3 * Interface to GiNaC's special tensors. */
6 * GiNaC Copyright (C) 1999-2014 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;
69 GINAC_DECLARE_UNARCHIVER(tensdelta);
72 /** This class represents a general metric tensor which can be used to
73 * raise/lower indices. If indexed, it must have exactly two indices of the
74 * same type which must be of class varidx or a subclass. */
75 class tensmetric : public tensor
77 GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor)
79 // functions overriding virtual functions from base classes
81 bool info(unsigned inf) const;
82 ex eval_indexed(const basic & i) const;
83 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
85 // non-virtual functions in this class
87 unsigned return_type() const { return return_types::commutative; }
88 void do_print(const print_context & c, unsigned level) const;
90 GINAC_DECLARE_UNARCHIVER(tensmetric);
93 /** This class represents a Minkowski metric tensor. It has all the
94 * properties of a metric tensor and is (as a matrix) equal to
95 * diag(1,-1,-1,...) or diag(-1,1,1,...). */
96 class minkmetric : public tensmetric
98 GINAC_DECLARE_REGISTERED_CLASS(minkmetric, tensmetric)
100 // other constructors
102 /** Construct Lorentz metric tensor with given signature. */
103 minkmetric(bool pos_sig);
105 // functions overriding virtual functions from base classes
107 bool info(unsigned inf) const;
108 ex eval_indexed(const basic & i) const;
110 /** Save (a.k.a. serialize) object into archive. */
111 void archive(archive_node& n) const;
112 /** Read (a.k.a. deserialize) object from archive. */
113 void read_archive(const archive_node& n, lst& syms);
114 // non-virtual functions in this class
116 unsigned return_type() const { return return_types::commutative; }
117 void do_print(const print_context & c, unsigned level) const;
118 void do_print_latex(const print_latex & c, unsigned level) const;
122 bool pos_sig; /**< If true, the metric is diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). */
124 GINAC_DECLARE_UNARCHIVER(minkmetric);
127 /** This class represents an antisymmetric spinor metric tensor which
128 * can be used to raise/lower indices of 2-component Weyl spinors. If
129 * indexed, it must have exactly two indices of the same type which
130 * must be of class spinidx or a subclass and have dimension 2. */
131 class spinmetric : public tensmetric
133 GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric)
135 // functions overriding virtual functions from base classes
137 bool info(unsigned inf) const;
138 ex eval_indexed(const basic & i) const;
139 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
142 void do_print(const print_context & c, unsigned level) const;
143 void do_print_latex(const print_latex & c, unsigned level) const;
145 GINAC_DECLARE_UNARCHIVER(spinmetric);
148 /** This class represents the totally antisymmetric epsilon tensor. If
149 * indexed, all indices must be of the same type and their number must
150 * be equal to the dimension of the index space. */
151 class tensepsilon : public tensor
153 GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
155 // other constructors
157 tensepsilon(bool minkowski, bool pos_sig);
159 // functions overriding virtual functions from base classes
161 bool info(unsigned inf) const;
162 ex eval_indexed(const basic & i) const;
163 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
165 /** Save (a.k.a. serialize) object into archive. */
166 void archive(archive_node& n) const;
167 /** Read (a.k.a. deserialize) object from archive. */
168 void read_archive(const archive_node& n, lst& syms);
169 // non-virtual functions in this class
171 unsigned return_type() const { return return_types::commutative; }
172 void do_print(const print_context & c, unsigned level) const;
173 void do_print_latex(const print_latex & c, unsigned level) const;
177 bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */
178 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. */
180 GINAC_DECLARE_UNARCHIVER(tensepsilon);
185 /** Create a delta tensor with specified indices. The indices must be of class
186 * idx or a subclass. The delta tensor is always symmetric and its trace is
187 * the dimension of the index space.
189 * @param i1 First index
190 * @param i2 Second index
191 * @return newly constructed delta tensor */
192 ex delta_tensor(const ex & i1, const ex & i2);
194 /** Create a symmetric metric tensor with specified indices. The indices
195 * must be of class varidx or a subclass. A metric tensor with one
196 * covariant and one contravariant index is equivalent to the delta tensor.
198 * @param i1 First index
199 * @param i2 Second index
200 * @return newly constructed metric tensor */
201 ex metric_tensor(const ex & i1, const ex & i2);
203 /** Create a Minkowski metric tensor with specified indices. The indices
204 * must be of class varidx or a subclass. The Lorentz metric is a symmetric
205 * tensor with a matrix representation of diag(1,-1,-1,...) (negative
206 * signature, the default) or diag(-1,1,1,...) (positive signature).
208 * @param i1 First index
209 * @param i2 Second index
210 * @param pos_sig Whether the signature is positive
211 * @return newly constructed Lorentz metric tensor */
212 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
214 /** Create a spinor metric tensor with specified indices. The indices must be
215 * of class spinidx or a subclass and have a dimension of 2. The spinor
216 * metric is an antisymmetric tensor with a matrix representation of
217 * [[ [[ 0, 1 ]], [[ -1, 0 ]] ]].
219 * @param i1 First index
220 * @param i2 Second index
221 * @return newly constructed spinor metric tensor */
222 ex spinor_metric(const ex & i1, const ex & i2);
224 /** Create an epsilon tensor in a Euclidean space with two indices. The
225 * indices must be of class idx or a subclass, and have a dimension of 2.
227 * @param i1 First index
228 * @param i2 Second index
229 * @return newly constructed epsilon tensor */
230 ex epsilon_tensor(const ex & i1, const ex & i2);
232 /** Create an epsilon tensor in a Euclidean space with three indices. The
233 * indices must be of class idx or a subclass, and have a dimension of 3.
235 * @param i1 First index
236 * @param i2 Second index
237 * @param i3 Third index
238 * @return newly constructed epsilon tensor */
239 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
241 /** Create an epsilon tensor in a Minkowski space with four indices. The
242 * indices must be of class varidx or a subclass, and have a dimension of 4.
244 * @param i1 First index
245 * @param i2 Second index
246 * @param i3 Third index
247 * @param i4 Fourth index
248 * @param pos_sig Whether the signature of the metric is positive
249 * @return newly constructed epsilon tensor */
250 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
254 #endif // ndef GINAC_TENSOR_H