#include "symbol.h"
#include "idx.h"
+#include <set>
+
namespace GiNaC {
* 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). */
+ * algebras (objects with different labels commutate). */
class clifford : public indexed
{
GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)
};
-/** This class represents the Dirac gamma5 object which anticommutes with
+/** This class represents the Dirac gamma5 object which anticommutates with
* all other gammas. */
class diracgamma5 : public tensor
{
/** Create a Clifford unit object.
*
* @param mu Index (must be of class varidx or a derived class)
- * @param metr Metric (must be of class tensor or a derived class)
+ * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix)
* @param rl Representation label
* @return newly constructed Clifford unit object */
ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0);
* @param rl Representation label */
ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0);
+/** Calculate dirac traces over the specified set of representation labels.
+ * 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 rls Set of representation labels
+ * @param trONE Expression to be returned as the trace of the unit matrix */
+ex dirac_trace(const ex & e, const std::set<unsigned char> & rls, const ex & trONE = 4);
+
+/** Calculate dirac traces over the specified list of representation labels.
+ * 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 rll List of representation labels
+ * @param trONE Expression to be returned as the trace of the unit matrix */
+ex dirac_trace(const ex & e, const lst & rll, const ex & trONE = 4);
+
/** 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.
*
* @param v List or vector of coordinates
* @param mu Index (must be of class varidx or a derived class)
- * @param metr Metric (must be of class tensor or a derived class)
+ * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix)
* @param rl Representation label
* @return Clifford vector with given components */
ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl = 0);