X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.h;h=17c70e1bf523250fa706d0ca72520821b0660486;hp=3fa3627d0dd6b9d131c4d0700ba4e01127650026;hb=7a9e31b4cf6bbdb07cc7364bcd7903e9fc15a995;hpb=ed94ac0dbcf6ee52d58b2399c25f474537f725fa

diff --git a/ginac/clifford.h b/ginac/clifford.h
index 3fa3627d..17c70e1b 100644
--- 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)
@@ -46,8 +48,8 @@ public:
 	clifford(const ex & b, const ex & mu,  const ex & metr, unsigned char rl = 0);
 
 	// internal constructors
-	clifford(unsigned char rl, const exvector & v, bool discardable = false,  const ex & metr = lorentz_g(varidx((new symbol)->setflag(status_flags::dynallocated), 4),varidx((new symbol)->setflag(status_flags::dynallocated), 4)));
-	clifford(unsigned char rl, std::auto_ptr<exvector> vp,  const ex & metr = lorentz_g(varidx((new symbol)->setflag(status_flags::dynallocated),4),varidx((new symbol)->setflag(status_flags::dynallocated),4)));
+	clifford(unsigned char rl, const ex & metr, const exvector & v, bool discardable = false);
+	clifford(unsigned char rl, const ex & metr, std::auto_ptr<exvector> vp);
 
 	// functions overriding virtual functions from base classes
 protected:
@@ -60,10 +62,10 @@ protected:
 
 	// non-virtual functions in this class
 public:
-	unsigned char get_representation_label() const {return representation_label;}
- 	ex get_metric() const {return metric;}
- 	ex get_metric(const ex & i, const ex & j) const;
- 	bool same_metric(const ex & other) const;
+	unsigned char get_representation_label() const { return representation_label; }
+	ex get_metric() const { return metric; }
+	ex get_metric(const ex & i, const ex & j) const;
+	bool same_metric(const ex & other) const;
 
 protected:
 	void do_print_dflt(const print_dflt & c, unsigned level) const;
@@ -72,7 +74,7 @@ protected:
 	// member variables
 private:
 	unsigned char representation_label; /**< Representation label to distinguish independent spin lines */
- 	ex metric;
+	ex metric;
 };
 
 
@@ -93,13 +95,14 @@ class cliffordunit : public tensor
 {
 	GINAC_DECLARE_REGISTERED_CLASS(cliffordunit, tensor)
 
-	  // other constructors
+	// other constructors
 protected:
-        cliffordunit(unsigned ti) : inherited(ti) {}
+	cliffordunit(unsigned ti) : inherited(ti) {}
                                                                                                     
 	// functions overriding virtual functions from base classes
 public:
 	bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+
 	// non-virtual functions in this class
 protected:
 	void do_print(const print_context & c, unsigned level) const;
@@ -123,7 +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
 {
@@ -188,7 +191,7 @@ ex dirac_ONE(unsigned char rl = 0);
 /** 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);
@@ -225,6 +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.
@@ -241,32 +264,67 @@ ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4);
  *  to check two expressions for equality. */
 ex canonicalize_clifford(const ex & e);
 
-/** Automorphism of the Clifford algebra, simply changes signs of all 
+/** Automorphism of the Clifford algebra, simply changes signs of all
  *  clifford units. */
-ex clifford_prime (const ex &e) ;
+ex clifford_prime(const ex & e);
 
-/** Main anti-automorphism of the Clifford algebra: make reversion 
- * and changes signs of all clifford units*/
-inline ex clifford_bar(const ex &e) { return clifford_prime(e.conjugate());};
+/** Main anti-automorphism of the Clifford algebra: makes reversion
+ *  and changes signs of all clifford units. */
+inline ex clifford_bar(const ex & e) { return clifford_prime(e.conjugate()); }
 
-/** Reversion of the Clifford algebra, coinsides with the conjugate() */
-inline ex clifford_star(const ex &e) {  return 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) ; 
+/** Calculation of the norm in the Clifford algebra. */
+ex clifford_norm(const ex & e);
 
-/** Calculation of the inverse in the Clifford algebra */
-ex clifford_inverse(const ex &e) ; 
+/** Calculation of the inverse in the Clifford algebra. */
+ex clifford_inverse(const ex & e);
 
-/** List or vector conversion into the Clifford vector 
+/** List or vector conversion into the Clifford vector.
+ *
  *  @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) ;
+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