From 725021581cc862520c1f04b253ecb86f28032f69 Mon Sep 17 00:00:00 2001 From: Christian Bauer Date: Wed, 20 Nov 2002 20:35:06 +0000 Subject: [PATCH] - added Dirac gammaL and gammaR objects (chiral projectors) - fixed a typo in add.cpp --- ginac/add.cpp | 2 +- ginac/clifford.cpp | 158 ++++++++++++++++++++++++++++++++++++++------- ginac/clifford.h | 42 ++++++++++-- ginac/tinfos.h | 2 + 4 files changed, 175 insertions(+), 29 deletions(-) diff --git a/ginac/add.cpp b/ginac/add.cpp index 1c995aa7..b3fd1f60 100644 --- a/ginac/add.cpp +++ b/ginac/add.cpp @@ -315,7 +315,7 @@ ex add::coeff(const ex & s, int n) const * x stands for a symbolic variables of type ex and c stands for such * an expression that contain a plain number. * - +(;c) -> c - * - +(x;1) -> x + * - +(x;0) -> x * * @param level cut-off in recursive evaluation */ ex add::eval(int level) const diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp index 1b3d034a..c7499db6 100644 --- a/ginac/clifford.cpp +++ b/ginac/clifford.cpp @@ -44,6 +44,8 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(diracone, tensor) GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor) GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma5, tensor) +GINAC_IMPLEMENT_REGISTERED_CLASS(diracgammaL, tensor) +GINAC_IMPLEMENT_REGISTERED_CLASS(diracgammaR, tensor) ////////// // default ctor, dtor, copy ctor, assignment operator and helpers ////////// @@ -64,6 +66,8 @@ DEFAULT_CTORS(diracone) DEFAULT_CTORS(diracgamma) DEFAULT_CTORS(diracgamma5) +DEFAULT_CTORS(diracgammaL) +DEFAULT_CTORS(diracgammaR) ////////// // other constructors ////////// @@ -117,6 +121,8 @@ DEFAULT_ARCHIVING(diracone) DEFAULT_ARCHIVING(diracgamma) DEFAULT_ARCHIVING(diracgamma5) +DEFAULT_ARCHIVING(diracgammaL) +DEFAULT_ARCHIVING(diracgammaR) ////////// // functions overriding virtual functions from base classes ////////// @@ -144,7 +150,9 @@ bool clifford::match_same_type(const basic & other) const void clifford::print(const print_context & c, unsigned level) const { - if (!is_a(seq[0]) && !is_a(seq[0]) && !is_a(seq[0])) { + if (!is_a(seq[0]) && !is_a(seq[0]) && + !is_a(seq[0]) && !is_a(seq[0]) && + !is_a(seq[0])) { // dirac_slash() object is printed differently if (is_a(c)) @@ -165,10 +173,14 @@ void clifford::print(const print_context & c, unsigned level) const DEFAULT_COMPARE(diracone) DEFAULT_COMPARE(diracgamma) DEFAULT_COMPARE(diracgamma5) +DEFAULT_COMPARE(diracgammaL) +DEFAULT_COMPARE(diracgammaR) DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}") DEFAULT_PRINT_LATEX(diracgamma, "gamma", "\\gamma") DEFAULT_PRINT_LATEX(diracgamma5, "gamma5", "{\\gamma^5}") +DEFAULT_PRINT_LATEX(diracgammaL, "gammaL", "{\\gamma_L}") +DEFAULT_PRINT_LATEX(diracgammaR, "gammaR", "{\\gamma_R}") /** This function decomposes gamma~mu -> (1, mu) and a\ -> (a.ix, ix) */ static void base_and_index(const ex & c, ex & b, ex & i) @@ -179,7 +191,7 @@ static void base_and_index(const ex & c, ex & b, ex & i) if (is_a(c.op(0))) { // proper dirac gamma object i = c.op(1); b = _ex1; - } else if (is_a(c.op(0))) { // gamma5 + } else if (is_a(c.op(0)) || is_a(c.op(0)) || is_a(c.op(0))) { // gamma5/L/R i = _ex0; b = _ex1; } else { // slash object, generate new dummy index @@ -272,7 +284,7 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other } /** Perform automatic simplification on noncommutative product of clifford - * objects. This removes superfluous ONEs, permutes gamma5's to the front + * objects. This removes superfluous ONEs, permutes gamma5/L/R's to the front * and removes squares of gamma objects. */ ex clifford::simplify_ncmul(const exvector & v) const { @@ -290,17 +302,67 @@ ex clifford::simplify_ncmul(const exvector & v) const bool something_changed = false; int sign = 1; - // Anticommute gamma5's to the front + // Anticommute gamma5/L/R's to the front if (s.size() >= 2) { exvector::iterator first = s.begin(), next_to_last = s.end() - 2; while (true) { exvector::iterator it = next_to_last; while (true) { exvector::iterator it2 = it + 1; - if (is_a(*it) && is_a(*it2) && !is_a(it->op(0)) && is_a(it2->op(0))) { - it->swap(*it2); - sign = -sign; - something_changed = true; + if (is_a(*it) && is_a(*it2)) { + ex e1 = it->op(0), e2 = it2->op(0); + + if (is_a(e2)) { + + if (is_a(e1) || is_a(e1)) { + + // gammaL/R gamma5 -> gamma5 gammaL/R + it->swap(*it2); + something_changed = true; + + } else if (!is_a(e1)) { + + // gamma5 gamma5 -> gamma5 gamma5 (do nothing) + // x gamma5 -> -gamma5 x + it->swap(*it2); + sign = -sign; + something_changed = true; + } + + } else if (is_a(e2)) { + + if (is_a(e1)) { + + // gammaR gammaL -> 0 + return _ex0; + + } else if (!is_a(e1) && !is_a(e1)) { + + // gammaL gammaL -> gammaL gammaL (do nothing) + // gamma5 gammaL -> gamma5 gammaL (do nothing) + // x gammaL -> gammaR x + it->swap(*it2); + *it = clifford(diracgammaR(), ex_to(*it).get_representation_label()); + something_changed = true; + } + + } else if (is_a(e2)) { + + if (is_a(e1)) { + + // gammaL gammaR -> 0 + return _ex0; + + } else if (!is_a(e1) && !is_a(e1)) { + + // gammaR gammaR -> gammaR gammaR (do nothing) + // gamma5 gammaR -> gamma5 gammaR (do nothing) + // x gammaR -> gammaL x + it->swap(*it2); + *it = clifford(diracgammaL(), ex_to(*it).get_representation_label()); + something_changed = true; + } + } } if (it == first) break; @@ -320,9 +382,14 @@ ex clifford::simplify_ncmul(const exvector & v) const ex & b = it[1]; if (!is_a(a) || !is_a(b)) continue; - bool a_is_diracgamma = is_a(a.op(0)); - bool b_is_diracgamma = is_a(b.op(0)); + + const ex & ag = a.op(0); + const ex & bg = b.op(0); + bool a_is_diracgamma = is_a(ag); + bool b_is_diracgamma = is_a(bg); + if (a_is_diracgamma && b_is_diracgamma) { + const ex & ia = a.op(1); const ex & ib = b.op(1); if (ia.is_equal(ib)) { // gamma~alpha gamma~alpha -> g~alpha~alpha @@ -330,20 +397,46 @@ ex clifford::simplify_ncmul(const exvector & v) const b = dirac_ONE(representation_label); something_changed = true; } - } else if (is_a(a.op(0)) && is_a(b.op(0))) { + + } else if ((is_a(ag) && is_a(bg))) { + // Remove squares of gamma5 a = dirac_ONE(representation_label); b = dirac_ONE(representation_label); something_changed = true; - } else if (!a_is_diracgamma && !b_is_diracgamma) { - const ex & ba = a.op(0); - const ex & bb = b.op(0); - if (ba.is_equal(bb)) { // a\ a\ -> a^2 - varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to(a.op(1)).get_dim()); - a = indexed(ba, ix) * indexed(bb, ix.toggle_variance()); - b = dirac_ONE(representation_label); - something_changed = true; - } + + } else if ((is_a(ag) && is_a(bg)) + || (is_a(ag) && is_a(bg))) { + + // Remove squares of gammaL/R + b = dirac_ONE(representation_label); + something_changed = true; + + } else if (is_a(ag) && is_a(bg)) { + + // gammaL and gammaR are orthogonal + return _ex0; + + } else if (is_a(ag) && is_a(bg)) { + + // gamma5 gammaL -> -gammaL + a = dirac_ONE(representation_label); + sign = -sign; + something_changed = true; + + } else if (is_a(ag) && is_a(bg)) { + + // gamma5 gammaR -> gammaR + a = dirac_ONE(representation_label); + something_changed = true; + + } else if (!a_is_diracgamma && !b_is_diracgamma && ag.is_equal(bg)) { + + // a\ a\ -> a^2 + varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to(a.op(1)).get_dim()); + a = indexed(ag, ix) * indexed(ag, ix.toggle_variance()); + b = dirac_ONE(representation_label); + something_changed = true; } } } @@ -388,6 +481,16 @@ ex dirac_gamma5(unsigned char rl) return clifford(diracgamma5(), rl); } +ex dirac_gammaL(unsigned char rl) +{ + return clifford(diracgammaL(), rl); +} + +ex dirac_gammaR(unsigned char rl) +{ + return clifford(diracgammaR(), rl); +} + ex dirac_gamma6(unsigned char rl) { return clifford(diracone(), rl) + clifford(diracgamma5(), rl); @@ -460,9 +563,13 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE) { if (is_a(e)) { - if (ex_to(e).get_representation_label() == rl - && is_a(e.op(0))) + if (!ex_to(e).get_representation_label() == rl) + return _ex0; + const ex & g = e.op(0); + if (is_a(g)) return trONE; + else if (is_a(g) || is_a(g)) + return trONE/2; else return _ex0; @@ -484,8 +591,11 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE) if (!is_clifford_tinfo(e.return_type_tinfo(), rl)) return _ex0; - // Expand product, if necessary - ex e_expanded = e.expand(); + // Substitute gammaL/R and expand product, if necessary + ex e_expanded = e.subs(lst( + dirac_gammaL(rl) == (dirac_ONE(rl)-dirac_gamma5(rl))/2, + dirac_gammaR(rl) == (dirac_ONE(rl)+dirac_gamma5(rl))/2 + )).expand(); if (!is_a(e_expanded)) return dirac_trace(e_expanded, rl, trONE); diff --git a/ginac/clifford.h b/ginac/clifford.h index 2d1680c2..2a9e73b1 100644 --- a/ginac/clifford.h +++ b/ginac/clifford.h @@ -52,8 +52,8 @@ public: void print(const print_context & c, unsigned level = 0) const; protected: - bool match_same_type(const basic & other) const; ex simplify_ncmul(const exvector & v) const; + bool match_same_type(const basic & other) const; ex thisexprseq(const exvector & v) const; ex thisexprseq(exvector * vp) const; unsigned return_type(void) const { return return_types::noncommutative; } @@ -104,6 +104,30 @@ public: }; +/** 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 +public: + void print(const print_context & c, unsigned level = 0) 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 +public: + void print(const print_context & c, unsigned level = 0) const; +}; + + // global functions /** Specialization of is_exactly_a(obj) for clifford objects. */ @@ -131,10 +155,20 @@ ex dirac_gamma(const ex & mu, unsigned char rl = 0); * @return newly constructed object */ ex dirac_gamma5(unsigned char rl = 0); -/** This returns (dirac_ONE(rl) + dirac_gamma5(rl)). */ -ex dirac_gamma6(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); -/** This returns (dirac_ONE(rl) - dirac_gamma5(rl)). */ +// These functions are deprecated. Use dirac_gammaL/R() instead. +ex dirac_gamma6(unsigned char rl = 0); ex dirac_gamma7(unsigned char rl = 0); /** Create a term of the form e_mu * gamma~mu with a unique index mu. diff --git a/ginac/tinfos.h b/ginac/tinfos.h index 03b7315e..657a1cd7 100644 --- a/ginac/tinfos.h +++ b/ginac/tinfos.h @@ -82,6 +82,8 @@ const unsigned TINFO_su3d = 0x000e100bU; const unsigned TINFO_diracone = 0x000e100cU; const unsigned TINFO_diracgamma = 0x000e100dU; const unsigned TINFO_diracgamma5 = 0x000e100eU; +const unsigned TINFO_diracgammaL = 0x000e100fU; +const unsigned TINFO_diracgammaR = 0x000e1010U; const unsigned TINFO_wildcard = 0x000f0001U; -- 2.44.0