X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Ftensor.h;h=3fae6b425a87d768b72cfc7053b5efdc7a6d0154;hp=220b69bcb56e4a493103497160788373f65ada62;hb=15e9408c64b6e9309a9f2388fd91f34101b52f40;hpb=094911eb78cacb6f2877a70c9ac74766df58ccea diff --git a/ginac/tensor.h b/ginac/tensor.h index 220b69bc..3fae6b42 100644 --- a/ginac/tensor.h +++ b/ginac/tensor.h @@ -3,7 +3,7 @@ * Interface to GiNaC's special tensors. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -37,11 +37,18 @@ class tensor : public basic // other constructors protected: - tensor(unsigned ti); + tensor(unsigned ti) : inherited(ti) {} - // functions overriding virtual functions from bases classes + // functions overriding virtual functions from base classes protected: unsigned return_type(void) const { return return_types::noncommutative_composite; } + + // non-virtual functions in this class +public: + /** Replace dummy index in contracted-with object by the contracting + * object's second index (used internally for delta and metric tensor + * contractions. */ + bool replace_contr_index(exvector::iterator self, exvector::iterator other) const; }; @@ -51,11 +58,11 @@ class tensdelta : public tensor { GINAC_DECLARE_REGISTERED_CLASS(tensdelta, tensor) - // functions overriding virtual functions from bases classes + // functions overriding virtual functions from base classes public: - void print(std::ostream & os, unsigned upper_precedence=0) const; + void print(const print_context & c, unsigned level = 0) const; ex eval_indexed(const basic & i) const; - bool contract_with(ex & self, ex & other) const; + bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const; }; @@ -66,11 +73,11 @@ class tensmetric : public tensor { GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor) - // functions overriding virtual functions from bases classes + // functions overriding virtual functions from base classes public: - void print(std::ostream & os, unsigned upper_precedence=0) const; + void print(const print_context & c, unsigned level = 0) const; ex eval_indexed(const basic & i) const; - bool contract_with(ex & self, ex & other) const; + bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const; }; @@ -86,9 +93,9 @@ public: /** Construct Lorentz metric tensor with given signature. */ minkmetric(bool pos_sig); - // functions overriding virtual functions from bases classes + // functions overriding virtual functions from base classes public: - void print(std::ostream & os, unsigned upper_precedence=0) const; + void print(const print_context & c, unsigned level = 0) const; ex eval_indexed(const basic & i) const; // member variables @@ -97,6 +104,22 @@ private: }; +/** This class represents an antisymmetric spinor metric tensor which + * can be used to raise/lower indices of 2-component Weyl spinors. If + * indexed, it must have exactly two indices of the same type which + * must be of class spinidx or a subclass and have dimension 2. */ +class spinmetric : public tensmetric +{ + GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric) + + // functions overriding virtual functions from base classes +public: + void print(const print_context & c, unsigned level = 0) const; + ex eval_indexed(const basic & i) const; + bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const; +}; + + /** This class represents the totally antisymmetric epsilon tensor. If * indexed, all indices must be of the same type and their number must * be equal to the dimension of the index space. */ @@ -104,17 +127,24 @@ class tensepsilon : public tensor { GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor) - // functions overriding virtual functions from bases classes + // other constructors +public: + tensepsilon(bool minkowski, bool pos_sig); + + // functions overriding virtual functions from base classes public: - void print(std::ostream & os, unsigned upper_precedence=0) const; + void print(const print_context & c, unsigned level = 0) const; + ex eval_indexed(const basic & i) const; + bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const; + + // member variables +private: + bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */ + 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. */ }; // utility functions -inline const tensor &ex_to_tensor(const ex &e) -{ - return static_cast(*e.bp); -} /** Create a delta tensor with specified indices. The indices must be of class * idx or a subclass. The delta tensor is always symmetric and its trace is @@ -125,9 +155,9 @@ inline const tensor &ex_to_tensor(const ex &e) * @return newly constructed delta tensor */ ex delta_tensor(const ex & i1, const ex & i2); -/** Create a metric tensor with specified indices. The indices must be of - * class varidx or a subclass. A metric tensor with one covariant and one - * contravariant index is equivalent to the delta tensor. +/** Create a symmetric metric tensor with specified indices. The indices + * must be of class varidx or a subclass. A metric tensor with one + * covariant and one contravariant index is equivalent to the delta tensor. * * @param i1 First index * @param i2 Second index @@ -145,14 +175,44 @@ ex metric_tensor(const ex & i1, const ex & i2); * @return newly constructed Lorentz metric tensor */ ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false); -/** Create an epsilon tensor with two indices. The indices must be of class - * idx or a subclass, and have a dimension of 2. +/** Create a spinor metric tensor with specified indices. The indices must be + * of class spinidx or a subclass and have a dimension of 2. The spinor + * metric is an antisymmetric tensor with a matrix representation of + * [[ [[ 0, 1 ]], [[ -1, 0 ]] ]]. + * + * @param i1 First index + * @param i2 Second index + * @return newly constructed spinor metric tensor */ +ex spinor_metric(const ex & i1, const ex & i2); + +/** Create an epsilon tensor in a Euclidean space with two indices. The + * indices must be of class idx or a subclass, and have a dimension of 2. * * @param i1 First index * @param i2 Second index * @return newly constructed epsilon tensor */ ex epsilon_tensor(const ex & i1, const ex & i2); +/** Create an epsilon tensor in a Euclidean space with three indices. The + * indices must be of class idx or a subclass, and have a dimension of 3. + * + * @param i1 First index + * @param i2 Second index + * @param i3 Third index + * @return newly constructed epsilon tensor */ +ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3); + +/** Create an epsilon tensor in a Minkowski space with four indices. The + * indices must be of class varidx or a subclass, and have a dimension of 4. + * + * @param i1 First index + * @param i2 Second index + * @param i3 Third index + * @param i4 Fourth index + * @param pos_sig Whether the signature of the metric is positive + * @return newly constructed epsilon tensor */ +ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false); + } // namespace GiNaC #endif // ndef __GINAC_TENSOR_H__