3 * Interface to GiNaC's color (SU(3) Lie algebra) objects. */
6 * GiNaC Copyright (C) 1999-2014 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
33 /** This class holds a generator T_a or the unity element of the Lie algebra
34 * of SU(3), as used for calculations in quantum chromodynamics. A
35 * representation label (an unsigned 8-bit integer) is used to distinguish
36 * elements from different Lie algebras (objects with different labels
37 * commutate). These objects implement an abstract representation of the
38 * group, not a specific matrix representation. The indices used for color
39 * objects should not have a variance. */
40 class color : public indexed
42 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);
51 void archive(archive_node& n) const;
52 void read_archive(const archive_node& n, lst& sym_lst);
54 // functions overriding virtual functions from base classes
56 ex eval_ncmul(const exvector & v) const;
57 bool match_same_type(const basic & other) const;
58 ex thiscontainer(const exvector & v) const;
59 ex thiscontainer(std::auto_ptr<exvector> vp) const;
60 unsigned return_type() const { return return_types::noncommutative; }
61 return_type_t return_type_tinfo() const;
63 // non-virtual functions in this class
65 unsigned char get_representation_label() const {return representation_label;}
69 unsigned char representation_label; /**< Representation label to distinguish independent color matrices coming from separated fermion lines */
71 GINAC_DECLARE_UNARCHIVER(color);
74 /** This class represents the su(3) unity element. */
75 class su3one : public tensor
77 GINAC_DECLARE_REGISTERED_CLASS(su3one, tensor)
79 // non-virtual functions in this class
81 void do_print(const print_context & c, unsigned level) const;
82 void do_print_latex(const print_latex & c, unsigned level) const;
84 GINAC_DECLARE_UNARCHIVER(su3one);
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;
100 GINAC_DECLARE_UNARCHIVER(su3t);
102 /** This class represents the tensor of antisymmetric su(3) structure
104 class su3f : public tensor
106 GINAC_DECLARE_REGISTERED_CLASS(su3f, tensor)
108 // functions overriding virtual functions from base classes
110 ex eval_indexed(const basic & i) const;
111 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
113 // non-virtual functions in this class
115 unsigned return_type() const { return return_types::commutative; }
116 void do_print(const print_context & c, unsigned level) const;
117 void do_print_latex(const print_latex & c, unsigned level) const;
119 GINAC_DECLARE_UNARCHIVER(su3f);
121 /** This class represents the tensor of symmetric su(3) structure constants. */
122 class su3d : public tensor
124 GINAC_DECLARE_REGISTERED_CLASS(su3d, tensor)
126 // functions overriding virtual functions from base classes
128 ex eval_indexed(const basic & i) const;
129 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
131 // non-virtual functions in this class
133 unsigned return_type() const { return return_types::commutative; }
134 void do_print(const print_context & c, unsigned level) const;
135 void do_print_latex(const print_latex & c, unsigned level) const;
137 GINAC_DECLARE_UNARCHIVER(su3d);
142 /** Create the su(3) unity element. This is an indexed object, although it
145 * @param rl Representation label
146 * @return newly constructed unity element */
147 ex color_ONE(unsigned char rl = 0);
149 /** Create an su(3) generator.
152 * @param rl Representation label
153 * @return newly constructed unity generator */
154 ex color_T(const ex & a, unsigned char rl = 0);
156 /** Create an su(3) antisymmetric structure constant.
158 * @param a First index
159 * @param b Second index
160 * @param c Third index
161 * @return newly constructed structure constant */
162 ex color_f(const ex & a, const ex & b, const ex & c);
164 /** Create an su(3) symmetric structure constant.
166 * @param a First index
167 * @param b Second index
168 * @param c Third index
169 * @return newly constructed structure constant */
170 ex color_d(const ex & a, const ex & b, const ex & c);
172 /** This returns the linear combination d.a.b.c+I*f.a.b.c. */
173 ex color_h(const ex & a, const ex & b, const ex & c);
175 /** Calculate color traces over the specified set of representation labels.
177 * @param e Expression to take the trace of
178 * @param rls Set of representation labels */
179 ex color_trace(const ex & e, const std::set<unsigned char> & rls);
181 /** Calculate color traces over the specified list of representation labels.
183 * @param e Expression to take the trace of
184 * @param rll List of representation labels */
185 ex color_trace(const ex & e, const lst & rll);
187 /** Calculate the trace of an expression containing color objects with a
188 * specified representation label.
190 * @param e Expression to take the trace of
191 * @param rl Representation label */
192 ex color_trace(const ex & e, unsigned char rl = 0);
196 #endif // ndef GINAC_COLOR_H