* Interface to GiNaC's clifford algebra (Dirac gamma) objects. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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
/** This class holds an object representing an element of the Clifford
* algebra (the Dirac gamma matrices). These objects only carry Lorentz
- * indices. Spinor indices are hidden. */
+ * 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). */
class clifford : public indexed
{
GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)
// other constructors
public:
- clifford(const ex & b);
- clifford(const ex & b, const ex & mu);
+ clifford(const ex & b, unsigned char rl = 0);
+ clifford(const ex & b, const ex & mu, unsigned char rl = 0);
// internal constructors
- clifford(const exvector & v, bool discardable = false);
- clifford(exvector * vp); // vp will be deleted
+ clifford(unsigned char rl, const exvector & v, bool discardable = false);
+ clifford(unsigned char rl, 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; }
+ 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() const {return representation_label;}
+
+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 */
};
{
GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor)
- // functions overriding virtual functions from bases classes
-public:
- void print(std::ostream & os, unsigned upper_precedence=0) 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;
};
{
GINAC_DECLARE_REGISTERED_CLASS(diracgamma, 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;
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
+ * all other gammas. */
+class diracgamma5 : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor)
+
+ // 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)
+
+ // 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)
+
+ // 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(void);
+ex dirac_ONE(unsigned char rl = 0);
/** Create a Dirac gamma object.
*
* @param mu Index (must be of class varidx or a derived class)
+ * @param rl Representation label
* @return newly constructed gamma object */
-ex dirac_gamma(const ex & mu);
+ex dirac_gamma(const ex & mu, unsigned char rl = 0);
+
+/** Create a Dirac gamma5 object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+ex dirac_gamma5(unsigned char rl = 0);
+
+/** Create a Dirac gammaL object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+ex dirac_gammaL(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 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.
+ * 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 rl Representation label
+ * @param trONE Expression to be returned as the trace of the unit matrix */
+ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4);
+
+/** Bring all products of clifford objects in an expression into a canonical
+ * order. This is not necessarily the most simple form but it will allow
+ * to check two expressions for equality. */
+ex canonicalize_clifford(const ex & e);
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff