3 * Interface to GiNaC's special tensors. */
6 * GiNaC Copyright (C) 1999-2005 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() 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 ex eval_indexed(const basic & i) const;
64 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
66 // non-virtual functions in this class
68 void do_print(const print_context & c, unsigned level) const;
69 void do_print_latex(const print_latex & c, unsigned level) const;
73 /** This class represents a general metric tensor which can be used to
74 * raise/lower indices. If indexed, it must have exactly two indices of the
75 * same type which must be of class varidx or a subclass. */
76 class tensmetric : public tensor
78 GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor)
80 // functions overriding virtual functions from base classes
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 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 ex eval_indexed(const basic & i) const;
107 // non-virtual functions in this class
109 void do_print(const print_context & c, unsigned level) const;
110 void do_print_latex(const print_latex & c, unsigned level) const;
114 bool pos_sig; /**< If true, the metric is diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). */
118 /** This class represents an antisymmetric spinor metric tensor which
119 * can be used to raise/lower indices of 2-component Weyl spinors. If
120 * indexed, it must have exactly two indices of the same type which
121 * must be of class spinidx or a subclass and have dimension 2. */
122 class spinmetric : public tensmetric
124 GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric)
126 // functions overriding virtual functions from base classes
128 ex eval_indexed(const basic & i) const;
129 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
131 // non-virtual functions in this class
133 void do_print(const print_context & c, unsigned level) const;
134 void do_print_latex(const print_latex & c, unsigned level) const;
138 /** This class represents the totally antisymmetric epsilon tensor. If
139 * indexed, all indices must be of the same type and their number must
140 * be equal to the dimension of the index space. */
141 class tensepsilon : public tensor
143 GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
145 // other constructors
147 tensepsilon(bool minkowski, bool pos_sig);
149 // functions overriding virtual functions from base classes
151 ex eval_indexed(const basic & i) const;
152 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
154 // non-virtual functions in this class
156 void do_print(const print_context & c, unsigned level) const;
157 void do_print_latex(const print_latex & c, unsigned level) const;
161 bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */
162 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. */
168 /** Create a delta tensor with specified indices. The indices must be of class
169 * idx or a subclass. The delta tensor is always symmetric and its trace is
170 * the dimension of the index space.
172 * @param i1 First index
173 * @param i2 Second index
174 * @return newly constructed delta tensor */
175 ex delta_tensor(const ex & i1, const ex & i2);
177 /** Create a symmetric metric tensor with specified indices. The indices
178 * must be of class varidx or a subclass. A metric tensor with one
179 * covariant and one contravariant index is equivalent to the delta tensor.
181 * @param i1 First index
182 * @param i2 Second index
183 * @return newly constructed metric tensor */
184 ex metric_tensor(const ex & i1, const ex & i2);
186 /** Create a Minkowski metric tensor with specified indices. The indices
187 * must be of class varidx or a subclass. The Lorentz metric is a symmetric
188 * tensor with a matrix representation of diag(1,-1,-1,...) (negative
189 * signature, the default) or diag(-1,1,1,...) (positive signature).
191 * @param i1 First index
192 * @param i2 Second index
193 * @param pos_sig Whether the signature is positive
194 * @return newly constructed Lorentz metric tensor */
195 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
197 /** Create a spinor metric tensor with specified indices. The indices must be
198 * of class spinidx or a subclass and have a dimension of 2. The spinor
199 * metric is an antisymmetric tensor with a matrix representation of
200 * [[ [[ 0, 1 ]], [[ -1, 0 ]] ]].
202 * @param i1 First index
203 * @param i2 Second index
204 * @return newly constructed spinor metric tensor */
205 ex spinor_metric(const ex & i1, const ex & i2);
207 /** Create an epsilon tensor in a Euclidean space with two indices. The
208 * indices must be of class idx or a subclass, and have a dimension of 2.
210 * @param i1 First index
211 * @param i2 Second index
212 * @return newly constructed epsilon tensor */
213 ex epsilon_tensor(const ex & i1, const ex & i2);
215 /** Create an epsilon tensor in a Euclidean space with three indices. The
216 * indices must be of class idx or a subclass, and have a dimension of 3.
218 * @param i1 First index
219 * @param i2 Second index
220 * @param i3 Third index
221 * @return newly constructed epsilon tensor */
222 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
224 /** Create an epsilon tensor in a Minkowski space with four indices. The
225 * indices must be of class varidx or a subclass, and have a dimension of 4.
227 * @param i1 First index
228 * @param i2 Second index
229 * @param i3 Third index
230 * @param i4 Fourth index
231 * @param pos_sig Whether the signature of the metric is positive
232 * @return newly constructed epsilon tensor */
233 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
237 #endif // ndef __GINAC_TENSOR_H__