/** @file clifford.h
*
- * Interface to GiNaC's clifford objects. */
+ * Interface to GiNaC's clifford algebra (Dirac gamma) objects. */
-#ifndef _CLIFFORD_H_
-#define _CLIFFORD_H_
-
-#include <string>
+/*
+ * 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
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ */
-class clifford;
+#ifndef __GINAC_CLIFFORD_H__
+#define __GINAC_CLIFFORD_H__
#include "indexed.h"
+#include "tensor.h"
+#include "symbol.h"
+#include "idx.h"
+
+namespace GiNaC {
-/** Base class for clifford object */
+
+/** 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. 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
{
-// member functions
+ GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)
- // default constructor, destructor, copy constructor assignment operator and helpers
+ // other constructors
public:
- clifford();
- ~clifford();
- clifford(clifford const & other);
- clifford const & operator=(clifford const & other);
+ clifford(const ex & b, 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, 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:
- void copy(clifford const & other);
- void destroy(bool call_parent);
+ ex eval_ncmul(const exvector & v) const;
+ bool match_same_type(const basic & other) const;
+ ex thiscontainer(const exvector & v) const;
+ ex thiscontainer(std::auto_ptr<exvector> vp) const;
+ unsigned return_type() const { return return_types::noncommutative; }
+ unsigned return_type_tinfo() const { return TINFO_clifford + representation_label; }
- // other constructors
+ // non-virtual functions in this class
public:
- explicit clifford(string const & initname);
+ 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;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+
+ // member variables
+private:
+ unsigned char representation_label; /**< Representation label to distinguish independent spin lines */
+ ex metric;
+};
+
+
+/** This class represents the Clifford algebra unity element. */
+class diracone : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor)
+
+ // 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;
+};
- // functions overriding virtual functions from base classes
+
+/** 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:
- basic * duplicate() const;
- void printraw(ostream & os) const;
- void printtree(ostream & os, unsigned indent) const;
- void print(ostream & os, unsigned upper_precedence=0) const;
- void printcsrc(ostream & os, unsigned type, unsigned upper_precedence=0) const;
- bool info(unsigned inf) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+ // non-virtual functions in this class
protected:
- int compare_same_type(basic const & other) const;
- ex simplify_ncmul(exvector const & v) const;
- unsigned calchash(void) const;
-
- // new virtual functions which can be overridden by derived classes
- // none
-
- // non-virtual functions in this class
+ 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 cliffordunit
+{
+ GINAC_DECLARE_REGISTERED_CLASS(diracgamma, cliffordunit)
+
+ // functions overriding virtual functions from base classes
public:
- void setname(string const & n);
-private:
- string & autoname_prefix(void);
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
-// member variables
+ // 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 gamma5 object which anticommutes with
+ * all other gammas. */
+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:
- string name;
- unsigned serial; // unique serial number for comparision
-private:
- static unsigned next_serial;
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
};
-// global constants
-extern const clifford some_clifford;
-extern type_info const & typeid_clifford;
+/** This class represents the Dirac gammaL object which behaves like
+ * 1/2 (1-gamma5). */
+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;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+};
+
+
+/** This class represents the Dirac gammaL object which behaves like
+ * 1/2 (1+gamma5). */
+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;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+};
+
+
+// global functions
+
+/** Specialization of is_exactly_a<clifford>(obj) for clifford objects. */
+template<> inline bool is_exactly_a<clifford>(const basic & obj)
+{
+ return obj.tinfo()==TINFO_clifford;
+}
+
+/** Create a Clifford unity object.
+ *
+ * @param rl Representation label
+ * @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)
+ * @param rl Representation label
+ * @return newly constructed gamma object */
+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 Dirac gammaL object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+ex dirac_gammaL(unsigned char rl = 0);
+
+/** Create a Dirac gammaR object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+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);
+
+/** 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 e Expression to take the trace of
+ * @param rl Representation label
+ * @param trONE Expression to be returned as the trace of the unit matrix */
+ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4);
+
+/** Bring all products of clifford objects in an expression into a canonical
+ * order. This is not necessarily the most simple form but it will allow
+ * 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);
-// macros
+/** Calculation of the norm in the Clifford algebra */
+ex clifford_norm(const ex &e) ;
-#define ex_to_clifford(X) static_cast<clifford const &>(*(X).bp)
+/** Calculation of the inverse in the Clifford algebra */
+ex clifford_inverse(const ex &e) ;
-#endif // ndef _CLIFFORD_H_
+/** 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__
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