3 * Interface to GiNaC's special tensors. */
6 * GiNaC Copyright (C) 1999-2008 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 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)
38 // functions overriding virtual functions from base classes
40 unsigned return_type() const { return return_types::noncommutative_composite; }
42 // non-virtual functions in this class
44 /** Replace dummy index in contracted-with object by the contracting
45 * object's second index (used internally for delta and metric tensor
47 bool replace_contr_index(exvector::iterator self, exvector::iterator other) const;
51 /** This class represents the delta tensor. If indexed, it must have exactly
52 * two indices of the same type. */
53 class tensdelta : public tensor
55 GINAC_DECLARE_REGISTERED_CLASS(tensdelta, tensor)
57 // functions overriding virtual functions from base classes
59 bool info(unsigned inf) const;
60 ex eval_indexed(const basic & i) const;
61 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
63 // non-virtual functions in this class
65 unsigned return_type() const { return return_types::commutative; }
66 void do_print(const print_context & c, unsigned level) const;
67 void do_print_latex(const print_latex & c, unsigned level) const;
71 /** This class represents a general metric tensor which can be used to
72 * raise/lower indices. If indexed, it must have exactly two indices of the
73 * same type which must be of class varidx or a subclass. */
74 class tensmetric : public tensor
76 GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor)
78 // functions overriding virtual functions from base classes
80 bool info(unsigned inf) const;
81 ex eval_indexed(const basic & i) const;
82 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
84 // non-virtual functions in this class
86 unsigned return_type() const { return return_types::commutative; }
87 void do_print(const print_context & c, unsigned level) const;
91 /** This class represents a Minkowski metric tensor. It has all the
92 * properties of a metric tensor and is (as a matrix) equal to
93 * diag(1,-1,-1,...) or diag(-1,1,1,...). */
94 class minkmetric : public tensmetric
96 GINAC_DECLARE_REGISTERED_CLASS(minkmetric, tensmetric)
100 /** Construct Lorentz metric tensor with given signature. */
101 minkmetric(bool pos_sig);
103 // functions overriding virtual functions from base classes
105 bool info(unsigned inf) const;
106 ex eval_indexed(const basic & i) const;
108 // non-virtual functions in this class
110 unsigned return_type() const { return return_types::commutative; }
111 void do_print(const print_context & c, unsigned level) const;
112 void do_print_latex(const print_latex & c, unsigned level) const;
116 bool pos_sig; /**< If true, the metric is diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). */
120 /** This class represents an antisymmetric spinor metric tensor which
121 * can be used to raise/lower indices of 2-component Weyl spinors. If
122 * indexed, it must have exactly two indices of the same type which
123 * must be of class spinidx or a subclass and have dimension 2. */
124 class spinmetric : public tensmetric
126 GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric)
128 // functions overriding virtual functions from base classes
130 bool info(unsigned inf) const;
131 ex eval_indexed(const basic & i) const;
132 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
134 // non-virtual functions in this class
136 void do_print(const print_context & c, unsigned level) const;
137 void do_print_latex(const print_latex & c, unsigned level) const;
141 /** This class represents the totally antisymmetric epsilon tensor. If
142 * indexed, all indices must be of the same type and their number must
143 * be equal to the dimension of the index space. */
144 class tensepsilon : public tensor
146 GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
148 // other constructors
150 tensepsilon(bool minkowski, bool pos_sig);
152 // functions overriding virtual functions from base classes
154 bool info(unsigned inf) const;
155 ex eval_indexed(const basic & i) const;
156 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
158 // non-virtual functions in this class
160 unsigned return_type() const { return return_types::commutative; }
161 void do_print(const print_context & c, unsigned level) const;
162 void do_print_latex(const print_latex & c, unsigned level) const;
166 bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */
167 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. */
173 /** Create a delta tensor with specified indices. The indices must be of class
174 * idx or a subclass. The delta tensor is always symmetric and its trace is
175 * the dimension of the index space.
177 * @param i1 First index
178 * @param i2 Second index
179 * @return newly constructed delta tensor */
180 ex delta_tensor(const ex & i1, const ex & i2);
182 /** Create a symmetric metric tensor with specified indices. The indices
183 * must be of class varidx or a subclass. A metric tensor with one
184 * covariant and one contravariant index is equivalent to the delta tensor.
186 * @param i1 First index
187 * @param i2 Second index
188 * @return newly constructed metric tensor */
189 ex metric_tensor(const ex & i1, const ex & i2);
191 /** Create a Minkowski metric tensor with specified indices. The indices
192 * must be of class varidx or a subclass. The Lorentz metric is a symmetric
193 * tensor with a matrix representation of diag(1,-1,-1,...) (negative
194 * signature, the default) or diag(-1,1,1,...) (positive signature).
196 * @param i1 First index
197 * @param i2 Second index
198 * @param pos_sig Whether the signature is positive
199 * @return newly constructed Lorentz metric tensor */
200 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
202 /** Create a spinor metric tensor with specified indices. The indices must be
203 * of class spinidx or a subclass and have a dimension of 2. The spinor
204 * metric is an antisymmetric tensor with a matrix representation of
205 * [[ [[ 0, 1 ]], [[ -1, 0 ]] ]].
207 * @param i1 First index
208 * @param i2 Second index
209 * @return newly constructed spinor metric tensor */
210 ex spinor_metric(const ex & i1, const ex & i2);
212 /** Create an epsilon tensor in a Euclidean space with two indices. The
213 * indices must be of class idx or a subclass, and have a dimension of 2.
215 * @param i1 First index
216 * @param i2 Second index
217 * @return newly constructed epsilon tensor */
218 ex epsilon_tensor(const ex & i1, const ex & i2);
220 /** Create an epsilon tensor in a Euclidean space with three indices. The
221 * indices must be of class idx or a subclass, and have a dimension of 3.
223 * @param i1 First index
224 * @param i2 Second index
225 * @param i3 Third index
226 * @return newly constructed epsilon tensor */
227 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
229 /** Create an epsilon tensor in a Minkowski space with four indices. The
230 * indices must be of class varidx or a subclass, and have a dimension of 4.
232 * @param i1 First index
233 * @param i2 Second index
234 * @param i3 Third index
235 * @param i4 Fourth index
236 * @param pos_sig Whether the signature of the metric is positive
237 * @return newly constructed epsilon tensor */
238 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
242 #endif // ndef __GINAC_TENSOR_H__