3 * Interface to GiNaC's color (SU(3) Lie algebra) objects. */
6 * GiNaC Copyright (C) 1999-2005 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
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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.
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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)
47 color(const ex & b, unsigned char rl = 0);
48 color(const ex & b, const ex & i1, unsigned char rl = 0);
50 // internal constructors
51 color(unsigned char rl, const exvector & v, bool discardable = false);
52 color(unsigned char rl, std::auto_ptr<exvector> vp);
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 unsigned return_type_tinfo() const { return TINFO_color + representation_label; }
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 */
73 /** This class represents the su(3) unity element. */
74 class su3one : public tensor
76 GINAC_DECLARE_REGISTERED_CLASS(su3one, tensor)
78 // non-virtual functions in this class
80 void do_print(const print_context & c, unsigned level) const;
81 void do_print_latex(const print_latex & c, unsigned level) const;
84 /** This class represents an su(3) generator. */
85 class su3t : public tensor
87 GINAC_DECLARE_REGISTERED_CLASS(su3t, tensor)
89 // functions overriding virtual functions from base classes
91 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
93 // non-virtual functions in this class
95 void do_print(const print_context & c, unsigned level) const;
96 void do_print_latex(const print_latex & c, unsigned level) const;
99 /** This class represents the tensor of antisymmetric su(3) structure
101 class su3f : public tensor
103 GINAC_DECLARE_REGISTERED_CLASS(su3f, tensor)
105 // functions overriding virtual functions from base classes
107 ex eval_indexed(const basic & i) const;
108 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
110 // non-virtual functions in this class
112 unsigned return_type() const { return return_types::commutative; }
113 void do_print(const print_context & c, unsigned level) const;
114 void do_print_latex(const print_latex & c, unsigned level) const;
117 /** This class represents the tensor of symmetric su(3) structure constants. */
118 class su3d : public tensor
120 GINAC_DECLARE_REGISTERED_CLASS(su3d, tensor)
122 // functions overriding virtual functions from base classes
124 ex eval_indexed(const basic & i) const;
125 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
127 // non-virtual functions in this class
129 unsigned return_type() const { return return_types::commutative; }
130 void do_print(const print_context & c, unsigned level) const;
131 void do_print_latex(const print_latex & c, unsigned level) const;
137 /** Specialization of is_exactly_a<color>(obj) for color objects. */
138 template<> inline bool is_exactly_a<color>(const basic & obj)
140 return obj.tinfo()==TINFO_color;
143 /** Create the su(3) unity element. This is an indexed object, although it
146 * @param rl Representation label
147 * @return newly constructed unity element */
148 ex color_ONE(unsigned char rl = 0);
150 /** Create an su(3) generator.
153 * @param rl Representation label
154 * @return newly constructed unity generator */
155 ex color_T(const ex & a, unsigned char rl = 0);
157 /** Create an su(3) antisymmetric structure constant.
159 * @param a First index
160 * @param b Second index
161 * @param c Third index
162 * @return newly constructed structure constant */
163 ex color_f(const ex & a, const ex & b, const ex & c);
165 /** Create an su(3) symmetric structure constant.
167 * @param a First index
168 * @param b Second index
169 * @param c Third index
170 * @return newly constructed structure constant */
171 ex color_d(const ex & a, const ex & b, const ex & c);
173 /** This returns the linear combination d.a.b.c+I*f.a.b.c. */
174 ex color_h(const ex & a, const ex & b, const ex & c);
176 /** Calculate color traces over the specified set of representation labels.
178 * @param e Expression to take the trace of
179 * @param rls Set of representation labels */
180 ex color_trace(const ex & e, const std::set<unsigned char> & rls);
182 /** Calculate color traces over the specified list of representation labels.
184 * @param e Expression to take the trace of
185 * @param rll List of representation labels */
186 ex color_trace(const ex & e, const lst & rll);
188 /** Calculate the trace of an expression containing color objects with a
189 * specified representation label.
191 * @param e Expression to take the trace of
192 * @param rl Representation label */
193 ex color_trace(const ex & e, unsigned char rl = 0);
198 #endif // ndef __GINAC_COLOR_H__