3 * Interface to GiNaC's color (SU(3) Lie algebra) objects. */
6 * GiNaC Copyright (C) 1999-2006 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
23 #ifndef __GINAC_COLOR_H__
24 #define __GINAC_COLOR_H__
34 /** This class holds a generator T_a or the unity element of the Lie algebra
35 * of SU(3), as used for calculations in quantum chromodynamics. A
36 * representation label (an unsigned 8-bit integer) is used to distinguish
37 * elements from different Lie algebras (objects with different labels
38 * commutate). These objects implement an abstract representation of the
39 * group, not a specific matrix representation. The indices used for color
40 * objects should not have a variance. */
41 class color : public indexed
43 GINAC_DECLARE_REGISTERED_CLASS(color, indexed)
45 static const tinfo_static_t return_type_tinfo_static[256];
49 color(const ex & b, unsigned char rl = 0);
50 color(const ex & b, const ex & i1, unsigned char rl = 0);
52 // internal constructors
53 color(unsigned char rl, const exvector & v, bool discardable = false);
54 color(unsigned char rl, std::auto_ptr<exvector> vp);
56 // functions overriding virtual functions from base classes
58 ex eval_ncmul(const exvector & v) const;
59 bool match_same_type(const basic & other) const;
60 ex thiscontainer(const exvector & v) const;
61 ex thiscontainer(std::auto_ptr<exvector> vp) const;
62 unsigned return_type() const { return return_types::noncommutative; }
63 tinfo_t return_type_tinfo() const { return color::return_type_tinfo_static+representation_label; }
65 // non-virtual functions in this class
67 unsigned char get_representation_label() const {return representation_label;}
71 unsigned char representation_label; /**< Representation label to distinguish independent color matrices coming from separated fermion lines */
75 /** This class represents the su(3) unity element. */
76 class su3one : public tensor
78 GINAC_DECLARE_REGISTERED_CLASS(su3one, tensor)
80 // non-virtual functions in this class
82 void do_print(const print_context & c, unsigned level) const;
83 void do_print_latex(const print_latex & c, unsigned level) const;
86 /** This class represents an su(3) generator. */
87 class su3t : public tensor
89 GINAC_DECLARE_REGISTERED_CLASS(su3t, tensor)
91 // functions overriding virtual functions from base classes
93 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
95 // non-virtual functions in this class
97 void do_print(const print_context & c, unsigned level) const;
98 void do_print_latex(const print_latex & c, unsigned level) const;
101 /** This class represents the tensor of antisymmetric su(3) structure
103 class su3f : public tensor
105 GINAC_DECLARE_REGISTERED_CLASS(su3f, tensor)
107 // functions overriding virtual functions from base classes
109 ex eval_indexed(const basic & i) const;
110 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
112 // non-virtual functions in this class
114 unsigned return_type() const { return return_types::commutative; }
115 void do_print(const print_context & c, unsigned level) const;
116 void do_print_latex(const print_latex & c, unsigned level) const;
119 /** This class represents the tensor of symmetric su(3) structure constants. */
120 class su3d : public tensor
122 GINAC_DECLARE_REGISTERED_CLASS(su3d, tensor)
124 // functions overriding virtual functions from base classes
126 ex eval_indexed(const basic & i) const;
127 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
129 // non-virtual functions in this class
131 unsigned return_type() const { return return_types::commutative; }
132 void do_print(const print_context & c, unsigned level) const;
133 void do_print_latex(const print_latex & c, unsigned level) const;
139 /** Create the su(3) unity element. This is an indexed object, although it
142 * @param rl Representation label
143 * @return newly constructed unity element */
144 ex color_ONE(unsigned char rl = 0);
146 /** Create an su(3) generator.
149 * @param rl Representation label
150 * @return newly constructed unity generator */
151 ex color_T(const ex & a, unsigned char rl = 0);
153 /** Create an su(3) antisymmetric structure constant.
155 * @param a First index
156 * @param b Second index
157 * @param c Third index
158 * @return newly constructed structure constant */
159 ex color_f(const ex & a, const ex & b, const ex & c);
161 /** Create an su(3) symmetric structure constant.
163 * @param a First index
164 * @param b Second index
165 * @param c Third index
166 * @return newly constructed structure constant */
167 ex color_d(const ex & a, const ex & b, const ex & c);
169 /** This returns the linear combination d.a.b.c+I*f.a.b.c. */
170 ex color_h(const ex & a, const ex & b, const ex & c);
172 /** Calculate color traces over the specified set of representation labels.
174 * @param e Expression to take the trace of
175 * @param rls Set of representation labels */
176 ex color_trace(const ex & e, const std::set<unsigned char> & rls);
178 /** Calculate color traces over the specified list of representation labels.
180 * @param e Expression to take the trace of
181 * @param rll List of representation labels */
182 ex color_trace(const ex & e, const lst & rll);
184 /** Calculate the trace of an expression containing color objects with a
185 * specified representation label.
187 * @param e Expression to take the trace of
188 * @param rl Representation label */
189 ex color_trace(const ex & e, unsigned char rl = 0);
194 #endif // ndef __GINAC_COLOR_H__