def __init__(self, i, j):
il = lorentz_key(i) if (i < 0) else i
jl = lorentz_key(j) if (j < 0) else j
array = [
tensor([
tensor([1], None),
tensor([0], None),
tensor([0], None),
tensor([0], None)
], jl),
tensor([
tensor([0], None),
tensor([-1], None),
tensor([0], None),
tensor([0], None)
], jl),
tensor([
tensor([0], None),
tensor([0], None),
tensor([-1], None),
tensor([0], None)
], jl),
tensor([
tensor([0], None),
tensor([0], None),
tensor([0], None),
tensor([-1], None)
], jl)
]
super(Metric, self).__init__(array, il)
def __init__(self,i,j):
il = lorentz_key(i) if (i<0) else i
jl = lorentz_key(j) if (j<0) else j
array = [tensor([tensor([ 1], None), tensor([ 0], None), tensor([ 0], None), tensor([ 0], None)], jl),
tensor([tensor([ 0], None), tensor([-1], None), tensor([ 0], None), tensor([ 0], None)], jl),
tensor([tensor([ 0], None), tensor([ 0], None), tensor([-1], None), tensor([ 0], None)], jl),
tensor([tensor([ 0], None), tensor([ 0], None), tensor([ 0], None), tensor([-1], None)], jl)]
super(Metric,self).__init__(array,il)
def __init__(self,i,j,k,l):
perms = list(permutations([0,1,2,3]))
il = lorentz_key(i) if (i<0) else i
jl = lorentz_key(j) if (j<0) else j
kl = lorentz_key(k) if (k<0) else k
ll = lorentz_key(l) if (l<0) else l
tmp = new(il, 4,{jl:4,kl:4,ll:4})
for perm in perms:
tmp.__setitem__({il:perm[0], jl:perm[1], kl:perm[2], ll:perm[3]},
tensor([parity(list(perm))], None))
super(Epsilon,self).__init__(tmp._array, tmp._toplevel_key)
def __init__(self, mu, i, j):
mul = lorentz_key(mu) if (mu<0) else mu
array = [gamma_0(i,j),
gamma_1(i,j),
gamma_2(i,j),
gamma_3(i,j),]
super(Gamma,self).__init__(array, mul)
def __init__(self, mu, i, j):
mul = lorentz_key(mu) if (mu < 0) else mu
array = [
gamma_0(i, j),
gamma_1(i, j),
gamma_2(i, j),
gamma_3(i, j),
]
super(Gamma, self).__init__(array, mul)
def __init__(self, i, j, k, l):
perms = list(permutations([0, 1, 2, 3]))
il = lorentz_key(i) if (i < 0) else i
jl = lorentz_key(j) if (j < 0) else j
kl = lorentz_key(k) if (k < 0) else k
ll = lorentz_key(l) if (l < 0) else l
tmp = new(il, 4, {jl: 4, kl: 4, ll: 4})
for perm in perms:
tmp.__setitem__(
{
il: perm[0],
jl: perm[1],
kl: perm[2],
ll: perm[3]
}, tensor([parity(list(perm))], None))
super(Epsilon, self).__init__(tmp._array, tmp._toplevel_key)
def __init__(self,i,n):
# our inde scheme starts at 0, so subtract 1 from n
# when naming the momenta
k = n-1
il = lorentz_key(i) if (i<0) else i
p_str = "p{0}[{1}]"
array = [tensor([c_variable(p_str.format(k,vect_gauge_dict[0]))], None),
tensor([c_variable(p_str.format(k,vect_gauge_dict[1]))], None),
tensor([c_variable(p_str.format(k,vect_gauge_dict[2]))], None),
tensor([c_variable(p_str.format(k,vect_gauge_dict[3]))], None)]
super(P,self).__init__(array,il)
def __init__(self, i, n):
# our inde scheme starts at 0, so subtract 1 from n
# when naming the momenta
k = n - 1
il = lorentz_key(i) if (i < 0) else i
p_str = "p{0}[{1}]"
array = [
tensor([c_variable(p_str.format(k, vect_gauge_dict[0]))], None),
tensor([c_variable(p_str.format(k, vect_gauge_dict[1]))], None),
tensor([c_variable(p_str.format(k, vect_gauge_dict[2]))], None),
tensor([c_variable(p_str.format(k, vect_gauge_dict[3]))], None)
]
super(P, self).__init__(array, il)
def __init__(self, i, n):
# our inde scheme starts at 0, so subtract 1 from n
# when naming the momenta
k = n - 1
il = lorentz_key(i) if (i < 0) else i
p_str = "p{0}{1}"
array = [
tensor([parse_expr(p_str.format(k, 0))], None),
tensor([parse_expr(p_str.format(k, 1))], None),
tensor([parse_expr(p_str.format(k, 2))], None),
tensor([parse_expr(p_str.format(k, 3))], None)
]
super(P, self).__init__(array, il)
test *= int(anticomm[{
'mu': ind,
'nu': ind,
'i': i,
'j': i
}]._array[0] == -2)
for i in range(4):
test *= int(anticomm[{'mu': 0, 'nu': 0, 'i': i, 'j': i}]._array[0] == 2)
require(test, "Dirac matrix anticommutator")
vector = tensor([
tensor([2], None),
tensor([0], None),
tensor([0], None),
tensor([2], None)
], lorentz_key('mu_5'))
vector2 = tensor([
tensor([2], None),
tensor([0], None),
tensor([0], None),
tensor([2], None)
], lorentz_key('mu_5'))
require(((vector * vector2)._array[0] == 0), "Mass")
vector = tensor([
tensor([2], None),
tensor([0], None),
tensor([0], None),
tensor([2], None)
], lorentz_key('mu_5'))
vector2 = tensor([
