#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"
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<varidx>(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;
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;
+}
+
+void clifford::print(const print_context & c, unsigned level = 0) const
+{
+ if (!is_a<diracgamma5>(seq[0]) && !is_a<diracgamma>(seq[0]) && !is_a<diracone>(seq[0])) {
+
+ // dirac_slash() object is printed differently
+ if (is_a<print_tree>(c))
+ inherited::print(c, level);
+ else if (is_a<print_latex>(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)
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<clifford>(c));
+ GINAC_ASSERT(c.nops() == 2);
+
+ if (is_a<diracgamma>(c.op(0))) { // proper dirac gamma object
+ i = c.op(1);
+ b = _ex1();
+ } else { // slash object, generate new dummy index
+ varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(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<clifford>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(is_a<diracgamma>(self->op(0)));
+ unsigned char rl = ex_to<clifford>(*self).get_representation_label();
- if (is_ex_of_type(*other, clifford)) {
+ if (is_a<clifford>(*other)) {
- 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) {
// gamma~mu gamma~alpha gamma.mu = (2-dim) gamma~alpha
} else if (other - self == 2
- && is_ex_of_type(self[1], clifford)) {
+ && is_a<clifford>(self[1])) {
*self = 2 - dim;
*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];
+ && is_a<clifford>(self[1])
+ && is_a<clifford>(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<clifford>(self[1])
+ && is_a<clifford>(self[2])
+ && is_a<clifford>(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
// (commutate contracted indices towards each other, simplify_indexed()
// will re-expand and re-run the simplification)
} else {
exvector::iterator it = self + 1, next_to_last = other - 1;
while (it != other) {
- if (!is_ex_of_type(*it, clifford))
+ if (!is_a<clifford>(*it))
return false;
- it++;
+ ++it;
}
it = self + 1;
// 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<diracone>(cit->op(0)))
s.push_back(*cit);
cit++;
}
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<diracgamma5>(it->op(0)) && is_a<diracgamma5>(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)) {
+ while (s.size() >= 2 && is_a<diracgamma5>(s[0].op(0)) && is_a<diracgamma5>(s[1].op(0))) {
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) {
+ if (!is_a<clifford>(it[0]))
+ continue;
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<diracgamma>(a.op(0)) && is_a<diracgamma>(b.op(0))) {
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<diracgamma>(a.op(0)) && !is_a<diracgamma>(b.op(0))) {
+ 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<idx>(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;
ex dirac_gamma(const ex & mu, unsigned char rl)
{
- if (!is_ex_of_type(mu, varidx))
+ if (!is_a<varidx>(mu))
throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
return clifford(diracgamma(), mu, 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()
exvector v(num - 2);
int sign = 1;
ex result;
- for (int i=1; i<num; i++) {
- for (int n=1, j=0; n<num; n++) {
+ for (unsigned i=1; i<num; i++) {
+ for (unsigned n=1, j=0; n<num; n++) {
if (n == i)
continue;
v[j++] = ix[n];
ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
{
- if (is_ex_of_type(e, clifford)) {
+ if (is_a<clifford>(e)) {
- if (ex_to_clifford(e).get_representation_label() == rl
- && is_ex_of_type(e.op(0), diracone))
+ if (ex_to<clifford>(e).get_representation_label() == rl
+ && is_a<diracone>(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.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
// Expand product, if necessary
ex e_expanded = e.expand();
- if (!is_ex_of_type(e_expanded, ncmul))
+ if (!is_a<ncmul>(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<diracgamma5>(e.op(0).op(0));
unsigned num = e.nops();
if (has_gamma5) {
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));
+ 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 * (eps0123(i1, i2, i3, i4) * 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);
+ exvector ix(num-1), bv(num-1);
for (unsigned i=1; i<num; i++)
- ix.push_back(e.op(i).op(1));
+ base_and_index(e.op(i), bv[i-1], ix[i-1]);
num--;
int *iv = new int[num];
ex result;
- for (int i=0; i<num-3; i++) {
+ for (unsigned i=0; i<num-3; i++) {
ex idx1 = ix[i];
- for (int j=i+1; j<num-2; j++) {
+ for (unsigned j=i+1; j<num-2; j++) {
ex idx2 = ix[j];
- for (int k=j+1; k<num-1; k++) {
+ for (unsigned k=j+1; k<num-1; k++) {
ex idx3 = ix[k];
- for (int l=k+1; l<num; l++) {
+ 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 (int n=0, t=4; n<num; n++) {
+ for (unsigned n=0, t=4; n<num; n++) {
if (n == i || n == j || n == k || n == l)
continue;
iv[t++] = n;
}
}
delete[] iv;
- return trONE * I * result;
+ return trONE * I * result * mul(bv);
} else { // no gamma5
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<num; i++)
- iv.push_back(e.op(i).op(1));
+ base_and_index(e.op(i), bv[i], iv[i]);
- return trONE * trace_string(iv.begin(), num);
+ return trONE * (trace_string(iv.begin(), num) * mul(bv)).simplify_indexed();
}
- }
- 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)
// Expand product, if necessary
ex rhs_expanded = rhs.expand();
- if (!is_ex_of_type(rhs_expanded, ncmul)) {
+ if (!is_a<ncmul>(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<clifford>(rhs.op(0)))
continue;
exvector v;
for (unsigned j=0; j<rhs.nops(); j++)
v.push_back(rhs.op(j));
- // Stupid bubble sort because we only want to swap adjacent gammas
+ // 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<diracgamma5>(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));
+ 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;
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
git://www.ginac.de / ginac.git / blobdiff