/** @file color.h
*
- * Interface to GiNaC's color objects. */
+ * Interface to GiNaC's color (SU(3) Lie algebra) objects. */
/*
* GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
#ifndef __GINAC_COLOR_H__
#define __GINAC_COLOR_H__
-#include <string>
-#include <vector>
#include "indexed.h"
-#include "ex.h"
+#include "tensor.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
-
-const unsigned MAX_REPRESENTATION_LABELS = 4;
-const unsigned COLOR_EIGHT = 8; // N*N-1
-const unsigned COLOR_THREE = 3; // N
-
-// Cint doesn't like vector<..,default_alloc> but malloc_alloc is
-// unstandardized and not supported by newer GCCs.
-#if defined(__GNUC__) && ((__GNUC__ == 2) && (__GNUC_MINOR__ < 97))
-typedef std::vector<exvector,malloc_alloc> exvectorvector;
-#else
-typedef std::vector<exvector> exvectorvector;
-#endif
-
-
-/** This class holds an object carrying color indices (of class coloridx).
- * It can represent the generators T_a and structure constants f_abc/d_abc
- * of SU(3), the unity element ONE of the Lie algebra of SU(3), or the
- * unity matrix delta8. Together, these objects are used to implement the
- * Lie algebra su(3), as required for calculations in quantum
- * chromodynamics. A representation label (an unsigned integer) is used to
- * distinguish elements from different Lie algebras (only objects with the
- * same representation label "interact" with each other). */
+
+
+/** This class holds a generator T_a or the unity element of the Lie algebra
+ * of SU(3), as used for calculations in quantum chromodynamics. A
+ * representation label (an unsigned 8-bit integer) is used to distinguish
+ * elements from different Lie algebras (objects with different labels
+ * commute). These objects implement an abstract representation of the
+ * group, not a specific matrix representation. The indices used for color
+ * objects should not have a variance. */
class color : public indexed
{
GINAC_DECLARE_REGISTERED_CLASS(color, indexed)
-// friends
-
- friend color color_ONE(unsigned rl);
- friend color color_T(const ex & a, unsigned rl);
- friend color color_f(const ex & a, const ex & b, const ex & c);
- friend color color_d(const ex & a, const ex & b, const ex & c);
- friend ex color_h(const ex & a, const ex & b, const ex & c);
- friend color color_delta8(const ex & a, const ex & b);
- friend unsigned subs_index_in_exvector(exvector & v, const ex & is, const ex & ir);
- friend void split_color_string_in_parts(const exvector & v, exvector & delta8vec,
- exvector & fvec, exvector & dvec,
- exvectorvector & Tvecs,
- exvectorvector & ONEvecs,
- exvector & unknownvec);
- friend exvector recombine_color_string(exvector & delta8vec, exvector & fvec,
- exvector & dvec, exvectorvector & Tvecs,
- exvectorvector & ONEvecs, exvector & unknownvec);
- friend ex color_trace_of_one_representation_label(const exvector & v);
- friend ex color_trace(const exvector & v, unsigned rl);
- friend ex simplify_pure_color_string(const ex & e);
- friend ex simplify_color(const ex & e);
-
-// types
-
+ // other constructors
public:
- /** Type of object */
- typedef enum {
- invalid, /**< not properly constructed */
- color_T, /**< one of the generators T_a of SU(3) (these are non-commutative) */
- color_f, /**< one of the antisymmetric structure constants f_abc of SU(3) */
- color_d, /**< one of the symmetric structure constants d_abc of SU(3) */
- color_delta8, /**< the unity matrix */
- color_ONE /**< the unity element of su(3) */
- } color_types;
-
-// member functions
+ color(const ex & b, unsigned char rl = 0);
+ color(const ex & b, const ex & i1, unsigned char rl = 0);
+
+ // internal constructors
+ color(unsigned char rl, const exvector & v, bool discardable = false);
+ color(unsigned char rl, exvector * vp); // vp will be deleted
- // other constructors
-protected:
- color(color_types const t, unsigned rl=0);
- color(color_types const t, const ex & i1, unsigned rl=0);
- color(color_types const t, const ex & i1, const ex & i2, unsigned rl=0);
- color(color_types const t, const ex & i1, const ex & i2, const ex & i3,
- unsigned rl=0);
- color(color_types const t, const exvector & iv, unsigned rl=0);
- color(color_types const t, exvector * ivp, unsigned rl=0);
-
// functions overriding virtual functions from base classes
-public:
- basic * duplicate() const;
- void printraw(std::ostream & os) const;
- void printtree(std::ostream & os, unsigned indent) const;
- void print(std::ostream & os, unsigned upper_precedence=0) const;
- bool info(unsigned inf) const;
- ex eval(int level=0) const;
protected:
- int compare_same_type(const basic & other) const;
- bool is_equal_same_type(const basic & other) const;
+ bool match_same_type(const basic & other) const;
ex simplify_ncmul(const exvector & v) const;
ex thisexprseq(const exvector & v) const;
ex thisexprseq(exvector * vp) const;
+ unsigned return_type(void) const { return return_types::noncommutative; }
+ unsigned return_type_tinfo(void) const { return TINFO_color + representation_label; }
- // new virtual functions which can be overridden by derived classes
- // none
-
// non-virtual functions in this class
-protected:
- bool all_of_type_coloridx(void) const;
-
-// member variables
+public:
+ unsigned char get_representation_label(void) const {return representation_label;}
-protected:
- color_types type; /**< Type of object (generator, structure constant etc.) */
- unsigned representation_label; /**< Representation label to distiguish independent color matrices coming from separated fermion lines */
+ // member variables
+private:
+ unsigned char representation_label; /**< Representation label to distinguish independent color matrices coming from separated fermion lines */
};
-// global functions
-inline const color &ex_to_color(const ex &e)
+
+/** This class represents the su(3) unity element. */
+class su3one : public tensor
{
- return static_cast<const color &>(*e.bp);
-}
+ GINAC_DECLARE_REGISTERED_CLASS(su3one, tensor)
-inline color &ex_to_nonconst_color(const ex &e)
+ // functions overriding virtual functions from base classes
+public:
+ void print(const print_context & c, unsigned level = 0) const;
+};
+
+/** This class represents an su(3) generator. */
+class su3t : public tensor
{
- return static_cast<color &>(*e.bp);
+ GINAC_DECLARE_REGISTERED_CLASS(su3t, tensor)
+
+ // functions overriding virtual functions from base classes
+public:
+ void print(const print_context & c, unsigned level = 0) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+};
+
+/** This class represents the tensor of antisymmetric su(3) structure
+ * constants. */
+class su3f : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(su3f, tensor)
+
+ // functions overriding virtual functions from base classes
+public:
+ void print(const print_context & c, unsigned level = 0) const;
+ ex eval_indexed(const basic & i) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+};
+
+/** This class represents the tensor of symmetric su(3) structure constants. */
+class su3d : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(su3d, tensor)
+
+ // functions overriding virtual functions from base classes
+public:
+ void print(const print_context & c, unsigned level = 0) const;
+ ex eval_indexed(const basic & i) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+};
+
+
+// global functions
+
+/** Specialization of is_exactly_a<color>(obj) for color objects. */
+template<> inline bool is_exactly_a<color>(const basic & obj)
+{
+ return obj.tinfo()==TINFO_color;
}
-color color_ONE(unsigned rl=0);
-color color_T(const ex & a, unsigned rl=0);
-color color_f(const ex & a, const ex & b, const ex & c);
-color color_d(const ex & a, const ex & b, const ex & c);
+/** Create the su(3) unity element. This is an indexed object, although it
+ * has no indices.
+ *
+ * @param rl Representation label
+ * @return newly constructed unity element */
+ex color_ONE(unsigned char rl = 0);
+
+/** Create an su(3) generator.
+ *
+ * @param a Index
+ * @param rl Representation label
+ * @return newly constructed unity generator */
+ex color_T(const ex & a, unsigned char rl = 0);
+
+/** Create an su(3) antisymmetric structure constant.
+ *
+ * @param a First index
+ * @param b Second index
+ * @param c Third index
+ * @return newly constructed structure constant */
+ex color_f(const ex & a, const ex & b, const ex & c);
+
+/** Create an su(3) symmetric structure constant.
+ *
+ * @param a First index
+ * @param b Second index
+ * @param c Third index
+ * @return newly constructed structure constant */
+ex color_d(const ex & a, const ex & b, const ex & c);
+
+/** This returns the linear combination d.a.b.c+I*f.a.b.c. */
ex color_h(const ex & a, const ex & b, const ex & c);
-color color_delta8(const ex & a, const ex & b);
-void split_color_string_in_parts(const exvector & v, exvector & delta8vec,
- exvector & fvec, exvector & dvec,
- exvectorvector & Tvecs,
- exvectorvector & ONEvecs,
- exvector & unknownvec);
-exvector recombine_color_string(exvector & delta8vec, exvector & fvec,
- exvector & dvec, exvectorvector & Tvecs,
- exvectorvector & ONEvecs, exvector & unknownvec);
-ex color_trace_of_one_representation_label(const exvector & v);
-ex color_trace(const exvector & v, unsigned rl=0);
-ex simplify_pure_color_string(const ex & e);
-ex simplify_color(const ex & e);
-
-ex brute_force_sum_color_indices(const ex & e);
-
-#ifndef NO_NAMESPACE_GINAC
+
+/** Calculate the trace of an expression containing color objects with a
+ * specified representation label.
+ *
+ * @param e Expression to take the trace of
+ * @param rl Representation label */
+ex color_trace(const ex & e, unsigned char rl = 0);
+
+
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
#endif // ndef __GINAC_COLOR_H__
git://www.ginac.de / ginac.git / blobdiff