* Return

[ginac.git] / ginac / clifford.h

diff --git a/ginac/clifford.h b/ginac/clifford.h
index f6a9820b6e9f08bfa5a1d6b21abf096d6f5da258..17c70e1bf523250fa706d0ca72520821b0660486 100644 (file)
--- a/ginac/clifford.h
+++ b/ginac/clifford.h
@@ -28,6 +28,8 @@
 #include "symbol.h"
 #include "idx.h"
 
+#include <set>
+
 namespace GiNaC {
 
 
@@ -35,7 +37,7 @@ 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)
@@ -124,7 +126,7 @@ protected:
 };
 
 
-/** 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
 {
@@ -226,6 +228,26 @@ ex dirac_gammaR(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.
@@ -253,7 +275,8 @@ inline ex clifford_bar(const ex & e) { return clifford_prime(e.conjugate()); }
 /** Reversion of the Clifford algebra, coincides with the conjugate(). */
 inline ex clifford_star(const ex & e) { return e.conjugate(); }
 
-ex delete_ONE(const ex &e);
+/** Replaces all dirac_ONE's in e with 1 (effectively removing them). */
+ex remove_dirac_ONE(const ex & e);
 
 /** Calculation of the norm in the Clifford algebra. */
 ex clifford_norm(const ex & e);
@@ -270,6 +293,39 @@ ex clifford_inverse(const ex & e);
  *  @return Clifford vector with given components */
 ex lst_to_clifford(const ex & v, const ex & mu,  const ex & metr, unsigned char rl = 0);
 
+/** An inverse function to lst_to_clifford(). For given Clifford vector extracts
+ *  its components with respect to given Clifford unit. Obtained components may 
+ *  contain Clifford units with a different metric. Extraction is based on 
+ *  the algebraic formula (e * c.i + c.i * e)/ pow(e.i, 2) for non-degenerate cases
+ *  (i.e. neither pow(e.i, 2) = 0).
+ *  
+ *  @param e Clifford expression to be decomposed into components
+ *  @param c Clifford unit defining the metric for splitting (should have numeric dimension of indices)
+ *  @param algebraic Use algebraic or symbolic algorithm for extractions */
+lst clifford_to_lst(const ex & e, const ex & c, bool algebraic=true);
+
+/** Calculations of Moebius transformations (conformal map) defined by a 2x2 Clifford matrix
+ *  (a b\\c d) in linear spaces with arbitrary signature. The expression is 
+ *  (a * x + b)/(c * x + d), where x is a vector build from list v with metric G.
+ *  (see Jan Cnops. An introduction to {D}irac operators on manifolds, v.24 of
+ *  Progress in Mathematical Physics. Birkhauser Boston Inc., Boston, MA, 2002.)
+ * 
+ *  @param a (1,1) entry of the defining matrix
+ *  @param b (1,2) entry of the defining matrix
+ *  @param c (2,1) entry of the defining matrix
+ *  @param d (2,2) entry of the defining matrix
+ *  @param v Vector to be transformed
+ *  @param G Metric of the surrounding space */
+ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G);
+
+/** The second form of Moebius transformations defined by a 2x2 Clifford matrix M
+ *  This function takes the transformation matrix M as a single entity.
+ * 
+ *  @param M the defining matrix
+ *  @param v Vector to be transformed
+ *  @param G Metric of the surrounding space */
+ex clifford_moebius_map(const ex & M, const ex & v, const ex & G);
+
 } // namespace GiNaC
 
 #endif // ndef __GINAC_CLIFFORD_H__