Quantization of Gravity and Finite Temperature Effects

I Y Park

doi:10.3390/particles4040035

Abstract

Gravity is perturbatively renormalizable for the physical states which can be conveniently defined via foliation-based quantization. In recent sequels, one-loop analysis was explicitly carried out for Einstein-scalar and Einstein-Maxwell systems. Various germane issues and all-loop renormalizability have been addressed. In the present work we make further progress by carrying out several additional tasks. Firstly, we present an alternative 4D-covariant derivation of the physical state condition by examining gauge choice-independence of a scattering amplitude. To this end, a careful dichotomy between the ordinary, and large gauge symmetries is required and appropriate gauge-fixing of the ordinary symmetry must be performed. Secondly, vacuum energy is analyzed in a finite-temperature setup. A variant optimal perturbation theory is implemented to two-loop. The renormalized mass determined by the optimal perturbation theory turns out to be on the order of the temperature, allowing one to avoid the cosmological constant problem. The third task that we take up is examination of the possibility of asymptotic freedom in finite-temperature quantum electrodynamics. In spite of the debates in the literature, the idea remains reasonable.

Highlights

Gravity is perturbatively renormalizable for the physical states which can be conveniently defined via foliation-based quantization
In the present work this scaling is quantitatively achieved in the course of improving the perturbative analysis by optimal perturbation theory (OPT) after standard thermal resummation, we show that there exists an OPT procedure that enforces the scaling
Whereas the physical state condition (PSC) was derived in the ADM formalism in the earlier works, in the present work we have derived it in the

Summary

Review of Gauge Symmetry and Its Fixing

The central idea on which the FBQ hinges is renormalizability of the physical sector associated with a 3D hypersurface in an asymptotic region. It is useful to distinguish the above residual symmetry from the conformaltype symmetry contained in the diffeomorphism The latter takes a special form and is associated with the trace part of the fluctuation metric. The first term in (4) takes the form of a conformal transformation This symmetry must be removed by gauge-fixing of the trace piece of the fluctuation metric [52]. (Once the momenta are defined, one may consider other types of boundary conditions.) Since an LGT will not, generally speaking, preserve the boundary conditions (because, for one thing, it will not preserve the momenta), different boundary conditions should be viewed as different sectors of the theory For this reason the large gauge symmetry is analogous to global symmetry or moduli. The physical state condition should be derived in the setup of an extended Hilbert space

Alternative Derivation of PSC

Vacuum Energy in Finite Temperature

Review of CC Problem

Finite-T Analysis and Resolution of CC Problem

On Potential QED Asymptotic Freedom

Conclusions