def c_der(self):
n = self.num_of_inds
factor = OpSum(i_op * Op(sigma4bar(n + 1, 0, -1)))
f = Op(
Tensor(self.c_name, [0] + list(range(-2, -n - 1, -1)),
is_field=True,
dimension=1.5,
statistics=fermion))
return factor * f.derivative(n + 1)
Op(lambdaDYD(0, 1), DYRc(2, 3, 4, 0), epsSU2(4, 5), phic(5), DL(2, 3, 1)),
Op(lambdaDYDc(0, 1), DLc(2, 3, 1), epsSU2(4, 5), phi(5), DYR(2, 3, 4, 0)))
# Integration
heavy_D = VectorLikeFermion("D", "DL", "DR", "DLc", "DRc", 3)
heavy_DY = VectorLikeFermion("DY", "DYL", "DYR", "DYLc", "DYRc", 4)
heavy_fields = [heavy_D, heavy_DY]
effective_lagrangian = integrate(heavy_fields, interaction_lagrangian, 6)
# Transformations of the effective Lgrangian
extra_SU2_identities = [(Op(phi(0), epsSU2(0, 1), phi(1)), OpSum()),
(Op(phic(0), epsSU2(0, 1), phic(1)), OpSum()),
(Op(qLc(0, 5, 1, -1), sigma4bar(2, 0, 3),
qL(3, 5, 4, -2), phic(4), D(2, phi(1))),
OpSum(
number_op(-0.5j) * basis.O3phiq(-1, -2),
number_op(-0.5j) * basis.O1phiq(-1, -2))),
(Op(qLc(0, 5, 1, -2), sigma4bar(2, 0, 3),
qL(3, 5, 4, -1), D(2, phic(4)), phi(1)),
OpSum(
number_op(0.5j) * basis.O3phiqc(-1, -2),
number_op(0.5j) * basis.O1phiqc(-1, -2)))]
rules = (rules_SU2 + eoms_SM + extra_SU2_identities +
basis.rules_basis_definitions)
transf_eff_lag = apply_rules(effective_lagrangian, rules, 2)
-Op(yd(0, 1), qLc(2, 3, -1, 0), dR(2, 3, 1)),
-Op(V(0, 1), yuc(0, 2), uRc(3, 4, 2), qL(3, 4, 5, 1), epsSU2(5, -1))))
r"""
Rule using the conjugate of the Higgs doublet equation of motion.
Substitute :math:`D^2\phi^\dagger` by
.. math::
\mu^2_\phi \phi^\dagger- 2\lambda_\phi (\phi^\dagger\phi) \phi^\dagger
- y^e_{ij} \bar{l}_{Li} e_{Rj} - y^d_{ij} \bar{q}_{Li} d_{Rj}
- V_{ki} y^{u*}_{kj} \bar{u}_{Rj} q^T_{Li} i\sigma^2
"""
eom_bFS = (
Op(D(0, bFS(0, -1))),
-OpSum(number_op(-Fraction(1, 2)) * Op(gb(), deltaFlavor(2, 4), lLc(0, 1, 2),
sigma4bar(-1, 0, 3), lL(3, 1, 4)),
number_op(Fraction(1, 6)) * Op(gb(), deltaFlavor(3, 5), qLc(0, 1, 2, 3),
sigma4bar(-1, 0, 4), qL(4, 1, 2, 5)),
number_op(-1) * Op(gb(), deltaFlavor(1, 3), eRc(0, 1),
sigma4(-1, 0, 2), eR(2, 3)),
number_op(-Fraction(1, 3)) * Op(gb(), deltaFlavor(2, 4), dRc(0, 1, 2),
sigma4(-1, 0, 3), dR(3, 1, 4)),
number_op(Fraction(2, 3)) * Op(gb(), deltaFlavor(2, 4), uRc(0, 1, 2),
sigma4(-1, 0, 3), uR(3, 1, 4)),
number_op(Fraction(1, 2)) * i_op * Op(gb(), phic(0), D(-1, phi(0))),
- number_op(Fraction(1, 2)) * i_op * Op(gb(), D(-1, phic(0)), phi(0))))
r"""
Rule using the :math:`U(1)` gauge field strength equation of motion.
Substitute :math:`D_\mu B^{\mu\nu}` by
.. math::
:math:`\epsilon_{\mu\nu\rho\sigma}` where :math:`\epsilon_{0123}=1`.
"""
sigmaTensor = TensorBuilder("sigmaTensor")
r"""
Lorentz tensor
:math:`\sigma^{\mu\nu}=\frac{i}{4}\left(
\sigma^\mu_{\alpha\dot{\gamma}}\bar{\sigma}^{\nu\dot{\gamma}\beta}-
\sigma^\nu_{\alpha\dot{\gamma}}\bar{\sigma}^{\mu\dot{\gamma}\beta}
\right)`.
"""
rule_Lorentz_free_epsUp = (
Op(epsUp(-1, -2), epsUpDot(-3, -4)),
OpSum(number_op(Fraction(1, 2)) * Op(
sigma4bar(0, -3, -1), sigma4bar(0, -4, -2))))
r"""
Substitute :math:`\epsilon^{\alpha\beta}\epsilon^{\dot{\alpha}\dot{\beta}}`
by
.. math::
-\frac{1}{2} \bar{\sigma}^{\mu,\dot{\alpha}\alpha}
\bar{\sigma}^{\dot{\beta}\beta}_\mu
"""
rule_Lorentz_free_epsDown = (
Op(epsDown(-1, -2), epsDownDot(-3, -4)),
OpSum(number_op(Fraction(1, 2)) * Op(
sigma4(0, -1, -3), sigma4(0, -2, -4))))
r"""
Substitute :math:`\epsilon_{\alpha\beta}\epsilon_{\dot{\alpha}\dot{\beta}}`