X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.cpp;h=1b3d034a9c41e6871ebb60aaab6f43de30d70d0e;hp=e62def5047707a969d313bafd0759b37e071112c;hb=de552105d0e4304d869f3d88729b34a613a11b45;hpb=2700b3fa9c3a81236e8ceccb6aa9d5ea5848a1a0 diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp index e62def50..1b3d034a 100644 --- a/ginac/clifford.cpp +++ b/ginac/clifford.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2002 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 @@ -20,21 +20,23 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include +#include + #include "clifford.h" #include "ex.h" #include "idx.h" #include "ncmul.h" #include "symbol.h" #include "numeric.h" // for I +#include "symmetry.h" #include "lst.h" #include "relational.h" +#include "mul.h" #include "print.h" #include "archive.h" -#include "debugmsg.h" #include "utils.h" -#include - namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS(clifford, indexed) @@ -43,12 +45,11 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor) GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma5, tensor) ////////// -// default constructor, destructor, copy constructor assignment operator and helpers +// default ctor, dtor, copy ctor, assignment operator and helpers ////////// clifford::clifford() : representation_label(0) { - debugmsg("clifford default constructor", LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_clifford; } @@ -72,7 +73,6 @@ DEFAULT_CTORS(diracgamma5) * @see dirac_ONE */ clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl) { - debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_clifford; } @@ -81,20 +81,17 @@ clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representatio * @see dirac_gamma */ clifford::clifford(const ex & b, const ex & mu, unsigned char rl) : inherited(b, mu), representation_label(rl) { - debugmsg("clifford constructor from ex,ex", LOGLEVEL_CONSTRUCT); - GINAC_ASSERT(is_ex_of_type(mu, varidx)); + GINAC_ASSERT(is_a(mu)); tinfo_key = TINFO_clifford; } -clifford::clifford(unsigned char rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl) +clifford::clifford(unsigned char rl, const exvector & v, bool discardable) : inherited(sy_none(), v, discardable), representation_label(rl) { - debugmsg("clifford constructor from unsigned char,exvector", LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_clifford; } -clifford::clifford(unsigned char rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl) +clifford::clifford(unsigned char rl, exvector * vp) : inherited(sy_none(), vp), representation_label(rl) { - debugmsg("clifford constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_clifford; } @@ -104,7 +101,6 @@ clifford::clifford(unsigned char rl, exvector * vp) : inherited(indexed::unknown clifford::clifford(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) { - debugmsg("clifford constructor from archive_node", LOGLEVEL_CONSTRUCT); unsigned rl; n.find_unsigned("label", rl); representation_label = rl; @@ -122,12 +118,12 @@ DEFAULT_ARCHIVING(diracgamma) DEFAULT_ARCHIVING(diracgamma5) ////////// -// functions overriding virtual functions from bases classes +// functions overriding virtual functions from base classes ////////// int clifford::compare_same_type(const basic & other) const { - GINAC_ASSERT(other.tinfo() == TINFO_clifford); + GINAC_ASSERT(is_a(other)); const clifford &o = static_cast(other); if (representation_label != o.representation_label) { @@ -138,6 +134,34 @@ int clifford::compare_same_type(const basic & other) const return inherited::compare_same_type(other); } +bool clifford::match_same_type(const basic & other) const +{ + GINAC_ASSERT(is_a(other)); + const clifford &o = static_cast(other); + + return representation_label == o.representation_label; +} + +void clifford::print(const print_context & c, unsigned level) const +{ + if (!is_a(seq[0]) && !is_a(seq[0]) && !is_a(seq[0])) { + + // dirac_slash() object is printed differently + if (is_a(c)) + inherited::print(c, level); + else if (is_a(c)) { + c.s << "{"; + seq[0].print(c, level); + c.s << "\\hspace{-1.0ex}/}"; + } else { + seq[0].print(c, level); + c.s << "\\"; + } + + } else + inherited::print(c, level); +} + DEFAULT_COMPARE(diracone) DEFAULT_COMPARE(diracgamma) DEFAULT_COMPARE(diracgamma5) @@ -146,17 +170,40 @@ DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}") DEFAULT_PRINT_LATEX(diracgamma, "gamma", "\\gamma") DEFAULT_PRINT_LATEX(diracgamma5, "gamma5", "{\\gamma^5}") +/** This function decomposes gamma~mu -> (1, mu) and a\ -> (a.ix, ix) */ +static void base_and_index(const ex & c, ex & b, ex & i) +{ + GINAC_ASSERT(is_a(c)); + GINAC_ASSERT(c.nops() == 2); + + if (is_a(c.op(0))) { // proper dirac gamma object + i = c.op(1); + b = _ex1; + } else if (is_a(c.op(0))) { // gamma5 + i = _ex0; + b = _ex1; + } else { // slash object, generate new dummy index + varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to(c.op(1)).get_dim()); + b = indexed(c.op(0), ix.toggle_variance()); + i = ix; + } +} + /** Contraction of a gamma matrix with something else. */ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const { - GINAC_ASSERT(is_ex_of_type(*self, clifford)); - GINAC_ASSERT(is_ex_of_type(*other, indexed)); - GINAC_ASSERT(is_ex_of_type(self->op(0), diracgamma)); - unsigned char rl = ex_to_clifford(*self).get_representation_label(); + GINAC_ASSERT(is_a(*self)); + GINAC_ASSERT(is_a(*other)); + GINAC_ASSERT(is_a(self->op(0))); + unsigned char rl = ex_to(*self).get_representation_label(); + + if (is_a(*other)) { - if (is_ex_of_type(*other, clifford)) { + // Contraction only makes sense if the represenation labels are equal + if (ex_to(*other).get_representation_label() != rl) + return false; - ex dim = ex_to_idx(self->op(1)).get_dim(); + ex dim = ex_to(self->op(1)).get_dim(); // gamma~mu gamma.mu = dim ONE if (other - self == 1) { @@ -166,19 +213,34 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other // gamma~mu gamma~alpha gamma.mu = (2-dim) gamma~alpha } else if (other - self == 2 - && is_ex_of_type(self[1], clifford)) { + && is_a(self[1])) { *self = 2 - dim; - *other = _ex1(); + *other = _ex1; return true; // gamma~mu gamma~alpha gamma~beta gamma.mu = 4 g~alpha~beta + (dim-4) gamam~alpha gamma~beta } else if (other - self == 3 - && is_ex_of_type(self[1], clifford) - && is_ex_of_type(self[2], clifford)) { - *self = 4 * lorentz_g(self[1].op(1), self[2].op(1)) * dirac_ONE(rl) + (dim - 4) * self[1] * self[2]; - self[1] = _ex1(); - self[2] = _ex1(); - *other = _ex1(); + && is_a(self[1]) + && is_a(self[2])) { + ex b1, i1, b2, i2; + base_and_index(self[1], b1, i1); + base_and_index(self[2], b2, i2); + *self = 4 * lorentz_g(i1, i2) * b1 * b2 * dirac_ONE(rl) + (dim - 4) * self[1] * self[2]; + self[1] = _ex1; + self[2] = _ex1; + *other = _ex1; + return true; + + // gamma~mu gamma~alpha gamma~beta gamma~delta gamma.mu = -2 gamma~delta gamma~beta gamma~alpha - (dim-4) gamam~alpha gamma~beta gamma~delta + } else if (other - self == 4 + && is_a(self[1]) + && is_a(self[2]) + && is_a(self[3])) { + *self = -2 * self[3] * self[2] * self[1] - (dim - 4) * self[1] * self[2] * self[3]; + self[1] = _ex1; + self[2] = _ex1; + self[3] = _ex1; + *other = _ex1; return true; // gamma~mu S gamma~alpha gamma.mu = 2 gamma~alpha S - gamma~mu S gamma.mu gamma~alpha @@ -187,21 +249,21 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other } else { exvector::iterator it = self + 1, next_to_last = other - 1; while (it != other) { - if (!is_ex_of_type(*it, clifford)) + if (!is_a(*it)) return false; - it++; + ++it; } it = self + 1; - ex S = _ex1(); + ex S = _ex1; while (it != next_to_last) { S *= *it; - *it++ = _ex1(); + *it++ = _ex1; } *self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last); - *next_to_last = _ex1(); - *other = _ex1(); + *next_to_last = _ex1; + *other = _ex1; return true; } } @@ -220,7 +282,7 @@ ex clifford::simplify_ncmul(const exvector & v) const // Remove superfluous ONEs exvector::const_iterator cit = v.begin(), citend = v.end(); while (cit != citend) { - if (!is_ex_of_type(cit->op(0), diracone)) + if (!is_a(*cit) || !is_a(cit->op(0))) s.push_back(*cit); cit++; } @@ -235,47 +297,58 @@ ex clifford::simplify_ncmul(const exvector & v) const exvector::iterator it = next_to_last; while (true) { exvector::iterator it2 = it + 1; - if (!is_ex_of_type(it->op(0), diracgamma5) && is_ex_of_type(it2->op(0), diracgamma5)) { + 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 (it == first) break; - it--; + --it; } if (next_to_last == first) break; - next_to_last--; + --next_to_last; } } - // Remove squares of gamma5 - while (s.size() >= 2 && is_ex_of_type(s[0].op(0), diracgamma5) && is_ex_of_type(s[1].op(0), diracgamma5)) { - s.erase(s.begin(), s.begin() + 2); - something_changed = true; - } - // Remove equal adjacent gammas if (s.size() >= 2) { - exvector::iterator it = s.begin(), itend = s.end() - 1; - while (it != itend) { + exvector::iterator it, itend = s.end() - 1; + for (it = s.begin(); it != itend; ++it) { ex & a = it[0]; ex & b = it[1]; - if (is_ex_of_type(a.op(0), diracgamma) && is_ex_of_type(b.op(0), diracgamma)) { + 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)); + if (a_is_diracgamma && b_is_diracgamma) { const ex & ia = a.op(1); const ex & ib = b.op(1); - if (ia.is_equal(ib)) { + if (ia.is_equal(ib)) { // gamma~alpha gamma~alpha -> g~alpha~alpha a = lorentz_g(ia, ib); b = dirac_ONE(representation_label); something_changed = true; } + } else if (is_a(a.op(0)) && is_a(b.op(0))) { + // 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; + } } - it++; } } - if (s.size() == 0) + if (s.empty()) return clifford(diracone(), representation_label) * sign; if (something_changed) return nonsimplified_ncmul(s) * sign; @@ -304,7 +377,7 @@ ex dirac_ONE(unsigned char rl) ex dirac_gamma(const ex & mu, unsigned char rl) { - if (!is_ex_of_type(mu, varidx)) + if (!is_a(mu)) throw(std::invalid_argument("index of Dirac gamma must be of type varidx")); return clifford(diracgamma(), mu, rl); @@ -327,8 +400,10 @@ ex dirac_gamma7(unsigned char rl) ex dirac_slash(const ex & e, const ex & dim, unsigned char rl) { - varidx mu((new symbol)->setflag(status_flags::dynallocated), dim); - return indexed(e, mu.toggle_variance()) * dirac_gamma(mu, rl); + // Slashed vectors are actually stored as a clifford object with the + // vector as its base expression and a (dummy) index that just serves + // for storing the space dimensionality + return clifford(e, varidx(0, dim), rl); } /** Check whether a given tinfo key (as returned by return_type_tinfo() @@ -369,8 +444,8 @@ static ex trace_string(exvector::const_iterator ix, unsigned num) exvector v(num - 2); int sign = 1; ex result; - for (int i=1; i(e)) { - if (ex_to_clifford(e).get_representation_label() == rl - && is_ex_of_type(e.op(0), diracone)) + if (ex_to(e).get_representation_label() == rl + && is_a(e.op(0))) return trONE; else - return _ex0(); - - } else if (is_ex_exactly_of_type(e, add)) { - - // Trace of sum = sum of traces - ex sum = _ex0(); - for (unsigned i=0; i(e_expanded)) return dirac_trace(e_expanded, rl, trONE); // gamma5 gets moved to the front so this check is enough - bool has_gamma5 = is_ex_of_type(e.op(0).op(0), diracgamma5); + bool has_gamma5 = is_a(e.op(0).op(0)); unsigned num = e.nops(); if (has_gamma5) { @@ -432,68 +498,84 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE) // Trace of gamma5 * odd number of gammas and trace of // gamma5 * gamma.mu * gamma.nu are zero if ((num & 1) == 0 || num == 3) - return _ex0(); + return _ex0; // Tr gamma5 gamma.mu gamma.nu gamma.rho gamma.sigma = 4I * epsilon(mu, nu, rho, sigma) - if (num == 5) - return trONE * I * eps0123(e.op(1).op(1), e.op(2).op(1), e.op(3).op(1), e.op(4).op(1)); + // (the epsilon is always 4-dimensional) + if (num == 5) { + ex b1, i1, b2, i2, b3, i3, b4, i4; + base_and_index(e.op(1), b1, i1); + base_and_index(e.op(2), b2, i2); + base_and_index(e.op(3), b3, i3); + base_and_index(e.op(4), b4, i4); + return trONE * I * (lorentz_eps(ex_to(i1).replace_dim(_ex4), ex_to(i2).replace_dim(_ex4), ex_to(i3).replace_dim(_ex4), ex_to(i4).replace_dim(_ex4)) * b1 * b2 * b3 * b4).simplify_indexed(); + } // Tr gamma5 S_2k = // I/4! * epsilon0123.mu1.mu2.mu3.mu4 * Tr gamma.mu1 gamma.mu2 gamma.mu3 gamma.mu4 S_2k - exvector ix; - ix.reserve(num - 1); + // (the epsilon is always 4-dimensional) + exvector ix(num-1), bv(num-1); for (unsigned i=1; i(idx1).replace_dim(_ex4), ex_to(idx2).replace_dim(_ex4), ex_to(idx3).replace_dim(_ex4), ex_to(idx4).replace_dim(_ex4)) * trace_string(v.begin(), num - 4); } } } } delete[] iv; - return trONE * I * result; + return trONE * I * result * mul(bv); } else { // no gamma5 // Trace of odd number of gammas is zero if ((num & 1) == 1) - return _ex0(); + return _ex0; // Tr gamma.mu gamma.nu = 4 g.mu.nu - if (num == 2) - return trONE * lorentz_g(e.op(0).op(1), e.op(1).op(1)); + if (num == 2) { + ex b1, i1, b2, i2; + base_and_index(e.op(0), b1, i1); + base_and_index(e.op(1), b2, i2); + return trONE * (lorentz_g(i1, i2) * b1 * b2).simplify_indexed(); + } - exvector iv; - iv.reserve(num); + exvector iv(num), bv(num); for (unsigned i=0; i 0) { + + // Trace maps to all other container classes (this includes sums) + pointer_to_map_function_2args fcn(dirac_trace, rl, trONE); + return e.map(fcn); + + } else + return _ex0; } ex canonicalize_clifford(const ex & e) @@ -512,11 +594,11 @@ ex canonicalize_clifford(const ex & e) // Expand product, if necessary ex rhs_expanded = rhs.expand(); - if (!is_ex_of_type(rhs_expanded, ncmul)) { + if (!is_a(rhs_expanded)) { srl.let_op(i) = (lhs == canonicalize_clifford(rhs_expanded)); continue; - } else if (!is_ex_of_type(rhs.op(0), clifford)) + } else if (!is_a(rhs.op(0))) continue; exvector v; @@ -526,13 +608,16 @@ ex canonicalize_clifford(const ex & e) // Stupid recursive bubble sort because we only want to swap adjacent gammas exvector::iterator it = v.begin(), next_to_last = v.end() - 1; - if (is_ex_of_type(it->op(0), diracgamma5)) - it++; + if (is_a(it->op(0))) + ++it; while (it != next_to_last) { - if (it[0].op(1).compare(it[1].op(1)) > 0) { + if (it[0].compare(it[1]) > 0) { ex save0 = it[0], save1 = it[1]; - it[0] = lorentz_g(it[0].op(1), it[1].op(1)); - it[1] = _ex2(); + ex b1, i1, b2, i2; + base_and_index(it[0], b1, i1); + base_and_index(it[1], b2, i2); + it[0] = (lorentz_g(i1, i2) * b1 * b2).simplify_indexed(); + it[1] = _ex2; ex sum = ncmul(v); it[0] = save1; it[1] = save0; @@ -540,12 +625,12 @@ ex canonicalize_clifford(const ex & e) srl.let_op(i) = (lhs == canonicalize_clifford(sum)); goto next_sym; } - it++; + ++it; } next_sym: ; } } - return aux.subs(srl); + return aux.subs(srl).simplify_indexed(); } } // namespace GiNaC