3 * Interface to GiNaC's special tensors. */
6 * GiNaC Copyright (C) 1999-2002 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)
40 tensor(unsigned ti) : inherited(ti) {}
42 // functions overriding virtual functions from base classes
44 unsigned return_type(void) const { return return_types::noncommutative_composite; }
46 // non-virtual functions in this class
48 /** Replace dummy index in contracted-with object by the contracting
49 * object's second index (used internally for delta and metric tensor
51 bool replace_contr_index(exvector::iterator self, exvector::iterator other) const;
55 /** This class represents the delta tensor. If indexed, it must have exactly
56 * two indices of the same type. */
57 class tensdelta : public tensor
59 GINAC_DECLARE_REGISTERED_CLASS(tensdelta, tensor)
61 // functions overriding virtual functions from base classes
63 void print(const print_context & c, unsigned level = 0) const;
64 ex eval_indexed(const basic & i) const;
65 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
69 /** This class represents a general metric tensor which can be used to
70 * raise/lower indices. If indexed, it must have exactly two indices of the
71 * same type which must be of class varidx or a subclass. */
72 class tensmetric : public tensor
74 GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor)
76 // functions overriding virtual functions from base classes
78 void print(const print_context & c, unsigned level = 0) const;
79 ex eval_indexed(const basic & i) const;
80 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
84 /** This class represents a Minkowski metric tensor. It has all the
85 * properties of a metric tensor and is (as a matrix) equal to
86 * diag(1,-1,-1,...) or diag(-1,1,1,...). */
87 class minkmetric : public tensmetric
89 GINAC_DECLARE_REGISTERED_CLASS(minkmetric, tensmetric)
93 /** Construct Lorentz metric tensor with given signature. */
94 minkmetric(bool pos_sig);
96 // functions overriding virtual functions from base classes
98 void print(const print_context & c, unsigned level = 0) const;
99 ex eval_indexed(const basic & i) const;
103 bool pos_sig; /**< If true, the metric is diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). */
107 /** This class represents an antisymmetric spinor metric tensor which
108 * can be used to raise/lower indices of 2-component Weyl spinors. If
109 * indexed, it must have exactly two indices of the same type which
110 * must be of class spinidx or a subclass and have dimension 2. */
111 class spinmetric : public tensmetric
113 GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric)
115 // functions overriding virtual functions from base classes
117 void print(const print_context & c, unsigned level = 0) const;
118 ex eval_indexed(const basic & i) const;
119 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
123 /** This class represents the totally antisymmetric epsilon tensor. If
124 * indexed, all indices must be of the same type and their number must
125 * be equal to the dimension of the index space. */
126 class tensepsilon : public tensor
128 GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
130 // other constructors
132 tensepsilon(bool minkowski, bool pos_sig);
134 // functions overriding virtual functions from base classes
136 void print(const print_context & c, unsigned level = 0) const;
137 ex eval_indexed(const basic & i) const;
138 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
142 bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */
143 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. */
149 /** Create a delta tensor with specified indices. The indices must be of class
150 * idx or a subclass. The delta tensor is always symmetric and its trace is
151 * the dimension of the index space.
153 * @param i1 First index
154 * @param i2 Second index
155 * @return newly constructed delta tensor */
156 ex delta_tensor(const ex & i1, const ex & i2);
158 /** Create a symmetric metric tensor with specified indices. The indices
159 * must be of class varidx or a subclass. A metric tensor with one
160 * covariant and one contravariant index is equivalent to the delta tensor.
162 * @param i1 First index
163 * @param i2 Second index
164 * @return newly constructed metric tensor */
165 ex metric_tensor(const ex & i1, const ex & i2);
167 /** Create a Minkowski metric tensor with specified indices. The indices
168 * must be of class varidx or a subclass. The Lorentz metric is a symmetric
169 * tensor with a matrix representation of diag(1,-1,-1,...) (negative
170 * signature, the default) or diag(-1,1,1,...) (positive signature).
172 * @param i1 First index
173 * @param i2 Second index
174 * @param pos_sig Whether the signature is positive
175 * @return newly constructed Lorentz metric tensor */
176 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
178 /** Create a spinor metric tensor with specified indices. The indices must be
179 * of class spinidx or a subclass and have a dimension of 2. The spinor
180 * metric is an antisymmetric tensor with a matrix representation of
181 * [[ [[ 0, 1 ]], [[ -1, 0 ]] ]].
183 * @param i1 First index
184 * @param i2 Second index
185 * @return newly constructed spinor metric tensor */
186 ex spinor_metric(const ex & i1, const ex & i2);
188 /** Create an epsilon tensor in a Euclidean space with two indices. The
189 * indices must be of class idx or a subclass, and have a dimension of 2.
191 * @param i1 First index
192 * @param i2 Second index
193 * @return newly constructed epsilon tensor */
194 ex epsilon_tensor(const ex & i1, const ex & i2);
196 /** Create an epsilon tensor in a Euclidean space with three indices. The
197 * indices must be of class idx or a subclass, and have a dimension of 3.
199 * @param i1 First index
200 * @param i2 Second index
201 * @param i3 Third index
202 * @return newly constructed epsilon tensor */
203 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
205 /** Create an epsilon tensor in a Minkowski space with four indices. The
206 * indices must be of class varidx or a subclass, and have a dimension of 4.
208 * @param i1 First index
209 * @param i2 Second index
210 * @param i3 Third index
211 * @param i4 Fourth index
212 * @param pos_sig Whether the signature of the metric is positive
213 * @return newly constructed epsilon tensor */
214 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
216 /** Create an epsilon tensor in a 4-dimensional projection of a D-dimensional
217 * Minkowski space. It vanishes whenever one of the indices is not in the
220 * @param i1 First index
221 * @param i2 Second index
222 * @param i3 Third index
223 * @param i4 Fourth index
224 * @param pos_sig Whether the signature of the metric is positive
225 * @return newly constructed epsilon tensor */
226 ex eps0123(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
230 #endif // ndef __GINAC_TENSOR_H__