def Vr(self, bosons, T, bosons_ring):
"""
The ring diagram (Daisy resummation)
"""
T2 = (T*T)[..., np.newaxis] + 1e-100
# the 1e-100 is to avoid divide by zero errors
T4 = T*T*T*T
m2, nb, c = bosons
ring, nbring = bosons_ring
y =np.sum(nbring*Jb((m2+ring)/T2), axis=-1) - np.sum(nbring*Jb(m2/T2), axis=-1)
return y*T4/(2*np.pi*np.pi)
def V1T(self, bosons, fermions, T, include_radiation=False):
"""
The one-loop finite-temperature potential.
This is generally not called directly, but is instead used by
:func:`Vtot`.
Note
----
The `Jf` and `Jb` functions used here are
aliases for :func:`finiteT.Jf_spline` and :func:`finiteT.Jb_spline`,
each of which accept mass over temperature *squared* as inputs
(this allows for negative mass-squared values, which I take to be the
real part of the defining integrals.
.. todo::
Implement new versions of Jf and Jb that return zero when m=0, only
adding in the field-independent piece later if
``include_radiation == True``. This should reduce floating point
errors when taking derivatives at very high temperature, where
the field-independent contribution is much larger than the
field-dependent contribution.
"""
# This does not need to be overridden.
T2 = (T * T)[..., np.newaxis] + 1e-100
# the 1e-100 is to avoid divide by zero errors
T4 = T * T * T * T
m2, nb, c = bosons
y = np.sum(nb * Jb(m2 / T2), axis=-1)
m2, nf = fermions
y += np.sum(nf * Jf(m2 / T2), axis=-1)
if include_radiation:
print("included")
print(self.num_boson_dof)
if self.num_boson_dof is not None:
nb = self.num_boson_dof - np.sum(nb)
y -= nb * np.pi**4 / 45.
if self.num_fermion_dof is not None:
nf = self.num_fermion_dof - np.sum(nf)
y -= nf * 7 * np.pi**4 / 360.
return y * T4 / (2 * np.pi * np.pi)