#include "ncmul.h"
#include "symbol.h"
#include "numeric.h" // for I
+#include "symmetry.h"
+#include "lst.h"
+#include "relational.h"
#include "print.h"
#include "archive.h"
#include "debugmsg.h"
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;
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_of_type(other, clifford));
const clifford &o = static_cast<const clifford &>(other);
if (representation_label != o.representation_label) {
return inherited::compare_same_type(other);
}
+bool clifford::match_same_type(const basic & other) const
+{
+ GINAC_ASSERT(is_of_type(other, clifford));
+ const clifford &o = static_cast<const clifford &>(other);
+
+ return representation_label == o.representation_label;
+}
+
DEFAULT_COMPARE(diracone)
DEFAULT_COMPARE(diracgamma)
DEFAULT_COMPARE(diracgamma5)
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();
+ unsigned char rl = ex_to<clifford>(*self).get_representation_label();
if (is_ex_of_type(*other, clifford)) {
- ex dim = ex_to_idx(self->op(1)).get_dim();
+ ex dim = ex_to<idx>(self->op(1)).get_dim();
// gamma~mu gamma.mu = dim ONE
if (other - self == 1) {
while (it != other) {
if (!is_ex_of_type(*it, clifford))
return false;
- it++;
+ ++it;
}
it = self + 1;
}
if (it == first)
break;
- it--;
+ --it;
}
if (next_to_last == first)
break;
- next_to_last--;
+ --next_to_last;
}
}
something_changed = true;
}
}
- it++;
+ ++it;
}
}
- if (s.size() == 0)
+ if (s.empty())
return clifford(diracone(), representation_label) * sign;
if (something_changed)
return nonsimplified_ncmul(s) * sign;
return ti == (TINFO_clifford + rl);
}
+/** Check whether a given tinfo key (as returned by return_type_tinfo()
+ * is that of a clifford object (with an arbitrary representation label). */
+static bool is_clifford_tinfo(unsigned ti)
+{
+ return (ti & ~0xff) == TINFO_clifford;
+}
+
+/** Take trace of a string of an even number of Dirac gammas given a vector
+ * of indices. */
+static ex trace_string(exvector::const_iterator ix, unsigned num)
+{
+ // Tr gamma.mu gamma.nu = 4 g.mu.nu
+ if (num == 2)
+ return lorentz_g(ix[0], ix[1]);
+
+ // Tr gamma.mu gamma.nu gamma.rho gamma.sig = 4 (g.mu.nu g.rho.sig + g.nu.rho g.mu.sig - g.mu.rho g.nu.sig
+ else if (num == 4)
+ return lorentz_g(ix[0], ix[1]) * lorentz_g(ix[2], ix[3])
+ + lorentz_g(ix[1], ix[2]) * lorentz_g(ix[0], ix[3])
+ - lorentz_g(ix[0], ix[2]) * lorentz_g(ix[1], ix[3]);
+
+ // Traces of 6 or more gammas are computed recursively:
+ // Tr gamma.mu1 gamma.mu2 ... gamma.mun =
+ // + g.mu1.mu2 * Tr gamma.mu3 ... gamma.mun
+ // - g.mu1.mu3 * Tr gamma.mu2 gamma.mu4 ... gamma.mun
+ // + g.mu1.mu4 * Tr gamma.mu3 gamma.mu3 gamma.mu5 ... gamma.mun
+ // - ...
+ // + g.mu1.mun * Tr gamma.mu2 ... gamma.mu(n-1)
+ exvector v(num - 2);
+ int sign = 1;
+ ex result;
+ for (unsigned i=1; i<num; i++) {
+ for (unsigned n=1, j=0; n<num; n++) {
+ if (n == i)
+ continue;
+ v[j++] = ix[n];
+ }
+ result += sign * lorentz_g(ix[0], ix[i]) * trace_string(v.begin(), num-2);
+ sign = -sign;
+ }
+ return result;
+}
+
ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
{
if (is_ex_of_type(e, clifford)) {
- if (ex_to_clifford(e).get_representation_label() == rl
+ if (ex_to<clifford>(e).get_representation_label() == rl
&& is_ex_of_type(e.op(0), diracone))
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.nops(); i++)
- sum += dirac_trace(e.op(i), rl, trONE);
- return sum;
-
} else if (is_ex_exactly_of_type(e, mul)) {
// Trace of product: pull out non-clifford factors
ex prod = _ex1();
for (unsigned i=0; i<e.nops(); i++) {
const ex &o = e.op(i);
- unsigned ti = o.return_type_tinfo();
if (is_clifford_tinfo(o.return_type_tinfo(), rl))
prod *= dirac_trace(o, rl, trONE);
else
if ((num & 1) == 0 || num == 3)
return _ex0();
- // Tr gamma5 S_2k =
- // I/4! * epsilon0123.mu1.mu2.mu3.mu4 * Tr gamma.mu1 gamma.mu2 gamma.mu3 gamma.mu4 S_2k
- ex dim = ex_to_idx(e.op(1).op(1)).get_dim();
- varidx mu1((new symbol)->setflag(status_flags::dynallocated), dim),
- mu2((new symbol)->setflag(status_flags::dynallocated), dim),
- mu3((new symbol)->setflag(status_flags::dynallocated), dim),
- mu4((new symbol)->setflag(status_flags::dynallocated), dim);
- exvector v;
- v.reserve(num + 3);
- v.push_back(dirac_gamma(mu1, rl));
- v.push_back(dirac_gamma(mu2, rl));
- v.push_back(dirac_gamma(mu3, rl));
- v.push_back(dirac_gamma(mu4, rl));
- for (int i=1; i<num; i++)
- v.push_back(e.op(i));
+ // 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));
- return (eps0123(mu1.toggle_variance(), mu2.toggle_variance(), mu3.toggle_variance(), mu4.toggle_variance()) *
- dirac_trace(ncmul(v), rl, trONE)).simplify_indexed() * I / 24;
+ // 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);
+ for (unsigned i=1; i<num; i++)
+ ix.push_back(e.op(i).op(1));
+ num--;
+ int *iv = new int[num];
+ ex result;
+ for (unsigned i=0; i<num-3; i++) {
+ ex idx1 = ix[i];
+ for (unsigned j=i+1; j<num-2; j++) {
+ ex idx2 = ix[j];
+ for (unsigned k=j+1; k<num-1; k++) {
+ ex idx3 = ix[k];
+ for (unsigned l=k+1; l<num; l++) {
+ ex idx4 = ix[l];
+ iv[0] = i; iv[1] = j; iv[2] = k; iv[3] = l;
+ exvector v;
+ v.reserve(num - 4);
+ for (unsigned n=0, t=4; n<num; n++) {
+ if (n == i || n == j || n == k || n == l)
+ continue;
+ iv[t++] = n;
+ v.push_back(ix[n]);
+ }
+ int sign = permutation_sign(iv, iv + num);
+ result += sign * eps0123(idx1, idx2, idx3, idx4)
+ * trace_string(v.begin(), num - 4);
+ }
+ }
+ }
+ }
+ delete[] iv;
+ return trONE * I * result;
} else { // no gamma5
if (num == 2)
return trONE * lorentz_g(e.op(0).op(1), e.op(1).op(1));
- // Traces of 4 or more gammas are computed recursively:
- // Tr gamma.mu1 gamma.mu2 ... gamma.mun =
- // + g.mu1.mu2 * Tr gamma.mu3 ... gamma.mun
- // - g.mu1.mu3 * Tr gamma.mu2 gamma.mu4 ... gamma.mun
- // + g.mu1.mu4 * Tr gamma.mu3 gamma.mu3 gamma.mu5 ... gamma.mun
- // - ...
- // + g.mu1.mun * Tr gamma.mu2 ... gamma.mu(n-1)
- exvector v(num - 2);
- int sign = 1;
- const ex &ix1 = e.op(0).op(1);
- ex result;
- for (int i=1; i<num; i++) {
- for (int n=1, j=0; n<num; n++) {
- if (n == i)
- continue;
- v[j++] = e.op(n);
- }
- result += sign * lorentz_g(ix1, e.op(i).op(1)) * dirac_trace(ncmul(v), rl, trONE);
- sign = -sign;
- }
- return result;
+ exvector iv;
+ iv.reserve(num);
+ for (unsigned i=0; i<num; i++)
+ iv.push_back(e.op(i).op(1));
+
+ return trONE * trace_string(iv.begin(), num);
}
- }
- return _ex0();
+ } else if (e.nops() > 0) {
+
+ // Trace maps to all other container classes (this includes sums)
+ pointer_to_map_function_2args<unsigned char, const ex &> fcn(dirac_trace, rl, trONE);
+ return e.map(fcn);
+
+ } else
+ return _ex0();
}
ex canonicalize_clifford(const ex & e)
{
- if (is_ex_exactly_of_type(e, add)) {
+ // Scan for any ncmul objects
+ lst srl;
+ ex aux = e.to_rational(srl);
+ for (unsigned i=0; i<srl.nops(); i++) {
- ex sum = _ex0();
- for (unsigned i=0; i<e.nops(); i++)
- sum += canonicalize_clifford(e.op(i));
- return sum;
+ ex lhs = srl.op(i).lhs();
+ ex rhs = srl.op(i).rhs();
- } else if (is_ex_exactly_of_type(e, mul)) {
+ if (is_ex_exactly_of_type(rhs, ncmul)
+ && rhs.return_type() == return_types::noncommutative
+ && is_clifford_tinfo(rhs.return_type_tinfo())) {
- ex prod = _ex1();
- for (unsigned i=0; i<e.nops(); i++)
- prod *= canonicalize_clifford(e.op(i));
- return prod;
+ // Expand product, if necessary
+ ex rhs_expanded = rhs.expand();
+ if (!is_ex_of_type(rhs_expanded, ncmul)) {
+ srl.let_op(i) = (lhs == canonicalize_clifford(rhs_expanded));
+ continue;
- } else if (is_ex_exactly_of_type(e, ncmul)) {
+ } else if (!is_ex_of_type(rhs.op(0), clifford))
+ continue;
- // Expand product, if necessary
- ex e_expanded = e.expand();
- if (!is_ex_of_type(e_expanded, ncmul))
- return canonicalize_clifford(e_expanded);
-
- if (!is_ex_of_type(e.op(0), clifford))
- return e;
-
- exvector v;
- v.reserve(e.nops());
- for (int i=0; i<e.nops(); i++)
- v.push_back(e.op(i));
-
- // Stupid 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++;
- while (it != next_to_last) {
- if (it[0].op(1).compare(it[1].op(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 sum = ncmul(v);
- it[0] = save1;
- it[1] = save0;
- sum -= ncmul(v);
- return canonicalize_clifford(sum);
+ exvector v;
+ v.reserve(rhs.nops());
+ for (unsigned j=0; j<rhs.nops(); j++)
+ v.push_back(rhs.op(j));
+
+ // 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;
+ while (it != next_to_last) {
+ if (it[0].op(1).compare(it[1].op(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 sum = ncmul(v);
+ it[0] = save1;
+ it[1] = save0;
+ sum -= ncmul(v, true);
+ srl.let_op(i) = (lhs == canonicalize_clifford(sum));
+ goto next_sym;
+ }
+ ++it;
}
- it++;
+next_sym: ;
}
- return ncmul(v);
}
-
- return e;
+ return aux.subs(srl);
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff