Generalized quantum field theory: perturbative computation and perspectives

TL;DR

This paper explores two interpretations of generalized Heisenberg algebras within quantum field theory, constructing models with q-deformed particles and variable mass particles, and computes key scattering processes.

Contribution

It introduces a novel quantum field theory framework based on generalized Heisenberg algebras, including explicit propagator calculations and scattering analysis.

Findings

Constructed a q-deformed particle quantum field theory.

Computed propagator and first-order scattering process.

Proposed a model with particles of varying mass from algebra states.

Abstract

We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we construct a quantum field theory that creates at any space-time point particles described by a q-deformed Heisenberg algebra and we compute the propagator and a specific first order scattering process. Concerning the second one, we draw attention to the possibility of constructing this theory where each state of a generalized Heisenberg algebra is interpreted as a particle with different mass.