Reconditioning in Discrete Quantum Field Theory

TL;DR

This paper develops a discrete quantum field theory framework focusing on a reconditioning process for transition probabilities in a lattice-based scattering operator, with implications for understanding dark energy and dark matter.

Contribution

It introduces a novel reconditioning method for transition probabilities in discrete quantum field theory, avoiding infinities typical in standard renormalization.

Findings

Reconditioning ensures total probability normalization at each energy-time scale.

Application to a simple scattering experiment demonstrates the method's effectiveness.

Potential astronomical tests could probe spacetime discreteness and dark matter/energy phenomena.

Abstract

We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator $S(x_0,r)$ where $x_0$ and $r$ are positive integers representing time and maximal total energy, respectively. The operator $S(x_0,r)$ is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy $(x_0,r)$. In order to maintain total unit probability, the transition probabilities need to be reconditioned at each $(x_0,r)$. This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of spacetime might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter.