spin lines */ +}; -// member variables -protected: - std::string name; - unsigned serial; // unique serial number for comparision -private: - static unsigned next_serial; +/** This class represents the Clifford algebra unity element. */ +class diracone : public tensor +{ + GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor) + + // functions overriding virtual functions from base classes +public: + 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 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; +}; + + +/** 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 base classes +public: + void print(const print_context & c, unsigned level = 0) const; }; -// global constants -extern const clifford some_clifford; -extern const std::type_info & typeid_clifford; +// global functions -// utility 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; } -#ifndef NO_NAMESPACE_GINAC +/** Create a Clifford unity object. + * + * @param rl Representation label + * @return newly constructed object */ +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, unsigned char rl = 0); + +/** Create a Dirac gamma5 object. + * + * @param rl Representation label + * @return newly constructed object */ +ex dirac_gamma5(unsigned char rl = 0); + +/** This returns (dirac_ONE(rl) + dirac_gamma5(rl)). */ +ex dirac_gamma6(unsigned char rl = 0); + +/** This returns (dirac_ONE(rl) - dirac_gamma5(rl)). */ +ex dirac_gamma7(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 -#endif // ndef NO_NAMESPACE_GINAC #endif // ndef __GINAC_CLIFFORD_H__