- dirac_trace() handles arbitrary expressions (even unexpanded), including

[ginac.git] / ginac / clifford.h

diff --git a/ginac/clifford.h b/ginac/clifford.h
index 50893c8153eed49fb56e9ea34d18f49abec73e76..af3cb7883568dea7fda15ade6d1abf191fd4ca99 100644 (file)
--- a/ginac/clifford.h
+++ b/ginac/clifford.h
@@ -31,19 +31,21 @@ 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. */
+ *  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, exvector * vp); // vp will be deleted
 
        // functions overriding virtual functions from base classes
 protected:
@@ -51,7 +53,15 @@ protected:
        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; }
+       unsigned return_type_tinfo(void) const { return TINFO_clifford + representation_label; }
+
+       // non-virtual functions in this class
+public:
+       unsigned char get_representation_label(void) const {return representation_label;}
+
+       // member variables
+private:
+       unsigned char representation_label; /**< Representation label to distinguish independent spin lines */
 };
 
 
@@ -78,6 +88,18 @@ public:
 };
 
 
+/** 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;
+};
+
+
 // global functions
 inline const clifford &ex_to_clifford(const ex &e)
 {
@@ -87,14 +109,37 @@ inline const clifford &ex_to_clifford(const ex &e)
 
 /** 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 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 rl Representation label */
+ex dirac_trace(const ex & e, unsigned char rl = 0);
 
 
 } // namespace GiNaC