3 * Interface to GiNaC's special tensors. */
6 * GiNaC Copyright (C) 1999-2024 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
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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.
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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 override { 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 override;
60 ex eval_indexed(const basic & i) const override;
61 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
63 unsigned return_type() const override { return return_types::commutative; }
65 // non-virtual functions in this class
67 void do_print(const print_context & c, unsigned level) const;
68 void do_print_latex(const print_latex & c, unsigned level) const;
70 GINAC_DECLARE_UNARCHIVER(tensdelta);
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 bool info(unsigned inf) const override;
83 ex eval_indexed(const basic & i) const override;
84 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
86 unsigned return_type() const override { return return_types::commutative; }
88 // non-virtual functions in this class
90 void do_print(const print_context & c, unsigned level) const;
92 GINAC_DECLARE_UNARCHIVER(tensmetric);
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 override;
110 ex eval_indexed(const basic & i) const override;
112 /** Save (a.k.a. serialize) object into archive. */
113 void archive(archive_node& n) const override;
114 /** Read (a.k.a. deserialize) object from archive. */
115 void read_archive(const archive_node& n, lst& syms) override;
117 unsigned return_type() const override { return return_types::commutative; }
119 // non-virtual functions in this class
121 void do_print(const print_context & c, unsigned level) const;
122 void do_print_latex(const print_latex & c, unsigned level) const;
126 bool pos_sig; /**< If true, the metric is diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). */
128 GINAC_DECLARE_UNARCHIVER(minkmetric);
131 /** This class represents an antisymmetric spinor metric tensor which
132 * can be used to raise/lower indices of 2-component Weyl spinors. If
133 * indexed, it must have exactly two indices of the same type which
134 * must be of class spinidx or a subclass and have dimension 2. */
135 class spinmetric : public tensmetric
137 GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric)
139 // functions overriding virtual functions from base classes
141 bool info(unsigned inf) const override;
142 ex eval_indexed(const basic & i) const override;
143 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
146 void do_print(const print_context & c, unsigned level) const;
147 void do_print_latex(const print_latex & c, unsigned level) const;
149 GINAC_DECLARE_UNARCHIVER(spinmetric);
152 /** This class represents the totally antisymmetric epsilon tensor. If
153 * indexed, all indices must be of the same type and their number must
154 * be equal to the dimension of the index space. */
155 class tensepsilon : public tensor
157 GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
159 // other constructors
161 tensepsilon(bool minkowski, bool pos_sig);
163 // functions overriding virtual functions from base classes
165 bool info(unsigned inf) const override;
166 ex eval_indexed(const basic & i) const override;
167 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
169 /** Save (a.k.a. serialize) object into archive. */
170 void archive(archive_node& n) const override;
171 /** Read (a.k.a. deserialize) object from archive. */
172 void read_archive(const archive_node& n, lst& syms) override;
174 unsigned return_type() const override { return return_types::commutative; }
176 // non-virtual functions in this class
178 void do_print(const print_context & c, unsigned level) const;
179 void do_print_latex(const print_latex & c, unsigned level) const;
183 bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */
184 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. */
186 GINAC_DECLARE_UNARCHIVER(tensepsilon);
191 /** Create a delta tensor with specified indices. The indices must be of class
192 * idx or a subclass. The delta tensor is always symmetric and its trace is
193 * the dimension of the index space.
195 * @param i1 First index
196 * @param i2 Second index
197 * @return newly constructed delta tensor */
198 ex delta_tensor(const ex & i1, const ex & i2);
200 /** Create a symmetric metric tensor with specified indices. The indices
201 * must be of class varidx or a subclass. A metric tensor with one
202 * covariant and one contravariant index is equivalent to the delta tensor.
204 * @param i1 First index
205 * @param i2 Second index
206 * @return newly constructed metric tensor */
207 ex metric_tensor(const ex & i1, const ex & i2);
209 /** Create a Minkowski metric tensor with specified indices. The indices
210 * must be of class varidx or a subclass. The Lorentz metric is a symmetric
211 * tensor with a matrix representation of diag(1,-1,-1,...) (negative
212 * signature, the default) or diag(-1,1,1,...) (positive signature).
214 * @param i1 First index
215 * @param i2 Second index
216 * @param pos_sig Whether the signature is positive
217 * @return newly constructed Lorentz metric tensor */
218 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
220 /** Create a spinor metric tensor with specified indices. The indices must be
221 * of class spinidx or a subclass and have a dimension of 2. The spinor
222 * metric is an antisymmetric tensor with a matrix representation of
223 * [[ [[ 0, 1 ]], [[ -1, 0 ]] ]].
225 * @param i1 First index
226 * @param i2 Second index
227 * @return newly constructed spinor metric tensor */
228 ex spinor_metric(const ex & i1, const ex & i2);
230 /** Create an epsilon tensor in a Euclidean space with two indices. The
231 * indices must be of class idx or a subclass, and have a dimension of 2.
233 * @param i1 First index
234 * @param i2 Second index
235 * @return newly constructed epsilon tensor */
236 ex epsilon_tensor(const ex & i1, const ex & i2);
238 /** Create an epsilon tensor in a Euclidean space with three indices. The
239 * indices must be of class idx or a subclass, and have a dimension of 3.
241 * @param i1 First index
242 * @param i2 Second index
243 * @param i3 Third index
244 * @return newly constructed epsilon tensor */
245 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
247 /** Create an epsilon tensor in a Minkowski space with four indices. The
248 * indices must be of class varidx or a subclass, and have a dimension of 4.
250 * @param i1 First index
251 * @param i2 Second index
252 * @param i3 Third index
253 * @param i4 Fourth index
254 * @param pos_sig Whether the signature of the metric is positive
255 * @return newly constructed epsilon tensor */
256 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
260 #endif // ndef GINAC_TENSOR_H