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 bool match_same_type(const basic & other) const;
55 ex simplify_ncmul(const exvector & v) const;
56 ex thisexprseq(const exvector & v) const;
57 ex thisexprseq(exvector * vp) const;
58 unsigned return_type(void) const { return return_types::noncommutative; }
59 unsigned return_type_tinfo(void) const { return TINFO_color + representation_label; }
61 // non-virtual functions in this class
63 unsigned char get_representation_label(void) 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 // functions overriding virtual functions from base classes
78 void print(const print_context & c, unsigned level = 0) const;
81 /** This class represents an su(3) generator. */
82 class su3t : public tensor
84 GINAC_DECLARE_REGISTERED_CLASS(su3t, tensor)
86 // functions overriding virtual functions from base classes
88 void print(const print_context & c, unsigned level = 0) const;
89 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
92 /** This class represents the tensor of antisymmetric su(3) structure
94 class su3f : public tensor
96 GINAC_DECLARE_REGISTERED_CLASS(su3f, tensor)
98 // functions overriding virtual functions from base classes
100 void print(const print_context & c, unsigned level = 0) const;
101 ex eval_indexed(const basic & i) const;
102 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
105 /** This class represents the tensor of symmetric su(3) structure constants. */
106 class su3d : public tensor
108 GINAC_DECLARE_REGISTERED_CLASS(su3d, tensor)
110 // functions overriding virtual functions from base classes
112 void print(const print_context & c, unsigned level = 0) const;
113 ex eval_indexed(const basic & i) const;
114 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
120 /** Return the color object handled by an ex. Deprecated: use ex_to<color>().
121 * This is unsafe: you need to check the type first. */
122 inline const color &ex_to_color(const ex &e)
124 return static_cast<const color &>(*e.bp);
127 /** Specialization of is_exactly_a<color>(obj) for color objects. */
128 template<> inline bool is_exactly_a<color>(const basic & obj)
130 return obj.tinfo()==TINFO_color;
133 /** Create the su(3) unity element. This is an indexed object, although it
136 * @param rl Representation label
137 * @return newly constructed unity element */
138 ex color_ONE(unsigned char rl = 0);
140 /** Create an su(3) generator.
143 * @param rl Representation label
144 * @return newly constructed unity generator */
145 ex color_T(const ex & a, unsigned char rl = 0);
147 /** Create an su(3) antisymmetric structure constant.
149 * @param a First index
150 * @param b Second index
151 * @param c Third index
152 * @return newly constructed structure constant */
153 ex color_f(const ex & a, const ex & b, const ex & c);
155 /** Create an su(3) symmetric structure constant.
157 * @param a First index
158 * @param b Second index
159 * @param c Third index
160 * @return newly constructed structure constant */
161 ex color_d(const ex & a, const ex & b, const ex & c);
163 /** This returns the linear combination d.a.b.c+I*f.a.b.c. */
164 ex color_h(const ex & a, const ex & b, const ex & c);
166 /** Calculate the trace of an expression containing color objects with a
167 * specified representation label.
169 * @param e Expression to take the trace of
170 * @param rl Representation label */
171 ex color_trace(const ex & e, unsigned char rl = 0);
176 #endif // ndef __GINAC_COLOR_H__