GiNaC/ginac/clifford.h

/** @file clifford.h
 *
 *  Interface to GiNaC's clifford algebra (Dirac gamma) objects. */

/*
 *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#ifndef __GINAC_CLIFFORD_H__
#define __GINAC_CLIFFORD_H__

#include "indexed.h"
#include "tensor.h"

namespace GiNaC {


/** This class holds an object representing an element of the Clifford
 *  algebra (the Dirac gamma matrices). These objects only carry Lorentz
 *  indices. Spinor indices are hidden. A representation label (an unsigned
 *  8-bit integer) is used to distinguish elements from different Clifford
 *  algebras (objects with different labels commute). */
class clifford : public indexed
{
        GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)

        // other constructors
public:
        clifford(const ex & b, unsigned char rl = 0);
        clifford(const ex & b, const ex & mu, unsigned char rl = 0);

        // internal constructors
        clifford(unsigned char rl, const exvector & v, bool discardable = false);
        clifford(unsigned char rl, exvector * vp); // vp will be deleted

        // functions overriding virtual functions from base classes
protected:
        ex simplify_ncmul(const exvector & v) const;
        ex thisexprseq(const exvector & v) const;
        ex thisexprseq(exvector * vp) const;
        unsigned return_type(void) const { return return_types::noncommutative; }
        unsigned return_type_tinfo(void) const { return TINFO_clifford + representation_label; }

        // non-virtual functions in this class
public:
        unsigned char get_representation_label(void) const {return representation_label;}

        // member variables
private:
        unsigned char representation_label; /**< Representation label to distinguish independent spin lines */
};


/** This class represents the Clifford algebra unity element. */
class diracone : public tensor
{
        GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor)

        // functions overriding virtual functions from bases classes
public:
        void print(const print_context & c, unsigned level = 0) const;
};


/** This class represents the Dirac gamma Lorentz vector. */
class diracgamma : public tensor
{
        GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor)

        // functions overriding virtual functions from bases classes
public:
        void print(const print_context & c, unsigned level = 0) const;
        bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
};


/** This class represents the Dirac gamma5 object which anticommutes with
 *  all other gammas. */
class diracgamma5 : public tensor
{
        GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor)

        // functions overriding virtual functions from bases classes
public:
        void print(const print_context & c, unsigned level = 0) const;
};


// global functions
inline const clifford &ex_to_clifford(const ex &e)
{
        return static_cast<const clifford &>(*e.bp);
}


/** Create a Clifford unity object.
 *
 *  @param rl Representation label
 *  @return newly constructed object */
ex dirac_ONE(unsigned char rl = 0);

/** Create a Dirac gamma object.
 *
 *  @param mu Index (must be of class varidx or a derived class)
 *  @param rl Representation label
 *  @return newly constructed gamma object */
ex dirac_gamma(const ex & mu, unsigned char rl = 0);

/** Create a Dirac gamma5 object.
 *
 *  @param rl Representation label
 *  @return newly constructed object */
ex dirac_gamma5(unsigned char rl = 0);

/** This returns (dirac_ONE(rl) + dirac_gamma5(rl)). */
ex dirac_gamma6(unsigned char rl = 0);

/** This returns (dirac_ONE(rl) - dirac_gamma5(rl)). */
ex dirac_gamma7(unsigned char rl = 0);

/** Create a term of the form e_mu * gamma~mu with a unique index mu.
 *
 *  @param dim Dimension of index
 *  @param rl Representation label */
ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0);

/** Calculate the trace of an expression containing gamma objects with
 *  a specified representation label. The computed trace is a linear
 *  functional that is equal to the usual trace only in D = 4 dimensions.
 *  In particular, the functional is not always cyclic in D != 4 dimensions
 *  when gamma5 is involved.
 *
 *  @param e Expression to take the trace of
 *  @param rl Representation label
 *  @param trONE Expression to be returned as the trace of the unit matrix */
ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4);

/** Bring all products of clifford objects in an expression into a canonical
 *  order. This is not necessarily the most simple form but it will allow
 *  to checking two expressions for equality. */
ex canonicalize_clifford(const ex & e);

} // namespace GiNaC

#endif // ndef __GINAC_CLIFFORD_H__
1	cbauer	1.1	/** @file clifford.h
2			*
3	cbauer	1.22	* Interface to GiNaC's clifford algebra (Dirac gamma) objects. */
4	cbauer	1.4
5			/*
6	kreckel	1.14	* GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
7	cbauer	1.2	*
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.
12			*
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.
17			*
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
21			*/
22	cbauer	1.1
23	cbauer	1.2	#ifndef __GINAC_CLIFFORD_H__
24			#define __GINAC_CLIFFORD_H__
25	cbauer	1.1
26	cbauer	1.22	#include "indexed.h"
27			#include "tensor.h"
28	cbauer	1.5
29			namespace GiNaC {
30	cbauer	1.1
31	cbauer	1.15
32			/** This class holds an object representing an element of the Clifford
33			* algebra (the Dirac gamma matrices). These objects only carry Lorentz
34	cbauer	1.25	* indices. Spinor indices are hidden. A representation label (an unsigned
35			* 8-bit integer) is used to distinguish elements from different Clifford
36			* algebras (objects with different labels commute). */
37	cbauer	1.22	class clifford : public indexed
38	cbauer	1.1	{
39	cbauer	1.22	GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)
40	cbauer	1.15
41	cbauer	1.12	// other constructors
42	cbauer	1.1	public:
43	cbauer	1.25	clifford(const ex & b, unsigned char rl = 0);
44			clifford(const ex & b, const ex & mu, unsigned char rl = 0);
45	cbauer	1.22
46			// internal constructors
47	cbauer	1.25	clifford(unsigned char rl, const exvector & v, bool discardable = false);
48			clifford(unsigned char rl, exvector * vp); // vp will be deleted
49	cbauer	1.1
50	cbauer	1.12	// functions overriding virtual functions from base classes
51	cbauer	1.1	protected:
52	cbauer	1.12	ex simplify_ncmul(const exvector & v) const;
53	cbauer	1.15	ex thisexprseq(const exvector & v) const;
54			ex thisexprseq(exvector * vp) const;
55	cbauer	1.22	unsigned return_type(void) const { return return_types::noncommutative; }
56	cbauer	1.25	unsigned return_type_tinfo(void) const { return TINFO_clifford + representation_label; }
57
58	cbauer	1.26	// non-virtual functions in this class
59			public:
60			unsigned char get_representation_label(void) const {return representation_label;}
61
62	cbauer	1.25	// member variables
63			private:
64			unsigned char representation_label; /*< Representation label to distinguish independent spin lines /
65	cbauer	1.22	};
66
67	cbauer	1.1
68	cbauer	1.23	/** This class represents the Clifford algebra unity element. */
69			class diracone : public tensor
70			{
71			GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor)
72
73			// functions overriding virtual functions from bases classes
74			public:
75	cbauer	1.24	void print(const print_context & c, unsigned level = 0) const;
76	cbauer	1.23	};
77
78
79	cbauer	1.22	/** This class represents the Dirac gamma Lorentz vector. */
80			class diracgamma : public tensor
81			{
82			GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor)
83	cbauer	1.1
84	cbauer	1.22	// functions overriding virtual functions from bases classes
85			public:
86	cbauer	1.24	void print(const print_context & c, unsigned level = 0) const;
87	cbauer	1.23	bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
88	cbauer	1.1	};
89
90	cbauer	1.22
91	cbauer	1.28	/** This class represents the Dirac gamma5 object which anticommutes with
92			* all other gammas. */
93	cbauer	1.25	class diracgamma5 : public tensor
94			{
95			GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor)
96
97			// functions overriding virtual functions from bases classes
98			public:
99			void print(const print_context & c, unsigned level = 0) const;
100			};
101
102
103	cbauer	1.15	// global functions
104	cbauer	1.5	inline const clifford &ex_to_clifford(const ex &e)
105			{
106			return static_cast<const clifford &>(*e.bp);
107			}
108	cbauer	1.15
109	cbauer	1.23
110			/** Create a Clifford unity object.
111			*
112	cbauer	1.25	* @param rl Representation label
113	cbauer	1.23	* @return newly constructed object */
114	cbauer	1.25	ex dirac_ONE(unsigned char rl = 0);
115	cbauer	1.22
116			/** Create a Dirac gamma object.
117			*
118			* @param mu Index (must be of class varidx or a derived class)
119	cbauer	1.25	* @param rl Representation label
120	cbauer	1.22	* @return newly constructed gamma object */
121	cbauer	1.25	ex dirac_gamma(const ex & mu, unsigned char rl = 0);
122
123			/** Create a Dirac gamma5 object.
124			*
125			* @param rl Representation label
126			* @return newly constructed object */
127			ex dirac_gamma5(unsigned char rl = 0);
128	cbauer	1.26
129	cbauer	1.29	/** This returns (dirac_ONE(rl) + dirac_gamma5(rl)). */
130			ex dirac_gamma6(unsigned char rl = 0);
131
132			/** This returns (dirac_ONE(rl) - dirac_gamma5(rl)). */
133			ex dirac_gamma7(unsigned char rl = 0);
134
135	cbauer	1.28	/** Create a term of the form e_mu * gamma~mu with a unique index mu.
136			*
137			* @param dim Dimension of index
138			* @param rl Representation label */
139			ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0);
140
141	cbauer	1.26	/** Calculate the trace of an expression containing gamma objects with
142	cbauer	1.27	* a specified representation label. The computed trace is a linear
143			* functional that is equal to the usual trace only in D = 4 dimensions.
144	cbauer	1.28	* In particular, the functional is not always cyclic in D != 4 dimensions
145			* when gamma5 is involved.
146	cbauer	1.26	*
147	cbauer	1.30	* @param e Expression to take the trace of
148			* @param rl Representation label
149			* @param trONE Expression to be returned as the trace of the unit matrix */
150			ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4);
151	cbauer	1.22
152	cbauer	1.31	/** Bring all products of clifford objects in an expression into a canonical
153			* order. This is not necessarily the most simple form but it will allow
154			* to checking two expressions for equality. */
155			ex canonicalize_clifford(const ex & e);
156	cbauer	1.1
157	cbauer	1.5	} // namespace GiNaC
158	cbauer	1.1
159	cbauer	1.2	#endif // ndef __GINAC_CLIFFORD_H__
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