#include "ex.h"
#include "idx.h"
#include "ncmul.h"
+#include "symbol.h"
#include "print.h"
#include "archive.h"
#include "debugmsg.h"
/** 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, indexed));
+ 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();
if (is_ex_of_type(other->op(0), diracgamma)) {
// gamma~mu*gamma.mu = dim*ONE
if (other - self == 1) {
*self = dim;
- *other = dirac_ONE();
+ *other = dirac_ONE(rl);
return true;
// gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
} else if (other - self == 3
&& is_ex_of_type(self[1], clifford)
&& is_ex_of_type(self[2], clifford)) {
- *self = 4 * metric_tensor(self[1].op(1), self[2].op(1)) * dirac_ONE() + (dim - 4) * self[1] * self[2];
+ *self = 4 * metric_tensor(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();
{
exvector s;
s.reserve(v.size());
+ unsigned rl = ex_to_clifford(v[0]).get_representation_label();
// Remove superfluous ONEs
exvector::const_iterator cit = v.begin(), citend = v.end();
const ex & ib = b.op(1);
if (ia.is_equal(ib)) {
a = lorentz_g(ia, ib);
- b = dirac_ONE();
+ b = dirac_ONE(rl);
something_changed = true;
}
}
}
if (s.size() == 0)
- return clifford(diracone()) * sign;
+ return clifford(diracone(), rl) * sign;
if (something_changed)
return nonsimplified_ncmul(s) * sign;
else
return clifford(diracgamma5(), 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);
+}
+
+/** Check whether a given tinfo key (as returned by return_type_tinfo()
+ * is that of a clifford object with the specified representation label. */
+static bool is_clifford_tinfo(unsigned ti, unsigned char rl)
+{
+ return ti == (TINFO_clifford + rl);
+}
+
+ex dirac_trace(const ex & e, unsigned char rl)
+{
+ if (is_ex_of_type(e, clifford)) {
+
+ if (ex_to_clifford(e).get_representation_label() == rl
+ && is_ex_of_type(e.op(0), diracone))
+ return _ex4();
+ 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);
+ 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);
+ else
+ prod *= o;
+ }
+ return prod;
+
+ } else if (is_ex_exactly_of_type(e, ncmul)) {
+
+ if (!is_clifford_tinfo(e.return_type_tinfo(), rl))
+ return _ex0();
+
+ // Expand product, if necessary
+ ex e_expanded = e.expand();
+ if (!is_ex_of_type(e_expanded, ncmul))
+ return dirac_trace(e_expanded, rl);
+
+ // gamma5 gets moved to the front so this check is enough
+ bool has_gamma5 = is_ex_of_type(e.op(0).op(0), diracgamma5);
+ unsigned num = e.nops();
+
+ if (has_gamma5) {
+
+ // 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();
+
+ // Tr gamma5 S_2k =
+ // 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));
+
+ return (eps0123(mu1.toggle_variance(), mu2.toggle_variance(), mu3.toggle_variance(), mu4.toggle_variance()) *
+ dirac_trace(ncmul(v), rl)).simplify_indexed() / 24;
+
+ } else { // no gamma5
+
+ // Trace of odd number of gammas is zero
+ if ((num & 1) == 1)
+ return _ex0();
+
+ // Tr gamma_mu gamma_nu = 4 g_mu_nu
+ if (num == 2)
+ return 4 * 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 =
+ // + eta_mu1_mu2 * Tr gamma_mu3 ... gamma_mun
+ // - eta_mu1_mu3 * Tr gamma_mu2 gamma_mu4 ... gamma_mun
+ // + eta_mu1_mu4 * Tr gamma_mu3 gamma_mu3 gamma_mu5 ... gamma_mun
+ // - ...
+ // + eta_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);
+ sign = -sign;
+ }
+ return result;
+ }
+ }
+
+ return _ex0();
+}
+
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff