So the two interesting physical limits give smaller thermal contribution in electron wave function as the relevant temperature limits can be defined as m < T < E and T < m < E, which ensures the renormalizability of QED at comparatively higher temperature as compared to self-mass.
Since the contribution to the coupling constant is always proportional to [T.sup.2]/[m.sup.2] and is sufficiently smaller than [alpha], that ensures the renormalizability at the temperatures below the decoupling temperature.
In fact, some of these approaches improve the renormalizability
of quantum fields so well that even the Landau poles disappear even for nonrenoramlizable theories [123,124].
in D-dimensional higher-order gravity," Physical Review D: Particles, Fields, Gravitation and Cosmology, vol.
Nonminimal coupling of the inflaton field and gravitational sector is inevitable from the renormalizability
of the corresponding field theory (see, for instance, ).
We consider only renormalizable self-interactions of the scalar fields, although renormalizability
in general has nothing to do with effective field theories.
Piguet, "All orders renormalizability
of a Lorentz and CPT violating quantum electrodynamics," Physical Review D, vol.
Valderrama, "Perturbative renormalizability
of chiral twopion exchange in nucleon-nucleon scattering: P and D waves," Physical Review C, vol.
Recall that HLG achieves power-counting renormalizability
by breaking diffeomorphism invariance.
However, serious problems must be faced in this approach, mainly the incompatibility between renormalizability
and unitarity, which are desired features in the quantum field theory formulation.
On the other hand, there are also models in which the dark energy nonminimally couples to gravity in order to provide quantum corrections and renormalizability
of the scalar field in the curved spacetime.
Although usually the scalar fields are minimally coupled to gravity, there are compelling reasons (e.g., quantum corrections and renormalizability
of the scalar field theory in curved space) to include an explicit nonminimal coupling between dark energy and gravity in the action [41-48].