/** @file clifford.h
*
- * Interface to GiNaC's clifford objects. */
+ * Interface to GiNaC's clifford algebra (Dirac gamma) objects. */
/*
- * GiNaC Copyright (C) 1999-2000 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 "indexed.h"
-#include "ex.h"
+#include "tensor.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
-/** Base class for clifford object */
+
+/** 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(const clifford & other);
- const clifford & operator=(const clifford & other);
-protected:
- void copy(const clifford & other);
- void destroy(bool call_parent);
+ clifford(const ex & b, unsigned char rl = 0);
+ clifford(const ex & b, const ex & mu, unsigned char rl = 0);
- // other constructors
-public:
- explicit clifford(const std::string & initname);
+ // 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
-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;
- void printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence=0) const;
- bool info(unsigned inf) const;
+ // functions overriding virtual functions from base classes
protected:
- int compare_same_type(const basic & other) const;
- ex simplify_ncmul(const exvector & v) const;
- unsigned calchash(void) const;
-
- // new virtual functions which can be overridden by derived classes
- // none
-
- // non-virtual functions in this class
+ 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; }
+
+ // non-virtual functions in this class
public:
- void setname(const std::string & n);
+ unsigned char get_representation_label(void) const {return representation_label;}
+
+ // member variables
private:
- std::string & autoname_prefix(void);
+ unsigned char representation_label; /**< Representation label to distinguish independent spin lines */
+};
-// member variables
-protected:
- std::string name;
- unsigned serial; // unique serial number for comparision
-private:
- static unsigned next_serial;
+/** 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:
+ 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 print(const print_context & c, unsigned level = 0) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
};
-// global constants
-extern const clifford some_clifford;
-extern const type_info & typeid_clifford;
+/** This class represents the Dirac gamma5 object which anticommutes 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;
+};
+
-// utility functions
+// global functions
inline const clifford &ex_to_clifford(const ex &e)
{
return static_cast<const clifford &>(*e.bp);
}
-#ifndef NO_NAMESPACE_GINAC
+
+/** 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);
+
+/** This returns (dirac_ONE(rl) + dirac_gamma5(rl)). */
+ex dirac_gamma6(unsigned char rl = 0);
+
+/** This returns (dirac_ONE(rl) - dirac_gamma5(rl)). */
+ex dirac_gamma7(unsigned char rl = 0);
+
+/** Create a term of the form e_mu * gamma~mu with a unique index mu.
+ *
+ * @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 checking two expressions for equality. */
+ex canonicalize_clifford(const ex & e);
+
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
#endif // ndef __GINAC_CLIFFORD_H__