def _trace_single_line1(t):
t = t.sorted_components()
components = t.components
ncomps = len(components)
g = LorentzIndex.metric
# gamma matirices are in a[i:j]
hit = 0
for i in range(ncomps):
if components[i] == GammaMatrix:
hit = 1
break
for j in range(i + hit, ncomps):
if components[j] != GammaMatrix:
break
else:
j = ncomps
numG = j - i
if numG == 0:
tcoeff = t.coeff
return t.nocoeff if tcoeff else t
if numG % 2 == 1:
return TensMul.from_data(S.Zero, [], [], [])
elif numG > 4:
# find the open matrix indices and connect them:
a = t.split()
ind1 = a[i].get_indices()[0]
ind2 = a[i + 1].get_indices()[0]
aa = a[:i] + a[i + 2:]
t1 = tensor_mul(*aa) * g(ind1, ind2)
t1 = t1.contract_metric(g)
args = [t1]
sign = 1
for k in range(i + 2, j):
sign = -sign
ind2 = a[k].get_indices()[0]
aa = a[:i] + a[i + 1:k] + a[k + 1:]
t2 = sign * tensor_mul(*aa) * g(ind1, ind2)
t2 = t2.contract_metric(g)
t2 = simplify_gpgp(t2, False)
args.append(t2)
t3 = TensAdd(*args)
t3 = _trace_single_line(t3)
return t3
else:
a = t.split()
t1 = _gamma_trace1(*a[i:j])
a2 = a[:i] + a[j:]
t2 = tensor_mul(*a2)
t3 = t1 * t2
if not t3:
return t3
t3 = t3.contract_metric(g)
return t3
def _trace_single_line1(t):
t = t.sorted_components()
components = t.components
ncomps = len(components)
g = LorentzIndex.metric
# gamma matirices are in a[i:j]
hit = 0
for i in range(ncomps):
if components[i] == GammaMatrix:
hit = 1
break
for j in range(i + hit, ncomps):
if components[j] != GammaMatrix:
break
else:
j = ncomps
numG = j - i
if numG == 0:
tcoeff = t.coeff
return t.nocoeff if tcoeff else t
if numG % 2 == 1:
return TensMul.from_data(S.Zero, [], [], [])
elif numG > 4:
# find the open matrix indices and connect them:
a = t.split()
ind1 = a[i].get_indices()[0]
ind2 = a[i + 1].get_indices()[0]
aa = a[:i] + a[i + 2:]
t1 = tensor_mul(*aa)*g(ind1, ind2)
t1 = t1.contract_metric(g)
args = [t1]
sign = 1
for k in range(i + 2, j):
sign = -sign
ind2 = a[k].get_indices()[0]
aa = a[:i] + a[i + 1:k] + a[k + 1:]
t2 = sign*tensor_mul(*aa)*g(ind1, ind2)
t2 = t2.contract_metric(g)
t2 = simplify_gpgp(t2, False)
args.append(t2)
t3 = TensAdd(*args)
t3 = _trace_single_line(t3)
return t3
else:
a = t.split()
t1 = _gamma_trace1(*a[i:j])
a2 = a[:i] + a[j:]
t2 = tensor_mul(*a2)
t3 = t1*t2
if not t3:
return t3
t3 = t3.contract_metric(g)
return t3
def _trace_single_line1(t):
t = t.sorted_components()
components = t.components
ncomps = len(components)
g = self.LorentzIndex.metric
sg = DiracSpinorIndex.delta
# gamma matirices are in a[i:j]
hit = 0
for i in range(ncomps):
if isinstance(components[i], GammaMatrixHead):
hit = 1
break
for j in range(i + hit, ncomps):
if not isinstance(components[j], GammaMatrixHead):
break
else:
j = ncomps
numG = j - i
if numG == 0:
spinor_free = [_[0] for _ in t._tids.free if _[0].tensortype is DiracSpinorIndex]
tcoeff = t.coeff
if spinor_free == [DiracSpinorIndex.auto_left, -DiracSpinorIndex.auto_right]:
t = t*DiracSpinorIndex.delta(-DiracSpinorIndex.auto_left, DiracSpinorIndex.auto_right)
t = t.contract_metric(sg)
return t/tcoeff if tcoeff else t
else:
return t/tcoeff if tcoeff else t
if numG % 2 == 1:
return TensMul.from_data(S.Zero, [], [], [])
elif numG > 4:
t = t.substitute_indices((-DiracSpinorIndex.auto_right, -DiracSpinorIndex.auto_index), (DiracSpinorIndex.auto_left, DiracSpinorIndex.auto_index))
a = t.split()
ind1, lind1, rind1 = a[i].args[-1]
ind2, lind2, rind2 = a[i + 1].args[-1]
aa = a[:i] + a[i + 2:]
t1 = tensor_mul(*aa)*g(ind1, ind2)*sg(lind1, rind1)*sg(lind2, rind2)
t1 = t1.contract_metric(g)
t1 = t1.contract_metric(sg)
args = [t1]
sign = 1
for k in range(i + 2, j):
sign = -sign
ind2, lind2, rind2 = a[k].args[-1]
aa = a[:i] + a[i + 1:k] + a[k + 1:]
t2 = sign*tensor_mul(*aa)*g(ind1, ind2)*sg(lind1, rind1)*sg(lind2, rind2)
t2 = t2.contract_metric(g)
t2 = t2.contract_metric(sg)
t2 = GammaMatrixHead.simplify_gpgp(t2, False)
args.append(t2)
t3 = TensAdd(*args)
#aa = _tensorlist_contract_metric(aa, g(ind1, ind2))
#t3 = t3.canon_bp()
t3 = self._trace_single_line(t3)
return t3
else:
a = t.split()
if len(t.components) == 1:
if t.components[0] is DiracSpinorIndex.delta:
return 4 # FIXME only for D=4
t1 = self._gamma_trace1(*a[i:j])
a2 = a[:i] + a[j:]
t2 = tensor_mul(*a2)
t3 = t1*t2
if not t3:
return t3
t3 = t3.contract_metric(g)
return t3
