/** @file clifford.h
*
- * Interface to GiNaC's clifford objects. */
+ * 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
#ifndef __GINAC_CLIFFORD_H__
#define __GINAC_CLIFFORD_H__
-#include <string>
-#include "lortensor.h"
+#include "indexed.h"
+#include "tensor.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
/** 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 always hidden in our implementation. */
-class clifford : public lortensor
+ * 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, lortensor)
+ GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)
-// friends
+ // other constructors
+public:
+ clifford(const ex & b, unsigned char rl = 0);
+ clifford(const ex & b, const ex & mu, unsigned char rl = 0);
- friend clifford clifford_gamma(const ex & mu);
+ // internal constructors
+ clifford(unsigned char rl, const exvector & v, bool discardable = false);
+ clifford(unsigned char rl, std::auto_ptr<exvector> vp);
- // other constructors
+ // functions overriding virtual functions from base classes
+protected:
+ 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:
- clifford(const std::string & n, const ex & mu);
- clifford(const std::string & n, const exvector & iv);
- clifford(const std::string & n, exvector * ivp);
+ 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 */
+};
+
+
+/** This class represents the Clifford algebra unity element. */
+class diracone : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(diracone, 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 gamma Lorentz vector. */
+class diracgamma : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor)
// functions overriding virtual functions from base classes
public:
- basic * duplicate() const;
- void printraw(std::ostream & os) const;
- void printtree(std::ostream & os, unsigned indent) const;
- void print(std::ostream & os, unsigned upper_precedence=0) const;
- bool info(unsigned inf) const;
- // ex eval(int level=0) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+
+ // non-virtual functions in this class
protected:
- int compare_same_type(const basic & other) const;
- bool is_equal_same_type(const basic & other) const;
- ex simplify_ncmul(const exvector & v) const;
- ex thisexprseq(const exvector & v) const;
- ex thisexprseq(exvector * vp) const;
-
- // new virtual functions which can be overridden by derived classes
- // none
-
+ 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
- // none
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+};
- // member variables
- // none
+
+/** 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;
}
-clifford clifford_gamma(const ex & mu);
+/** Create a Clifford unity object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+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, 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);
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
#endif // ndef __GINAC_CLIFFORD_H__
git://www.ginac.de / ginac.git / blobdiff