3 * Interface to GiNaC's color (SU(3) Lie algebra) objects. */
6 * GiNaC Copyright (C) 1999-2004 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_COLOR_H__
24 #define __GINAC_COLOR_H__
32 /** This class holds a generator T_a or the unity element of the Lie algebra
33 * of SU(3), as used for calculations in quantum chromodynamics. A
34 * representation label (an unsigned 8-bit integer) is used to distinguish
35 * elements from different Lie algebras (objects with different labels
36 * commute). These objects implement an abstract representation of the
37 * group, not a specific matrix representation. The indices used for color
38 * objects should not have a variance. */
39 class color : public indexed
41 GINAC_DECLARE_REGISTERED_CLASS(color, indexed)
45 color(const ex & b, unsigned char rl = 0);
46 color(const ex & b, const ex & i1, unsigned char rl = 0);
48 // internal constructors
49 color(unsigned char rl, const exvector & v, bool discardable = false);
50 color(unsigned char rl, std::auto_ptr<exvector> vp);
52 // functions overriding virtual functions from base classes
54 ex eval_ncmul(const exvector & v) const;
55 bool match_same_type(const basic & other) const;
56 ex thiscontainer(const exvector & v) const;
57 ex thiscontainer(std::auto_ptr<exvector> vp) const;
58 unsigned return_type() const { return return_types::noncommutative; }
59 unsigned return_type_tinfo() const { return TINFO_color + representation_label; }
61 // non-virtual functions in this class
63 unsigned char get_representation_label() const {return representation_label;}
67 unsigned char representation_label; /**< Representation label to distinguish independent color matrices coming from separated fermion lines */
71 /** This class represents the su(3) unity element. */
72 class su3one : public tensor
74 GINAC_DECLARE_REGISTERED_CLASS(su3one, tensor)
76 // non-virtual functions in this class
78 void do_print(const print_context & c, unsigned level) const;
79 void do_print_latex(const print_latex & c, unsigned level) const;
82 /** This class represents an su(3) generator. */
83 class su3t : public tensor
85 GINAC_DECLARE_REGISTERED_CLASS(su3t, tensor)
87 // functions overriding virtual functions from base classes
89 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
91 // non-virtual functions in this class
93 void do_print(const print_context & c, unsigned level) const;
94 void do_print_latex(const print_latex & c, unsigned level) const;
97 /** This class represents the tensor of antisymmetric su(3) structure
99 class su3f : public tensor
101 GINAC_DECLARE_REGISTERED_CLASS(su3f, tensor)
103 // functions overriding virtual functions from base classes
105 ex eval_indexed(const basic & i) const;
106 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
108 // non-virtual functions in this class
110 void do_print(const print_context & c, unsigned level) const;
111 void do_print_latex(const print_latex & c, unsigned level) const;
114 /** This class represents the tensor of symmetric su(3) structure constants. */
115 class su3d : public tensor
117 GINAC_DECLARE_REGISTERED_CLASS(su3d, tensor)
119 // functions overriding virtual functions from base classes
121 ex eval_indexed(const basic & i) const;
122 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
124 // non-virtual functions in this class
126 void do_print(const print_context & c, unsigned level) const;
127 void do_print_latex(const print_latex & c, unsigned level) const;
133 /** Specialization of is_exactly_a<color>(obj) for color objects. */
134 template<> inline bool is_exactly_a<color>(const basic & obj)
136 return obj.tinfo()==TINFO_color;
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 the trace of an expression containing color objects with a
173 * specified representation label.
175 * @param e Expression to take the trace of
176 * @param rl Representation label */
177 ex color_trace(const ex & e, unsigned char rl = 0);
182 #endif // ndef __GINAC_COLOR_H__