Properties of a Discrete Quantum Field Theory
Micheal S. Berger, Naoki Yamatsu
TL;DR
This paper investigates a scalar quantum field theory on a discrete spatial lattice, focusing on renormalization, the periodic momentum space, and the analytic structure of scattering amplitudes, revealing new branch point phenomena.
Contribution
It introduces an analysis of the renormalization and analytic properties of a discrete scalar quantum field theory, highlighting novel features like a second branch point in scattering amplitudes.
Findings
Renormalization of the lattice propagator is characterized.
Periodic nature of momentum space affects scattering amplitude analyticity.
A second branch point in scattering amplitudes is identified.
Abstract
A scalar quantum field theory defined on a discrete spatial coordinate is examined. The renormalization of the lattice propagator is discussed with an emphasis on the periodic nature of the associated momentum coordinate. The analytic properties of the scattering amplitudes indicate the development of a second branch point on which the branch cut from the optical theorem terminates.
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