3 * Interface to GiNaC's clifford algebra (Dirac gamma) objects. */
6 * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23 #ifndef __GINAC_CLIFFORD_H__
24 #define __GINAC_CLIFFORD_H__
32 /** This class holds an object representing an element of the Clifford
33 * algebra (the Dirac gamma matrices). These objects only carry Lorentz
34 * indices. Spinor indices are hidden. A representation label (an unsigned
35 * 8-bit integer) is used to distinguish elements from different Clifford
36 * algebras (objects with different labels commute). */
37 class clifford : public indexed
39 GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)
43 clifford(const ex & b, unsigned char rl = 0);
44 clifford(const ex & b, const ex & mu, unsigned char rl = 0);
46 // internal constructors
47 clifford(unsigned char rl, const exvector & v, bool discardable = false);
48 clifford(unsigned char rl, std::auto_ptr<exvector> vp);
50 // functions overriding virtual functions from base classes
52 ex eval_ncmul(const exvector & v) const;
53 bool match_same_type(const basic & other) const;
54 ex thiscontainer(const exvector & v) const;
55 ex thiscontainer(std::auto_ptr<exvector> vp) const;
56 unsigned return_type() const { return return_types::noncommutative; }
57 unsigned return_type_tinfo() const { return TINFO_clifford + representation_label; }
59 // non-virtual functions in this class
61 unsigned char get_representation_label() const {return representation_label;}
64 void do_print_dflt(const print_dflt & c, unsigned level) const;
65 void do_print_latex(const print_latex & c, unsigned level) const;
69 unsigned char representation_label; /**< Representation label to distinguish independent spin lines */
73 /** This class represents the Clifford algebra unity element. */
74 class diracone : public tensor
76 GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor)
78 // non-virtual functions in this class
80 void do_print(const print_context & c, unsigned level) const;
81 void do_print_latex(const print_latex & c, unsigned level) const;
85 /** This class represents the Dirac gamma Lorentz vector. */
86 class diracgamma : public tensor
88 GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor)
90 // functions overriding virtual functions from base classes
92 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
94 // non-virtual functions in this class
96 void do_print(const print_context & c, unsigned level) const;
97 void do_print_latex(const print_latex & c, unsigned level) const;
101 /** This class represents the Dirac gamma5 object which anticommutes with
102 * all other gammas. */
103 class diracgamma5 : public tensor
105 GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor)
107 // non-virtual functions in this class
109 void do_print(const print_context & c, unsigned level) const;
110 void do_print_latex(const print_latex & c, unsigned level) const;
114 /** This class represents the Dirac gammaL object which behaves like
116 class diracgammaL : public tensor
118 GINAC_DECLARE_REGISTERED_CLASS(diracgammaL, tensor)
120 // non-virtual functions in this class
122 void do_print(const print_context & c, unsigned level) const;
123 void do_print_latex(const print_latex & c, unsigned level) const;
127 /** This class represents the Dirac gammaL object which behaves like
129 class diracgammaR : public tensor
131 GINAC_DECLARE_REGISTERED_CLASS(diracgammaR, tensor)
133 // non-virtual functions in this class
135 void do_print(const print_context & c, unsigned level) const;
136 void do_print_latex(const print_latex & c, unsigned level) const;
142 /** Specialization of is_exactly_a<clifford>(obj) for clifford objects. */
143 template<> inline bool is_exactly_a<clifford>(const basic & obj)
145 return obj.tinfo()==TINFO_clifford;
148 /** Create a Clifford unity object.
150 * @param rl Representation label
151 * @return newly constructed object */
152 ex dirac_ONE(unsigned char rl = 0);
154 /** Create a Dirac gamma object.
156 * @param mu Index (must be of class varidx or a derived class)
157 * @param rl Representation label
158 * @return newly constructed gamma object */
159 ex dirac_gamma(const ex & mu, unsigned char rl = 0);
161 /** Create a Dirac gamma5 object.
163 * @param rl Representation label
164 * @return newly constructed object */
165 ex dirac_gamma5(unsigned char rl = 0);
167 /** Create a Dirac gammaL object.
169 * @param rl Representation label
170 * @return newly constructed object */
171 ex dirac_gammaL(unsigned char rl = 0);
173 /** Create a Dirac gammaR object.
175 * @param rl Representation label
176 * @return newly constructed object */
177 ex dirac_gammaR(unsigned char rl = 0);
179 /** Create a term of the form e_mu * gamma~mu with a unique index mu.
181 * @param e Original expression
182 * @param dim Dimension of index
183 * @param rl Representation label */
184 ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0);
186 /** Calculate the trace of an expression containing gamma objects with
187 * a specified representation label. The computed trace is a linear
188 * functional that is equal to the usual trace only in D = 4 dimensions.
189 * In particular, the functional is not always cyclic in D != 4 dimensions
190 * when gamma5 is involved.
192 * @param e Expression to take the trace of
193 * @param rl Representation label
194 * @param trONE Expression to be returned as the trace of the unit matrix */
195 ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4);
197 /** Bring all products of clifford objects in an expression into a canonical
198 * order. This is not necessarily the most simple form but it will allow
199 * to check two expressions for equality. */
200 ex canonicalize_clifford(const ex & e);
204 #endif // ndef __GINAC_CLIFFORD_H__