Alexander Shalyt-Margolin. The Equivalence Principle Applicability Boundaries, Qft in Flat Space and Measurability I.free Quantum Fields

Natural Sciences / Physics / Quantum field theory

Submitted on: Jan 09, 2019, 14:38:21

Description: The present paper continues a study of a quantum field theory in terms of the {bf measurability} notion introduced in the previous authorâE™s works. It should be noted that, without detriment to the consideration and results, we can lift some initial restrictions (limiting conditions) imposed in the above-mentioned papers. Specifically, it is not supposed initially that a theory involves some minimal length. Starting from some maximal momentum, we can use it subsequently together with a specific formula to derive the quantity with a dimension of length that is called the {bf primary} length. The first part of this paper is devoted to analysis of the applicability limit of Einstein's Equivalence Principle (EP). It is noted that a natural applicability limit of this Principle, associated with the development of quantum-gravitational effects at PlanckâE™s scales, is absolute, its more accurate estimation being dependent on the processes under study and on the sizes of the corresponding particles. It is shown that, neglecting the applicability limit of EP, one can obtain senseless results on estimation of the relevant quantities within the scope of the well-known Quantum Field Theory (QFT). Besides, such a neglect may be responsible for ultraviolet divergences in this theory. In the second part of the work the author presents the general principles and mathematical apparatus for framing QFT in terms of the {bf measurability} notion introduced by the author earlier, considering the above-mentioned remark concerning replacement of a minimal length by the {bf primary} length. Next the author studies QFT in the {bf measurable} form for free quantum fields at low energies $Ell E_p$. In such QFT in the general case it is expedient to indicate the energy regions, where EP is valid and where it loses its force, in an effort to find a natural solution of the ultraviolet divergences problem.