Massless Scalar Field Theory in a Quantised Space-Time
J.~C.~Breckenridge, T.~G.~Steele (University of Saskatchewan) V., Elias, (University of Western Ontario)
TL;DR
This paper introduces a novel non-local massless scalar field theory in a quantised flat space-time with a fundamental length scale, avoiding ultraviolet and IR divergences in calculations.
Contribution
It develops a new method for constructing scalar field theories in quantised space-time without explicit spacetime averaging, and computes key functions at one-loop level without divergences.
Findings
Two- and four-point functions calculated at one-loop level.
No ultraviolet divergences encountered in the theory.
No infrared divergences in the processes considered.
Abstract
A method is developed to construct a non-local massless scalar field theory in a flat quantised space-time generated by an operator algebra. Implicit in the operator algebra is a fundamental length scale of the space-time. The fundamental two-point function of free fields is constructed by assuming that the causal Green functions still have support on the light cone in the operator algebra quantised space-time. In contrast to previous stochastic approaches, the method introduced here requires no explicit averaging over spacetime coordinates. The two- and four-point functions of~ theory are calculated to the one-loop level, and no ultraviolet divergences are encountered. It is also demonstrated that there are no IR divergences in the processes considered.
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