Finsleroid--Relativistic Time--Asymmetric Space and Quantized Fields

TL;DR

This paper introduces a new relativistic space geometry called Finsleroid-relativistic space, develops a method for quantizing relativistic fields within it, and proposes solutions to field equations that could address divergence issues.

Contribution

It formulates a novel approach for relativistic field quantization in Finsleroid space, extending the geometric framework beyond pseudoeuclidean geometry.

Findings

Field equations are solvable via conformal flatness.

Expansion in non-plane waves is established for all parameter values.

Natural regulators are proposed to handle divergences.

Abstract

For well-defined Finsleroid-relativistic space $\cE_g^{SR}$ (with the upperscript SR meaning Special-Relativistic) due only to accounting a characteristic parameter $g$ which measures the deviation of the geometry from its pseudoeuclidean precursor, the creation of the respective quantization programs for relativistic physical fields seems to be an urgent task. The parameter may take on the values over all the real range; at $g=0$ the space is reduced to become an ordinary pseudoeuclidean one. In the present work, the formulation of theory for relativistic physical fields in such a space is initiated. A general method to solve respective scalar, electromagnetic, and spinor field equations is proposed basing on the conformal flatness. At any value of the parameter, the expansion of the relativistic fields with respect to non-plane waves appeared is found, which proposes a base upon which the fields can be quantized in context of the Finsleroid-relativistic approach. Remarkably, the regulators can naturally be proposed to overcome divergences in relativistic field integrals. The respective key and basic concepts involved are presented. For short, the abbreviations FMF, FMT, and FHF will be used for the Finsleroid-relativistic metric function, the associated metric tensor, and the associated Hamiltonian function, respectively.