* Interface to GiNaC's clifford algebra (Dirac gamma) objects. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2004 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
#include "indexed.h"
#include "tensor.h"
+#include "symbol.h"
+#include "idx.h"
+
+#include <set>
namespace GiNaC {
* algebra (the Dirac gamma matrices). These objects only carry Lorentz
* indices. Spinor indices are hidden. A representation label (an unsigned
* 8-bit integer) is used to distinguish elements from different Clifford
- * algebras (objects with different labels commute). */
+ * algebras (objects with different labels commutate). */
class clifford : public indexed
{
GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)
// other constructors
public:
clifford(const ex & b, unsigned char rl = 0);
- clifford(const ex & b, const ex & mu, unsigned char rl = 0);
+ clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl = 0);
// internal constructors
- clifford(unsigned char rl, const exvector & v, bool discardable = false);
- clifford(unsigned char rl, exvector * vp); // vp will be deleted
+ clifford(unsigned char rl, const ex & metr, const exvector & v, bool discardable = false);
+ clifford(unsigned char rl, const ex & metr, std::auto_ptr<exvector> vp);
// functions overriding virtual functions from base classes
protected:
- ex simplify_ncmul(const exvector & v) const;
- ex thisexprseq(const exvector & v) const;
- ex thisexprseq(exvector * vp) const;
- unsigned return_type(void) const { return return_types::noncommutative; }
- unsigned return_type_tinfo(void) const { return TINFO_clifford + representation_label; }
+ ex eval_ncmul(const exvector & v) const;
+ bool match_same_type(const basic & other) const;
+ ex thiscontainer(const exvector & v) const;
+ ex thiscontainer(std::auto_ptr<exvector> vp) const;
+ unsigned return_type() const { return return_types::noncommutative; }
+ unsigned return_type_tinfo() const { return TINFO_clifford + representation_label; }
// non-virtual functions in this class
public:
- unsigned char get_representation_label(void) const {return representation_label;}
+ unsigned char get_representation_label() const { return representation_label; }
+ ex get_metric() const { return metric; }
+ ex get_metric(const ex & i, const ex & j) const;
+ bool same_metric(const ex & other) const;
+
+protected:
+ void do_print_dflt(const print_dflt & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
// member variables
private:
unsigned char representation_label; /**< Representation label to distinguish independent spin lines */
+ ex metric;
};
{
GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor)
- // functions overriding virtual functions from bases classes
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+};
+
+
+/** This class represents the Clifford algebra generators (units). */
+class cliffordunit : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(cliffordunit, tensor)
+
+ // other constructors
+protected:
+ cliffordunit(unsigned ti) : inherited(ti) {}
+
+ // functions overriding virtual functions from base classes
public:
- void print(const print_context & c, unsigned level = 0) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
};
/** This class represents the Dirac gamma Lorentz vector. */
-class diracgamma : public tensor
+class diracgamma : public cliffordunit
{
- GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor)
+ GINAC_DECLARE_REGISTERED_CLASS(diracgamma, cliffordunit)
- // functions overriding virtual functions from bases classes
+ // functions overriding virtual functions from base classes
public:
- void print(const print_context & c, unsigned level = 0) const;
bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
};
-/** This class represents the Dirac gamma5 object which anticommutes with
+/** This class represents the Dirac gamma5 object which anticommutates with
* all other gammas. */
class diracgamma5 : public tensor
{
GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor)
- // functions overriding virtual functions from bases classes
-public:
- void print(const print_context & c, unsigned level = 0) const;
+ // functions overriding virtual functions from base classes
+ ex conjugate() const;
+
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+};
+
+
+/** This class represents the Dirac gammaL object which behaves like
+ * 1/2 (1-gamma5). */
+class diracgammaL : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(diracgammaL, tensor)
+
+ // functions overriding virtual functions from base classes
+ ex conjugate() const;
+
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+};
+
+
+/** This class represents the Dirac gammaL object which behaves like
+ * 1/2 (1+gamma5). */
+class diracgammaR : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(diracgammaR, tensor)
+
+ // functions overriding virtual functions from base classes
+ ex conjugate() const;
+
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
};
// global functions
-inline const clifford &ex_to_clifford(const ex &e)
+
+/** Specialization of is_exactly_a<clifford>(obj) for clifford objects. */
+template<> inline bool is_exactly_a<clifford>(const basic & obj)
{
- return static_cast<const clifford &>(*e.bp);
+ return obj.tinfo()==TINFO_clifford;
}
-
/** Create a Clifford unity object.
*
* @param rl Representation label
* @return newly constructed object */
ex dirac_ONE(unsigned char rl = 0);
+/** Create a Clifford unit object.
+ *
+ * @param mu Index (must be of class varidx or a derived class)
+ * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix)
+ * @param rl Representation label
+ * @return newly constructed Clifford unit object */
+ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0);
+
/** Create a Dirac gamma object.
*
* @param mu Index (must be of class varidx or a derived class)
* @return newly constructed object */
ex dirac_gamma5(unsigned char rl = 0);
-/** This returns (dirac_ONE(rl) + dirac_gamma5(rl)). */
-ex dirac_gamma6(unsigned char rl = 0);
+/** Create a Dirac gammaL object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+ex dirac_gammaL(unsigned char rl = 0);
-/** This returns (dirac_ONE(rl) - dirac_gamma5(rl)). */
-ex dirac_gamma7(unsigned char rl = 0);
+/** Create a Dirac gammaR object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+ex dirac_gammaR(unsigned char rl = 0);
/** Create a term of the form e_mu * gamma~mu with a unique index mu.
*
+ * @param e Original expression
* @param dim Dimension of index
* @param rl Representation label */
ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0);
+/** Calculate dirac traces over the specified set of representation labels.
+ * The computed trace is a linear functional that is equal to the usual
+ * trace only in D = 4 dimensions. In particular, the functional is not
+ * always cyclic in D != 4 dimensions when gamma5 is involved.
+ *
+ * @param e Expression to take the trace of
+ * @param rls Set of representation labels
+ * @param trONE Expression to be returned as the trace of the unit matrix */
+ex dirac_trace(const ex & e, const std::set<unsigned char> & rls, const ex & trONE = 4);
+
+/** Calculate dirac traces over the specified list of representation labels.
+ * The computed trace is a linear functional that is equal to the usual
+ * trace only in D = 4 dimensions. In particular, the functional is not
+ * always cyclic in D != 4 dimensions when gamma5 is involved.
+ *
+ * @param e Expression to take the trace of
+ * @param rll List of representation labels
+ * @param trONE Expression to be returned as the trace of the unit matrix */
+ex dirac_trace(const ex & e, const lst & rll, const ex & trONE = 4);
+
/** Calculate the trace of an expression containing gamma objects with
* a specified representation label. The computed trace is a linear
* functional that is equal to the usual trace only in D = 4 dimensions.
* to check two expressions for equality. */
ex canonicalize_clifford(const ex & e);
+/** Automorphism of the Clifford algebra, simply changes signs of all
+ * clifford units. */
+ex clifford_prime(const ex & e);
+
+/** Main anti-automorphism of the Clifford algebra: makes reversion
+ * and changes signs of all clifford units. */
+inline ex clifford_bar(const ex & e) { return clifford_prime(e.conjugate()); }
+
+/** Reversion of the Clifford algebra, coincides with the conjugate(). */
+inline ex clifford_star(const ex & e) { return e.conjugate(); }
+
+ex delete_ONE(const ex &e);
+
+/** Calculation of the norm in the Clifford algebra. */
+ex clifford_norm(const ex & e);
+
+/** Calculation of the inverse in the Clifford algebra. */
+ex clifford_inverse(const ex & e);
+
+/** List or vector conversion into the Clifford vector.
+ *
+ * @param v List or vector of coordinates
+ * @param mu Index (must be of class varidx or a derived class)
+ * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix)
+ * @param rl Representation label
+ * @return Clifford vector with given components */
+ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl = 0);
+
} // namespace GiNaC
#endif // ndef __GINAC_CLIFFORD_H__
git://www.ginac.de / ginac.git / blobdiff