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
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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., 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 integer) is used to distinguish
35 * elements from different Lie algebra representations (only objects with
36 * the same label "interact" with each other). These objects implement an
37 * abstract representation of the group, not a specific matrix
38 * representation. The indices used for color objects should not have a
40 class color : public indexed
42 GINAC_DECLARE_REGISTERED_CLASS(color, indexed)
46 color(const ex & b, unsigned rl = 0);
47 color(const ex & b, const ex & i1, unsigned rl = 0);
49 // internal constructors
50 color(unsigned rl, const exvector & v, bool discardable = false);
51 color(unsigned rl, exvector * vp); // vp will be deleted
53 // functions overriding virtual functions from base classes
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; }
63 unsigned representation_label; /**< Representation label to distinguish independent color matrices coming from separated fermion lines */
67 /** This class represents the su(3) unity element. */
68 class su3one : public tensor
70 GINAC_DECLARE_REGISTERED_CLASS(su3one, tensor)
72 // functions overriding virtual functions from bases classes
74 void print(const print_context & c, unsigned level = 0) const;
77 /** This class represents an su(3) generator. */
78 class su3t : public tensor
80 GINAC_DECLARE_REGISTERED_CLASS(su3t, tensor)
82 // functions overriding virtual functions from bases classes
84 void print(const print_context & c, unsigned level = 0) const;
87 /** This class represents the tensor of antisymmetric su(3) structure
89 class su3f : public tensor
91 GINAC_DECLARE_REGISTERED_CLASS(su3f, tensor)
93 // functions overriding virtual functions from bases classes
95 void print(const print_context & c, unsigned level = 0) const;
96 ex eval_indexed(const basic & i) const;
97 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
100 /** This class represents the tensor of symmetric su(3) structure constants. */
101 class su3d : public tensor
103 GINAC_DECLARE_REGISTERED_CLASS(su3d, tensor)
105 // functions overriding virtual functions from bases classes
107 void print(const print_context & c, unsigned level = 0) const;
108 ex eval_indexed(const basic & i) const;
109 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
114 inline const color &ex_to_color(const ex &e)
116 return static_cast<const color &>(*e.bp);
120 /** Create the su(3) unity element. This is an indexed object, although it
123 * @param rl Representation label
124 * @return newly constructed unity element */
125 ex color_ONE(unsigned rl = 0);
127 /** Create an su(3) generator.
130 * @param rl Representation label
131 * @return newly constructed unity generator */
132 ex color_T(const ex & a, unsigned rl = 0);
134 /** Create an su(3) antisymmetric structure constant.
136 * @param a First index
137 * @param b Second index
138 * @param c Third index
139 * @return newly constructed structure constant */
140 ex color_f(const ex & a, const ex & b, const ex & c);
142 /** Create an su(3) symmetric structure constant.
144 * @param a First index
145 * @param b Second index
146 * @param c Third index
147 * @return newly constructed structure constant */
148 ex color_d(const ex & a, const ex & b, const ex & c);
150 /** This returns the linear combination d.a.b.c+I*f.a.b.c. */
151 ex color_h(const ex & a, const ex & b, const ex & c);
156 #endif // ndef __GINAC_COLOR_H__