Deformed Quantum Field Theory, Thermodynamics at Low and High Energies, and Gravity. II. Deformation Parameter

A.E Shalyt-Margolin

doi:10.5923/j.ijtmp.20120203.04

Abstract

The principal objective of this paper is to show that deformation of the General Relativity within the scope of both the Generalized Uncertainty Principle (UV-cutoff) and the Extended Uncertainty Principle (IR-cutoff) in the cases when the corresponding gravitational equations have a thermodynamic interpretation may be studied in terms of a small parameter introduced in previous works of the author. From this viewpoint the parameter is though to be universal. Consideration is given to the possibility for extension of the obtained results to more general cases. Possible generalization of the uncertainty relation for the pair (cosmological constant, space-time volume), where the cosmological constant is regarded as a dynamic quantity at high and low energies, is analyzed. This paper is devoted to the 70-th Anniversary of Professor Nikolai Maksimovich Shumeiko, Director of the Belarusian Particles and High Energy Physics National Centre.

Highlights

In the last decade numerous works devoted to a Quantum Field Theory (QFT) at Planck’s scale[1,2,3] have been published
This interest stems from the facts that (i) at these scales it is expected to reveal the effects of a Quantum Gravity (QG), and this still unresolved theory is intriguing all the researchers engaged in the field of theoretical physics; (ii) modern accelerators, in particular LHC, have the capacity of achieving the energies at which some QG effects may be exhibited
We demonstrate that in the cases when the Thermodynamics Approach[16,17,18,19,20,21] is applicable to the General Relativity the deformation of GR with Generalized Uncertainty Principle (GUP) and Extended Uncertainty Principle (EUP) may be a natural result of the α -representation

Summary

Introduction

In the last decade numerous works devoted to a Quantum Field Theory (QFT) at Planck’s scale[1,2,3] have been published (the author has no pretensions of being exhaustive in his references). It is clear that Quantum Field Theory (QFT) at Planck’s scales, and possibly at very large scales as well, undergoes changes associated with the appearance of additional parameters related to (i) a minimal length (on the order of the Planck’s length) and (ii)a minimum momentum. The Gravitational Thermodynamics (GT) is understood as thermodynamics of spaces with horizon[18, 20]

Gravitational Thermodynamics with GUP

The Cosmological Constant Problem and QFT with GUP and SGUP

G kBT dS

Some Comments and Problems of Interest

Conclusions