/** @file clifford.h
*
- * Interface to GiNaC's clifford objects. */
+ * Interface to GiNaC's clifford algebra (Dirac gamma) objects. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2001 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 <ginac/indexed.h>
+#include "indexed.h"
+#include "tensor.h"
-/** Base class for clifford object */
+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 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
{
-// member functions
+ GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)
- // default constructor, destructor, copy constructor assignment operator and helpers
+ // other constructors
public:
- clifford();
- ~clifford();
- clifford(clifford const & other);
- clifford const & operator=(clifford const & other);
+ clifford(const ex & b, unsigned char rl = 0);
+ clifford(const ex & b, const ex & mu, 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
+
+ // functions overriding virtual functions from base classes
protected:
- void copy(clifford const & other);
- void destroy(bool call_parent);
+ 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; }
- // other constructors
+ // non-virtual functions in this class
public:
- explicit clifford(string const & initname);
+ unsigned char get_representation_label(void) const {return representation_label;}
+
+ // member variables
+private:
+ unsigned char representation_label; /**< Representation label to distinguish independent spin lines */
+};
+
- // functions overriding virtual functions from base classes
+/** This class represents the Clifford algebra unity element. */
+class diracone : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor)
+
+ // functions overriding virtual functions from bases classes
public:
- basic * duplicate() const;
- void printraw(ostream & os) const;
- void printtree(ostream & os, unsigned indent) const;
- void print(ostream & os, unsigned upper_precedence=0) const;
- void printcsrc(ostream & os, unsigned type, unsigned upper_precedence=0) const;
- bool info(unsigned inf) const;
-protected:
- int compare_same_type(basic const & other) const;
- ex simplify_ncmul(exvector const & v) const;
- unsigned calchash(void) const;
-
- // new virtual functions which can be overridden by derived classes
- // none
-
- // non-virtual functions in this class
+ void print(const print_context & c, unsigned level = 0) const;
+};
+
+
+/** This class represents the Dirac gamma Lorentz vector. */
+class diracgamma : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor)
+
+ // functions overriding virtual functions from bases classes
public:
- void setname(string const & n);
-private:
- string & autoname_prefix(void);
+ void print(const print_context & c, unsigned level = 0) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+};
-// member variables
-protected:
- string name;
- unsigned serial; // unique serial number for comparision
-private:
- static unsigned next_serial;
+/** This class represents the Dirac gamma5 object. */
+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;
};
-// global constants
-extern const clifford some_clifford;
-extern type_info const & typeid_clifford;
+// global functions
+inline const clifford &ex_to_clifford(const ex &e)
+{
+ return static_cast<const clifford &>(*e.bp);
+}
+
-// macros
+/** Create a Clifford unity object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+ex dirac_ONE(unsigned char rl = 0);
-#define ex_to_clifford(X) static_cast<clifford const &>(*(X).bp)
+/** 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);
-#endif // ndef __GINAC_CLIFFORD_H__
+/** Create a Dirac gamma5 object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+ex dirac_gamma5(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 non-cyclic in D != 4 dimensions when
+ * gamma5 is involved.
+ *
+ * @param rl Representation label */
+ex dirac_trace(const ex & e, unsigned char rl = 0);
+} // namespace GiNaC
+
+#endif // ndef __GINAC_CLIFFORD_H__
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