UV-finite scalar field theory with unitarity

TL;DR

This paper presents a method to construct a scalar field theory that is both UV-finite and perturbatively unitary by defining an infinite sum of propagators with specific coefficients and masses, demonstrated on  theory.

Contribution

It introduces a novel UV completion approach for scalar field theories ensuring finiteness and unitarity using infinite propagator sums and analytic continuation.

Findings

Successfully constructed a UV-finite, unitary  scalar theory.

Demonstrated the approach with explicit Feynman diagram calculations.

Proved unitarity using Cutkosky's rules.

Abstract

In this paper we show how to define the UV completion of a scalar field theory such that it is both UV-finite and perturbatively unitary. In the UV completed theory, the propagator is an infinite sum of ordinary propagators. To eliminate the UV divergences, we choose the coefficients and masses in the propagator to satisfy certain algebraic relations, and define the infinite sums involved in Feynman diagram calculation by analytic continuation. Unitarity can be proved relatively easily by Cutkosky's rules. The theory is equivalent to infinitely many particles with specific masses and interactions. We take the $\phi^4$ theory as an example and demonstrate our idea through explicit Feynman diagram computation.