X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.h;h=ef08f72bc75fb381bb2662e0ca3efe9c770da39b;hp=667d7befd9d400749188f8af6f28bcecee1ce83e;hb=e08cda1854bdb82f6706ec269233577690ae00e4;hpb=bc6dacb50cc13691efc466d2cc1900048158ec8d diff --git a/ginac/clifford.h b/ginac/clifford.h index 667d7bef..ef08f72b 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) 1999-2004 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2010 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 @@ -17,19 +17,20 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#ifndef __GINAC_CLIFFORD_H__ -#define __GINAC_CLIFFORD_H__ +#ifndef GINAC_CLIFFORD_H +#define GINAC_CLIFFORD_H #include "indexed.h" #include "tensor.h" #include "symbol.h" #include "idx.h" -namespace GiNaC { +#include +namespace GiNaC { /** This class holds an object representing an element of the Clifford * algebra (the Dirac gamma matrices). These objects only carry Lorentz @@ -39,42 +40,51 @@ namespace GiNaC { class clifford : public indexed { GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed) - // other constructors public: clifford(const ex & b, unsigned char rl = 0); - clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl = 0); + clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl = 0, int comm_sign = -1); // internal constructors - clifford(unsigned char rl, const ex & metr, const exvector & v, bool discardable = false); - clifford(unsigned char rl, const ex & metr, std::auto_ptr vp); + clifford(unsigned char rl, const ex & metr, int comm_sign, const exvector & v, bool discardable = false); + clifford(unsigned char rl, const ex & metr, int comm_sign, std::auto_ptr vp); // functions overriding virtual functions from base classes +public: + unsigned precedence() const { return 65; } + void archive(archive_node& n) const; + void read_archive(const archive_node& n, lst& sym_lst); protected: 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; } - + return_type_t return_type_tinfo() const; // 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; + virtual ex get_metric(const ex & i, const ex & j, bool symmetrised = false) const; bool same_metric(const ex & other) const; + int get_commutator_sign() const { return commutator_sign; } //**< See the member variable commutator_sign */ + + inline size_t nops() const {return inherited::nops() + 1; } + ex op(size_t i) const; + ex & let_op(size_t i); + ex subs(const exmap & m, unsigned options = 0) 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: +protected: unsigned char representation_label; /**< Representation label to distinguish independent spin lines */ - ex metric; + ex metric; /**< Metric of the space, all constructors make it an indexed object */ + int commutator_sign; /**< It is the sign in the definition e~i e~j +/- e~j e~i = B(i, j) + B(j, i)*/ }; - +GINAC_DECLARE_UNARCHIVER(clifford); /** This class represents the Clifford algebra unity element. */ class diracone : public tensor @@ -86,6 +96,7 @@ protected: void do_print(const print_context & c, unsigned level) const; void do_print_latex(const print_latex & c, unsigned level) const; }; +GINAC_DECLARE_UNARCHIVER(diracone); /** This class represents the Clifford algebra generators (units). */ @@ -93,10 +104,6 @@ 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: bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const; @@ -122,6 +129,7 @@ protected: void do_print(const print_context & c, unsigned level) const; void do_print_latex(const print_latex & c, unsigned level) const; }; +GINAC_DECLARE_UNARCHIVER(diracgamma); /** This class represents the Dirac gamma5 object which anticommutates with @@ -138,6 +146,7 @@ protected: void do_print(const print_context & c, unsigned level) const; void do_print_latex(const print_latex & c, unsigned level) const; }; +GINAC_DECLARE_UNARCHIVER(diracgamma5); /** This class represents the Dirac gammaL object which behaves like @@ -154,6 +163,7 @@ protected: void do_print(const print_context & c, unsigned level) const; void do_print_latex(const print_latex & c, unsigned level) const; }; +GINAC_DECLARE_UNARCHIVER(diracgammaL); /** This class represents the Dirac gammaL object which behaves like @@ -170,14 +180,18 @@ protected: void do_print(const print_context & c, unsigned level) const; void do_print_latex(const print_latex & c, unsigned level) const; }; +GINAC_DECLARE_UNARCHIVER(diracgammaR); // global functions -/** Specialization of is_exactly_a(obj) for clifford objects. */ -template<> inline bool is_exactly_a(const basic & obj) +/** Check whether a given return_type_t object (as returned by return_type_tinfo() + * is that of a clifford object (with an arbitrary representation label). + * + * @param ti tinfo key */ +inline bool is_clifford_tinfo(const return_type_t& ti) { - return obj.tinfo()==TINFO_clifford; + return *(ti.tinfo) == typeid(clifford); } /** Create a Clifford unity object. @@ -189,7 +203,7 @@ 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 metr Metric (should be indexed, tensmetric or a derived class, or a matrix) * @param rl Representation label * @return newly constructed Clifford unit object */ ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0); @@ -226,6 +240,26 @@ ex dirac_gammaR(unsigned char rl = 0); * @param rl Representation label */ 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. @@ -253,7 +287,21 @@ 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); +/** Replaces dirac_ONE's (with a representation_label no less than rl) in e with 1. + * For the default value rl = 0 remove all of them. Aborts if e contains any + * clifford_unit with representation_label to be removed. + * + * @param e Expression to be processed + * @param rl Value of representation label + * @param options Defines some internal use */ +ex remove_dirac_ONE(const ex & e, unsigned char rl = 0, unsigned options = 0); + +/** Returns the maximal representation label of a clifford object + * if e contains at least one, otherwise returns -1 + * + * @param e Expression to be processed + * @ignore_ONE defines if clifford_ONE should be ignored in the search*/ +char clifford_max_label(const ex & e, bool ignore_ONE = false); /** Calculation of the norm in the Clifford algebra. */ ex clifford_norm(const ex & e); @@ -265,11 +313,51 @@ ex clifford_inverse(const ex & e); * * @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 metr Metric (should be indexed, tensmetric or a derived class, or a matrix) * @param rl Representation label + * @param e Clifford unit object * @return Clifford vector with given components */ ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl = 0); +ex lst_to_clifford(const ex & v, const ex & e); + +/** An inverse function to lst_to_clifford(). For given Clifford vector extracts + * its components with respect to given Clifford unit. Obtained components may + * contain Clifford units with a different metric. Extraction is based on + * the algebraic formula (e * c.i + c.i * e)/ pow(e.i, 2) for non-degenerate cases + * (i.e. neither pow(e.i, 2) = 0). + * + * @param e Clifford expression to be decomposed into components + * @param c Clifford unit defining the metric for splitting (should have numeric dimension of indices) + * @param algebraic Use algebraic or symbolic algorithm for extractions + * @return List of components of a Clifford vector*/ +lst clifford_to_lst(const ex & e, const ex & c, bool algebraic=true); + +/** Calculations of Moebius transformations (conformal map) defined by a 2x2 Clifford matrix + * (a b\\c d) in linear spaces with arbitrary signature. The expression is + * (a * x + b)/(c * x + d), where x is a vector build from list v with metric G. + * (see Jan Cnops. An introduction to {D}irac operators on manifolds, v.24 of + * Progress in Mathematical Physics. Birkhauser Boston Inc., Boston, MA, 2002.) + * + * @param a (1,1) entry of the defining matrix + * @param b (1,2) entry of the defining matrix + * @param c (2,1) entry of the defining matrix + * @param d (2,2) entry of the defining matrix + * @param v Vector to be transformed + * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored + * @param rl Representation label + * @return List of components of the transformed vector*/ +ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G, unsigned char rl = 0); + +/** The second form of Moebius transformations defined by a 2x2 Clifford matrix M + * This function takes the transformation matrix M as a single entity. + * + * @param M the defining matrix + * @param v Vector to be transformed + * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored + * @param rl Representation label + * @return List of components of the transformed vector*/ +ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl = 0); } // namespace GiNaC -#endif // ndef __GINAC_CLIFFORD_H__ +#endif // ndef GINAC_CLIFFORD_H