3 * Interface to GiNaC's color (SU(3) Lie algebra) objects. */
6 * GiNaC Copyright (C) 1999-2001 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, exvector * vp); // vp will be deleted
52 // functions overriding virtual functions from base classes
54 ex simplify_ncmul(const exvector & v) const;
55 ex thisexprseq(const exvector & v) const;
56 ex thisexprseq(exvector * vp) const;
57 unsigned return_type(void) const { return return_types::noncommutative; }
58 unsigned return_type_tinfo(void) const { return TINFO_color + representation_label; }
60 // non-virtual functions in this class
62 unsigned char get_representation_label(void) const {return representation_label;}
66 unsigned char representation_label; /**< Representation label to distinguish independent color matrices coming from separated fermion lines */
70 /** This class represents the su(3) unity element. */
71 class su3one : public tensor
73 GINAC_DECLARE_REGISTERED_CLASS(su3one, tensor)
75 // functions overriding virtual functions from bases classes
77 void print(const print_context & c, unsigned level = 0) const;
80 /** This class represents an su(3) generator. */
81 class su3t : public tensor
83 GINAC_DECLARE_REGISTERED_CLASS(su3t, tensor)
85 // functions overriding virtual functions from bases classes
87 void print(const print_context & c, unsigned level = 0) const;
88 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
91 /** This class represents the tensor of antisymmetric su(3) structure
93 class su3f : public tensor
95 GINAC_DECLARE_REGISTERED_CLASS(su3f, tensor)
97 // functions overriding virtual functions from bases classes
99 void print(const print_context & c, unsigned level = 0) const;
100 ex eval_indexed(const basic & i) const;
101 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
104 /** This class represents the tensor of symmetric su(3) structure constants. */
105 class su3d : public tensor
107 GINAC_DECLARE_REGISTERED_CLASS(su3d, tensor)
109 // functions overriding virtual functions from bases classes
111 void print(const print_context & c, unsigned level = 0) const;
112 ex eval_indexed(const basic & i) const;
113 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
118 inline const color &ex_to_color(const ex &e)
120 return static_cast<const color &>(*e.bp);
124 /** Create the su(3) unity element. This is an indexed object, although it
127 * @param rl Representation label
128 * @return newly constructed unity element */
129 ex color_ONE(unsigned char rl = 0);
131 /** Create an su(3) generator.
134 * @param rl Representation label
135 * @return newly constructed unity generator */
136 ex color_T(const ex & a, unsigned char rl = 0);
138 /** Create an su(3) antisymmetric structure constant.
140 * @param a First index
141 * @param b Second index
142 * @param c Third index
143 * @return newly constructed structure constant */
144 ex color_f(const ex & a, const ex & b, const ex & c);
146 /** Create an su(3) symmetric structure constant.
148 * @param a First index
149 * @param b Second index
150 * @param c Third index
151 * @return newly constructed structure constant */
152 ex color_d(const ex & a, const ex & b, const ex & c);
154 /** This returns the linear combination d.a.b.c+I*f.a.b.c. */
155 ex color_h(const ex & a, const ex & b, const ex & c);
157 /** Calculate the trace of an expression containing color objects with a
158 * specified representation label.
160 * @param rl Representation label */
161 ex color_trace(const ex & e, unsigned char rl = 0);
166 #endif // ndef __GINAC_COLOR_H__