3 * Interface to GiNaC's special tensors. */
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_TENSOR_H__
24 #define __GINAC_TENSOR_H__
31 /** This class holds one of GiNaC's predefined special tensors such as the
32 * delta and the metric tensors. They are represented without indices.
33 * To attach indices to them, wrap them in an object of class indexed. */
34 class tensor : public basic
36 GINAC_DECLARE_REGISTERED_CLASS(tensor, basic)
42 // functions overriding virtual functions from bases classes
44 unsigned return_type(void) const { return return_types::noncommutative_composite; }
48 /** This class represents the delta tensor. If indexed, it must have exactly
49 * two indices of the same type. */
50 class tensdelta : public tensor
52 GINAC_DECLARE_REGISTERED_CLASS(tensdelta, tensor)
54 // functions overriding virtual functions from bases classes
56 void print(const print_context & c, unsigned level = 0) const;
57 ex eval_indexed(const basic & i) const;
58 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
62 /** This class represents a general metric tensor which can be used to
63 * raise/lower indices. If indexed, it must have exactly two indices of the
64 * same type which must be of class varidx or a subclass. */
65 class tensmetric : public tensor
67 GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor)
69 // functions overriding virtual functions from bases classes
71 void print(const print_context & c, unsigned level = 0) const;
72 ex eval_indexed(const basic & i) const;
73 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
77 /** This class represents a Minkowski metric tensor. It has all the
78 * properties of a metric tensor and is (as a matrix) equal to
79 * diag(1,-1,-1,...) or diag(-1,1,1,...). */
80 class minkmetric : public tensmetric
82 GINAC_DECLARE_REGISTERED_CLASS(minkmetric, tensmetric)
86 /** Construct Lorentz metric tensor with given signature. */
87 minkmetric(bool pos_sig);
89 // functions overriding virtual functions from bases classes
91 void print(const print_context & c, unsigned level = 0) const;
92 ex eval_indexed(const basic & i) const;
96 bool pos_sig; /**< If true, the metric is diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). */
100 /** This class represents an antisymmetric spinor metric tensor which
101 * can be used to raise/lower indices of 2-component Weyl spinors. If
102 * indexed, it must have exactly two indices of the same type which
103 * must be of class spinidx or a subclass and have dimension 2. */
104 class spinmetric : public tensmetric
106 GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric)
108 // functions overriding virtual functions from bases classes
110 void print(const print_context & c, unsigned level = 0) const;
111 ex eval_indexed(const basic & i) const;
112 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
116 /** This class represents the totally antisymmetric epsilon tensor. If
117 * indexed, all indices must be of the same type and their number must
118 * be equal to the dimension of the index space. */
119 class tensepsilon : public tensor
121 GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
123 // other constructors
125 tensepsilon(bool minkowski, bool pos_sig);
127 // functions overriding virtual functions from bases classes
129 void print(const print_context & c, unsigned level = 0) const;
130 ex eval_indexed(const basic & i) const;
134 bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */
135 bool pos_sig; /**< If true, the metric is assumed to be diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). This is only relevant if minkowski = true. */
140 inline const tensor &ex_to_tensor(const ex &e)
142 return static_cast<const tensor &>(*e.bp);
145 /** Create a delta tensor with specified indices. The indices must be of class
146 * idx or a subclass. The delta tensor is always symmetric and its trace is
147 * the dimension of the index space.
149 * @param i1 First index
150 * @param i2 Second index
151 * @return newly constructed delta tensor */
152 ex delta_tensor(const ex & i1, const ex & i2);
154 /** Create a symmetric metric tensor with specified indices. The indices
155 * must be of class varidx or a subclass. A metric tensor with one
156 * covariant and one contravariant index is equivalent to the delta tensor.
158 * @param i1 First index
159 * @param i2 Second index
160 * @return newly constructed metric tensor */
161 ex metric_tensor(const ex & i1, const ex & i2);
163 /** Create a Minkowski metric tensor with specified indices. The indices
164 * must be of class varidx or a subclass. The Lorentz metric is a symmetric
165 * tensor with a matrix representation of diag(1,-1,-1,...) (negative
166 * signature, the default) or diag(-1,1,1,...) (positive signature).
168 * @param i1 First index
169 * @param i2 Second index
170 * @param pos_sig Whether the signature is positive
171 * @return newly constructed Lorentz metric tensor */
172 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
174 /** Create a spinor metric tensor with specified indices. The indices must be
175 * of class spinidx or a subclass and have a dimension of 2. The spinor
176 * metric is an antisymmetric tensor with a matrix representation of
177 * [[ [[ 0, 1 ]], [[ -1, 0 ]] ]].
179 * @param i1 First index
180 * @param i2 Second index
181 * @return newly constructed spinor metric tensor */
182 ex spinor_metric(const ex & i1, const ex & i2);
184 /** Create an epsilon tensor in a Euclidean space with two indices. The
185 * indices must be of class idx or a subclass, and have a dimension of 2.
187 * @param i1 First index
188 * @param i2 Second index
189 * @return newly constructed epsilon tensor */
190 ex epsilon_tensor(const ex & i1, const ex & i2);
192 /** Create an epsilon tensor in a Euclidean space with three indices. The
193 * indices must be of class idx or a subclass, and have a dimension of 3.
195 * @param i1 First index
196 * @param i2 Second index
197 * @param i3 Third index
198 * @return newly constructed epsilon tensor */
199 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
201 /** Create an epsilon tensor in a Minkowski space with four indices. The
202 * indices must be of class varidx or a subclass, and have a dimension of 4.
204 * @param i1 First index
205 * @param i2 Second index
206 * @param i3 Third index
207 * @param i4 Fourth index
208 * @param pos_sig Whether the signature of the metric is positive
209 * @return newly constructed epsilon tensor */
210 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
212 /** Create an epsilon tensor in a 4-dimensional projection of a D-dimensional
213 * Minkowski space. It vanishes whenever one of the indices is not in the
216 * @param i1 First index
217 * @param i2 Second index
218 * @param i3 Third index
219 * @param i4 Fourth index
220 * @param pos_sig Whether the signature of the metric is positive
221 * @return newly constructed epsilon tensor */
222 ex eps0123(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
226 #endif // ndef __GINAC_TENSOR_H__