Added contribution from Vladimir Kisil: generalization of clifford algebra:

[ginac.git] / ginac / clifford.h

diff --git a/ginac/clifford.h b/ginac/clifford.h
index f551abb71febcd2936d444bc74f51612edf38f46..3fa3627d0dd6b9d131c4d0700ba4e01127650026 100644 (file)
--- a/ginac/clifford.h
+++ b/ginac/clifford.h
@@ -3,7 +3,7 @@
  *  Interface to GiNaC's clifford algebra (Dirac gamma) objects. */
 
 /*
- *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2004 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
@@ -25,6 +25,8 @@
 
 #include "indexed.h"
 #include "tensor.h"
+#include "symbol.h"
+#include "idx.h"
 
 namespace GiNaC {
 
@@ -41,11 +43,11 @@ class clifford : public indexed
        // other constructors
 public:
        clifford(const ex & b, unsigned char rl = 0);
-       clifford(const ex & b, const ex & mu, unsigned char rl = 0);
+       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);
-       clifford(unsigned char rl, std::auto_ptr<exvector> vp);
+       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)));
 
        // functions overriding virtual functions from base classes
 protected:
@@ -59,6 +61,9 @@ 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;
 
 protected:
        void do_print_dflt(const print_dflt & c, unsigned level) const;
@@ -67,6 +72,7 @@ protected:
        // member variables
 private:
        unsigned char representation_label; /**< Representation label to distinguish independent spin lines */
+       ex metric;
 };
 
 
@@ -82,10 +88,29 @@ protected:
 };
 
 
+/** This class represents the Clifford algebra generators (units). */
+class cliffordunit : public tensor
+{
+       GINAC_DECLARE_REGISTERED_CLASS(cliffordunit, tensor)
+
+         // other constructors
+protected:
+        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;
+       void do_print_latex(const print_latex & c, unsigned level) const;
+};
+
+
 /** This class represents the Dirac gamma Lorentz vector. */
-class diracgamma : public tensor
+class diracgamma : public cliffordunit
 {
-       GINAC_DECLARE_REGISTERED_CLASS(diracgamma, tensor)
+       GINAC_DECLARE_REGISTERED_CLASS(diracgamma, cliffordunit)
 
        // functions overriding virtual functions from base classes
 public:
@@ -104,6 +129,9 @@ class diracgamma5 : public tensor
 {
        GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor)
 
+       // functions overriding virtual functions from base classes
+       ex conjugate() const;
+
        // non-virtual functions in this class
 protected:
        void do_print(const print_context & c, unsigned level) const;
@@ -117,6 +145,9 @@ class diracgammaL : public tensor
 {
        GINAC_DECLARE_REGISTERED_CLASS(diracgammaL, tensor)
 
+       // functions overriding virtual functions from base classes
+       ex conjugate() const;
+
        // non-virtual functions in this class
 protected:
        void do_print(const print_context & c, unsigned level) const;
@@ -130,6 +161,9 @@ class diracgammaR : public tensor
 {
        GINAC_DECLARE_REGISTERED_CLASS(diracgammaR, tensor)
 
+       // functions overriding virtual functions from base classes
+       ex conjugate() const;
+
        // non-virtual functions in this class
 protected:
        void do_print(const print_context & c, unsigned level) const;
@@ -151,6 +185,14 @@ template<> inline bool is_exactly_a<clifford>(const basic & obj)
  *  @return newly constructed object */
 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 rl Representation label
+ *  @return newly constructed Clifford unit object */
+ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0);
+
 /** Create a Dirac gamma object.
  *
  *  @param mu Index (must be of class varidx or a derived class)
@@ -178,6 +220,7 @@ ex dirac_gammaR(unsigned char rl = 0);
 
 /** Create a term of the form e_mu * gamma~mu with a unique index mu.
  *
+ *  @param e Original expression
  *  @param dim Dimension of index
  *  @param rl Representation label */
 ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0);
@@ -198,6 +241,33 @@ 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 
+ *  clifford units. */
+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());};
+
+/** Reversion of the Clifford algebra, coinsides with the conjugate() */
+inline ex clifford_star(const ex &e) {  return e.conjugate();};
+
+ex delete_ONE (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) ; 
+
+/** 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 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) ;
+
 } // namespace GiNaC
 
 #endif // ndef __GINAC_CLIFFORD_H__