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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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.
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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
39 class color : public indexed
41 GINAC_DECLARE_REGISTERED_CLASS(color, indexed)
45 color(const ex & b, unsigned rl = 0);
46 color(const ex & b, const ex & i1, unsigned rl = 0);
48 // internal constructors
49 color(unsigned rl, const exvector & v, bool discardable = false);
50 color(unsigned 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; }
62 unsigned representation_label; /**< Representation label to distinguish independent color matrices coming from separated fermion lines */
66 /** This class represents the su(3) unity element. */
67 class su3one : public tensor
69 GINAC_DECLARE_REGISTERED_CLASS(su3one, tensor)
71 // functions overriding virtual functions from bases classes
73 void print(std::ostream & os, unsigned upper_precedence=0) const;
76 /** This class represents an su(3) generator. */
77 class su3t : public tensor
79 GINAC_DECLARE_REGISTERED_CLASS(su3t, tensor)
81 // functions overriding virtual functions from bases classes
83 void print(std::ostream & os, unsigned upper_precedence=0) const;
86 /** This class represents the tensor of antisymmetric su(3) structure
88 class su3f : public tensor
90 GINAC_DECLARE_REGISTERED_CLASS(su3f, tensor)
92 // functions overriding virtual functions from bases classes
94 void print(std::ostream & os, unsigned upper_precedence=0) const;
95 // ex eval_indexed(const basic & i) const;
96 // bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
99 /** This class represents the tensor of symmetric su(3) structure constants. */
100 class su3d : public tensor
102 GINAC_DECLARE_REGISTERED_CLASS(su3d, tensor)
104 // functions overriding virtual functions from bases classes
106 void print(std::ostream & os, unsigned upper_precedence=0) const;
107 // ex eval_indexed(const basic & i) const;
108 // bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
113 inline const color &ex_to_color(const ex &e)
115 return static_cast<const color &>(*e.bp);
119 /** Create the su(3) unity element. This is an indexed object, although it
122 * @param rl Representation label
123 * @return newly constructed unity element */
124 ex color_ONE(unsigned rl = 0);
126 /** Create an su(3) generator.
129 * @param rl Representation label
130 * @return newly constructed unity generator */
131 ex color_T(const ex & a, unsigned rl = 0);
133 /** Create an su(3) antisymmetric structure constant.
135 * @param a First index
136 * @param b Second index
137 * @param c Third index
138 * @return newly constructed structure constant */
139 ex color_f(const ex & a, const ex & b, const ex & c);
141 /** Create an su(3) symmetric structure constant.
143 * @param a First index
144 * @param b Second index
145 * @param c Third index
146 * @return newly constructed structure constant */
147 ex color_d(const ex & a, const ex & b, const ex & c);
149 /** This returns the linear combination d.a.b.c+I*f.a.b.c. */
150 ex color_h(const ex & a, const ex & b, const ex & c);
155 #endif // ndef __GINAC_COLOR_H__