def test_weights(self):
self.assertEqual(parse_weight('3'), Weight([3]))
self.assertEqual(parse_weight('1 2'), Weight([1, 2]))
self.assertEqual(parse_weight('8 -9 1'), Weight([8, -9, 1]))
self.assertEqual(parse_weight(' 1 8 -5 -11 4 2 '),
Weight([1, 8, -5, -11, 4, 2]))
def highest_root(self):
if self.series == Series.A:
return Weight(
[1] + [0] * (self.rank - 2) + [1] if self.rank > 1 else [2]
)
if self.series == Series.B:
return Weight([0, 1] + [0] * (self.rank - 2))
if self.series == Series.C:
return Weight([2] + [0] * (self.rank - 1))
if self.series == Series.D:
return Weight([0, 1] + [0] * (self.rank - 2))
if self.series == Series.E:
if self.rank == 6:
return Weight([0, 0, 0, 0, 0, 1])
elif self.rank == 7:
return Weight([1, 0, 0, 0, 0, 0, 0])
elif self.rank == 8:
return Weight([0, 0, 0, 0, 0, 0, 1, 0])
if self.series == Series.F:
return Weight([1, 0, 0, 0])
if self.series == Series.G:
return Weight([1, 0])
def test_covariants_higgs(self):
covariants = EFT(sm_gauge_algebra, [phi, phic]).covariants(3)
known_covariants = {
(Weight([0, 0]), Weight([0, 0, 1]), (-0.5, )):
Counter({
(phic._to_operator(), 0): 1,
(phi * phic**2, 0): 1
}),
(Weight([1, 1]), Weight([0, 0, 1]), (-0.5, )):
Counter({(phic._to_operator(), 1): 1})
}
for key in known_covariants:
self.assertEqual(covariants[key], known_covariants[key])
def level_vector(self):
return Weight(
itertools.chain.from_iterable(
simple_algebra.level_vector
for simple_algebra in self
)
)
def test_highest_root(self):
known_highest_roots = {
self.a1: Weight([2]),
self.a2: Weight([1, 1]),
self.b4: Weight([0, 1, 0, 0]),
self.c6: Weight([2, 0, 0, 0, 0, 0]),
self.d5: Weight([0, 1, 0, 0, 0]),
self.e6: Weight([0, 0, 0, 0, 0, 1]),
self.e7: Weight([1, 0, 0, 0, 0, 0, 0]),
self.e8: Weight([0, 0, 0, 0, 0, 0, 1, 0]),
self.f4: Weight([1, 0, 0, 0]),
self.g2: Weight([1, 0])
}
for algebra, root in known_highest_roots.items():
self.assertEqual(algebra.highest_root, root)
def _semisimple_weight_system(self):
algebras = self.algebra.simple_algebras
split_highest_weight = self.algebra.split_weight(self.highest_weight)
split_weights = (
Irrep(algebra, weight).weight_system.weights.elements()
for algebra, weight in zip(algebras, split_highest_weight))
return WeightSystem(
Weight(list(itertools.chain.from_iterable(weights)))
for weights in itertools.product(*split_weights))
def conjugate(self):
lorentz_highest_weight = Weight(
reversed(self.lorentz_irrep.highest_weight))
return Field(name=self.name + "*",
lorentz_irrep=Irrep(lorentz_algebra,
lorentz_highest_weight),
internal_irrep=self.internal_irrep.conjugate,
charges=[-charge for charge in self.charges],
statistics=self.statistics,
dimension=self.dimension,
number_of_derivatives=self.number_of_derivatives,
number_of_flavors=self.number_of_flavors)
def differentiate(self, times, use_eom=True):
if use_eom or self._force_use_eom:
highest_weight = (Weight([times, times]) +
self.lorentz_irrep.highest_weight)
lorentz_irreps = [Irrep(lorentz_algebra, highest_weight)]
else:
lorentz_irreps = (
self.lorentz_irrep *
vector.power(times, statistics=Statistics.BOSON)).elements()
return (Field(name=self.name,
lorentz_irrep=lorentz_irrep,
internal_irrep=self.internal_irrep,
charges=self.charges,
statistics=self.statistics,
dimension=self.dimension + times,
number_of_derivatives=self.number_of_derivatives + times,
number_of_flavors=self.number_of_flavors)
for lorentz_irrep in lorentz_irreps)
def test_split_weight(self):
self.assertEqual(
self.algebra.split_weight(Weight([
1,
2, 5,
-8, 3, 4, 5, 4, 2, 11, 2, 4,
0, -2, -3, -4, 5, 7, 6,
4, 3, 4, 3, 4, 3, 4,
0, 0
])),
[
Weight([1]),
Weight([2, 5]),
Weight([-8, 3, 4, 5, 4, 2, 11, 2, 4]),
Weight([0, -2, -3, -4, 5, 7, 6]),
Weight([4, 3, 4, 3, 4, 3, 4]),
Weight([0, 0])
]
)
def test_positive_roots(self):
known_positive_roots = {
SimpleAlgebra(Series.A, 2): {
Weight([1, 1]),
Weight([2, -1]), Weight([-1, 2])
},
SimpleAlgebra(Series.C, 2): {
Weight([2, 0]),
Weight([0, 1]),
Weight([2, -1]), Weight([-2, 2])
},
SimpleAlgebra(Series.G, 2): {
Weight([1, 0]),
Weight([-1, 3]),
Weight([0, 1]),
Weight([1, -1]),
Weight([2, -3]), Weight([-1, 2])
},
SimpleAlgebra(Series.A, 3): {
Weight([1, 0, 1]),
Weight([1, 1, -1]), Weight([-1, 1, 1]),
Weight([2, -1, 0]), Weight([-1, 2, -1]), Weight([0, -1, 2])
},
SimpleAlgebra(Series.B, 3): {
Weight([0, 1, 0]),
Weight([1, -1, 2]),
Weight([1, 0, 0]), Weight([-1, 0, 2]),
Weight([1, 1, -2]), Weight([-1, 1, 0]),
Weight([2, -1, 0]), Weight([-1, 2, -2]), Weight([0, -1, 2])
},
SimpleAlgebra(Series.C, 3): {
Weight([2, 0, 0]),
Weight([0, 1, 0]),
Weight([1, -1, 1]), Weight([-2, 2, 0]),
Weight([1, 1, -1]), Weight([-1, 0, 1]),
Weight([2, -1, 0]), Weight([-1, 2, -1]), Weight([0, -2, 2])
},
SimpleAlgebra(Series.A, 4): {
Weight([1, 0, 0, 1]),
Weight([1, 0, 1, -1]), Weight([-1, 1, 0, 1]),
Weight([1, 1, -1, 0]), Weight([-1, 1, 1, -1]),
Weight([0, -1, 1, 1]),
Weight([2, -1, 0, 0]), Weight([-1, 2, -1, 0]),
Weight([0, -1, 2, -1]), Weight([0, 0, -1, 2])
},
SimpleAlgebra(Series.D, 5): {
Weight([0, 1, 0, 0, 0]),
Weight([1, -1, 1, 0, 0]),
Weight([-1, 0, 1, 0, 0]), Weight([1, 0, -1, 1, 1]),
Weight([-1, 1, -1, 1, 1]), Weight([1, 0, 0, -1, 1]),
Weight([1, 0, 0, 1, -1]),
Weight([0, -1, 0, 1, 1]), Weight([-1, 1, 0, -1, 1]),
Weight([-1, 1, 0, 1, -1]), Weight([1, 0, 1, -1, -1]),
Weight([0, -1, 1, -1, 1]), Weight([0, -1, 1, 1, -1]),
Weight([-1, 1, 1, -1, -1]), Weight([1, 1, -1, 0, 0]),
Weight([0, 0, -1, 0, 2]), Weight([0, 0, -1, 2, 0]),
Weight([0, -1, 2, -1, -1]), Weight([-1, 2, -1, 0, 0]),
Weight([2, -1, 0, 0, 0])
}
}
for algebra, roots in known_positive_roots.items():
self.assertEqual(set(Irrep.positive_roots(algebra)), roots)
def lorentz_irrep(n, m):
return Irrep(lorentz_algebra, Weight([round(2 * n), round(2 * m)]))
def singlet(algebra):
return Irrep(algebra, Weight([0] * algebra.rank))
def parse_weight(code):
return Weight(map(int, code.split()))
def test_su3_tensor_products(self):
SU3_algebra = SimpleAlgebra(Series.A, 2)
name_irrep_table = {
'1': Irrep(SU3_algebra, Weight([0, 0])),
'3': Irrep(SU3_algebra, Weight([1, 0])),
'6': Irrep(SU3_algebra, Weight([2, 0])),
'8': Irrep(SU3_algebra, Weight([1, 1])),
'10': Irrep(SU3_algebra, Weight([3, 0])),
'15': Irrep(SU3_algebra, Weight([2, 1])),
"15'": Irrep(SU3_algebra, Weight([4, 0])),
'21': Irrep(SU3_algebra, Weight([0, 5])),
'24': Irrep(SU3_algebra, Weight([1, 3])),
'27': Irrep(SU3_algebra, Weight([2, 2]))
}
def SU3_irrep(name):
if name in name_irrep_table:
return name_irrep_table[name]
else:
return name_irrep_table[name[:-1]].conjugate
known_decompositions = [
(
SU3_irrep('3*') * SU3_irrep('3*'),
[SU3_irrep('3'), SU3_irrep('6*')]
),
(
SU3_irrep('3') * SU3_irrep('3*'),
[SU3_irrep('1'), SU3_irrep('8')]
),
(
SU3_irrep('6') * SU3_irrep('3'),
[SU3_irrep('8'), SU3_irrep('10')]
),
(
SU3_irrep('6') * SU3_irrep('3*'),
[SU3_irrep('3'), SU3_irrep('15')]
),
(
SU3_irrep('6') * SU3_irrep('6'),
[SU3_irrep('6*'), SU3_irrep('15'), SU3_irrep("15'")]
),
(
SU3_irrep('6') * SU3_irrep('6*'),
[SU3_irrep('1'), SU3_irrep('8'), SU3_irrep('27')]
),
(
SU3_irrep('8') * SU3_irrep('3'),
[SU3_irrep('3'), SU3_irrep('6*'), SU3_irrep('15')],
),
(
SU3_irrep('8') * SU3_irrep('6*'),
[SU3_irrep('3'), SU3_irrep('6*'),
SU3_irrep('15'), SU3_irrep('24')]
),
(
SU3_irrep('8') * SU3_irrep('8'),
[SU3_irrep('1'), SU3_irrep('8'), SU3_irrep('8'),
SU3_irrep('10'), SU3_irrep('10*'), SU3_irrep('27')]
)
]
for product, decomposition in known_decompositions:
self.assertEqual(product, collections.Counter(decomposition))
def join_weights(self, weights):
return Weight(itertools.chain.from_iterable(weights))
def sum_of_positive_roots(self):
return Weight([1] * self.rank)
def test_representation(self):
known_weights = {
Irrep(
SimpleAlgebra(Series.D, 5),
Weight([0, 0, 0, 0, 1])
):
collections.Counter([
Weight([0, 0, 0, 0, 1]),
Weight([0, 0, 1, 0, -1]),
Weight([0, 1, -1, 1, 0]),
Weight([1, -1, 0, 1, 0]), Weight([0, 1, 0, -1, 0]),
Weight([-1, 0, 0, 1, 0]), Weight([1, -1, 1, -1, 0]),
Weight([-1, 0, 1, -1, 0]), Weight([1, 0, -1, 0, 1]),
Weight([-1, 1, -1, 0, 1]), Weight([1, 0, 0, 0, -1]),
Weight([0, -1, 0, 0, 1]), Weight([-1, 1, 0, 0, -1]),
Weight([0, -1, 1, 0, -1]),
Weight([0, 0, -1, 1, 0]),
Weight([0, 0, 0, -1, 0])
]),
Irrep(
SimpleAlgebra(Series.E, 6),
Weight([1, 0, 0, 0, 0, 0])
):
collections.Counter([
Weight([1, 0, 0, 0, 0, 0]),
Weight([-1, 1, 0, 0, 0, 0]),
Weight([0, -1, 1, 0, 0, 0]),
Weight([0, 0, -1, 1, 0, 1]),
Weight([0, 0, 0, -1, 1, 1]), Weight([0, 0, 0, 1, 0, -1]),
Weight([0, 0, 0, 0, -1, 1]), Weight([0, 0, 1, -1, 1, -1]),
Weight([0, 0, 1, 0, -1, -1]), Weight([0, 1, -1, 0, 1, 0]),
Weight([0, 1, -1, 1, -1, 0]), Weight([1, -1, 0, 0, 1, 0]),
Weight([0, 1, 0, -1, 0, 0]), Weight([1, -1, 0, 1, -1, 0]),
Weight([-1, 0, 0, 0, 1, 0]),
Weight([1, -1, 1, -1, 0, 0]), Weight([-1, 0, 0, 1, -1, 0]),
Weight([1, 0, -1, 0, 0, 1]), Weight([-1, 0, 1, -1, 0, 0]),
Weight([1, 0, 0, 0, 0, -1]), Weight([-1, 1, -1, 0, 0, 1]),
Weight([-1, 1, 0, 0, 0, -1]), Weight([0, -1, 0, 0, 0, 1]),
Weight([0, -1, 1, 0, 0, -1]),
Weight([0, 0, -1, 1, 0, 0]),
Weight([0, 0, 0, -1, 1, 0]),
Weight([0, 0, 0, 0, -1, 0])
])
}
for irrep, weights in known_weights.items():
self.assertEqual(irrep.weight_system.weights, weights)