3 * Interface to GiNaC's special tensors. */
6 * GiNaC Copyright (C) 1999-2007 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)
40 tensor(tinfo_t 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 bool info(unsigned inf) const;
64 ex eval_indexed(const basic & i) const;
65 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
67 // non-virtual functions in this class
69 unsigned return_type() const { return return_types::commutative; }
70 void do_print(const print_context & c, unsigned level) const;
71 void do_print_latex(const print_latex & c, unsigned level) const;
75 /** This class represents a general metric tensor which can be used to
76 * raise/lower indices. If indexed, it must have exactly two indices of the
77 * same type which must be of class varidx or a subclass. */
78 class tensmetric : public tensor
80 GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor)
82 // functions overriding virtual functions from base classes
84 bool info(unsigned inf) const;
85 ex eval_indexed(const basic & i) const;
86 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
88 // non-virtual functions in this class
90 unsigned return_type() const { return return_types::commutative; }
91 void do_print(const print_context & c, unsigned level) const;
95 /** This class represents a Minkowski metric tensor. It has all the
96 * properties of a metric tensor and is (as a matrix) equal to
97 * diag(1,-1,-1,...) or diag(-1,1,1,...). */
98 class minkmetric : public tensmetric
100 GINAC_DECLARE_REGISTERED_CLASS(minkmetric, tensmetric)
102 // other constructors
104 /** Construct Lorentz metric tensor with given signature. */
105 minkmetric(bool pos_sig);
107 // functions overriding virtual functions from base classes
109 bool info(unsigned inf) const;
110 ex eval_indexed(const basic & i) const;
112 // non-virtual functions in this class
114 unsigned return_type() const { return return_types::commutative; }
115 void do_print(const print_context & c, unsigned level) const;
116 void do_print_latex(const print_latex & c, unsigned level) const;
120 bool pos_sig; /**< If true, the metric is diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). */
124 /** This class represents an antisymmetric spinor metric tensor which
125 * can be used to raise/lower indices of 2-component Weyl spinors. If
126 * indexed, it must have exactly two indices of the same type which
127 * must be of class spinidx or a subclass and have dimension 2. */
128 class spinmetric : public tensmetric
130 GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric)
132 // functions overriding virtual functions from base classes
134 bool info(unsigned inf) const;
135 ex eval_indexed(const basic & i) const;
136 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
138 // non-virtual functions in this class
140 void do_print(const print_context & c, unsigned level) const;
141 void do_print_latex(const print_latex & c, unsigned level) const;
145 /** This class represents the totally antisymmetric epsilon tensor. If
146 * indexed, all indices must be of the same type and their number must
147 * be equal to the dimension of the index space. */
148 class tensepsilon : public tensor
150 GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
152 // other constructors
154 tensepsilon(bool minkowski, bool pos_sig);
156 // functions overriding virtual functions from base classes
158 bool info(unsigned inf) const;
159 ex eval_indexed(const basic & i) const;
160 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
162 // non-virtual functions in this class
164 unsigned return_type() const { return return_types::commutative; }
165 void do_print(const print_context & c, unsigned level) const;
166 void do_print_latex(const print_latex & c, unsigned level) const;
170 bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */
171 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. */
177 /** Create a delta tensor with specified indices. The indices must be of class
178 * idx or a subclass. The delta tensor is always symmetric and its trace is
179 * the dimension of the index space.
181 * @param i1 First index
182 * @param i2 Second index
183 * @return newly constructed delta tensor */
184 ex delta_tensor(const ex & i1, const ex & i2);
186 /** Create a symmetric metric tensor with specified indices. The indices
187 * must be of class varidx or a subclass. A metric tensor with one
188 * covariant and one contravariant index is equivalent to the delta tensor.
190 * @param i1 First index
191 * @param i2 Second index
192 * @return newly constructed metric tensor */
193 ex metric_tensor(const ex & i1, const ex & i2);
195 /** Create a Minkowski metric tensor with specified indices. The indices
196 * must be of class varidx or a subclass. The Lorentz metric is a symmetric
197 * tensor with a matrix representation of diag(1,-1,-1,...) (negative
198 * signature, the default) or diag(-1,1,1,...) (positive signature).
200 * @param i1 First index
201 * @param i2 Second index
202 * @param pos_sig Whether the signature is positive
203 * @return newly constructed Lorentz metric tensor */
204 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
206 /** Create a spinor metric tensor with specified indices. The indices must be
207 * of class spinidx or a subclass and have a dimension of 2. The spinor
208 * metric is an antisymmetric tensor with a matrix representation of
209 * [[ [[ 0, 1 ]], [[ -1, 0 ]] ]].
211 * @param i1 First index
212 * @param i2 Second index
213 * @return newly constructed spinor metric tensor */
214 ex spinor_metric(const ex & i1, const ex & i2);
216 /** Create an epsilon tensor in a Euclidean space with two indices. The
217 * indices must be of class idx or a subclass, and have a dimension of 2.
219 * @param i1 First index
220 * @param i2 Second index
221 * @return newly constructed epsilon tensor */
222 ex epsilon_tensor(const ex & i1, const ex & i2);
224 /** Create an epsilon tensor in a Euclidean space with three indices. The
225 * indices must be of class idx or a subclass, and have a dimension of 3.
227 * @param i1 First index
228 * @param i2 Second index
229 * @param i3 Third index
230 * @return newly constructed epsilon tensor */
231 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
233 /** Create an epsilon tensor in a Minkowski space with four indices. The
234 * indices must be of class varidx or a subclass, and have a dimension of 4.
236 * @param i1 First index
237 * @param i2 Second index
238 * @param i3 Third index
239 * @param i4 Fourth index
240 * @param pos_sig Whether the signature of the metric is positive
241 * @return newly constructed epsilon tensor */
242 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
246 #endif // ndef __GINAC_TENSOR_H__