# Quantum q-Field Theory: q-Schr\"odinger and q-Klein-Gordon Fields

## TL;DR

This paper develops a quantum field theory framework for q-deformed Schr"odinger and Klein-Gordon fields, analyzing their behavior at various energy scales and deriving key quantities like self-energy and propagator for specific q values.

## Contribution

It introduces a generalized QFT for q-fields, connecting them to standard theories near q=1 and providing analytical results for special q values.

## Key findings

- q-fields reduce to standard QFTs near q=1
- Analytical expressions for self-energy and propagator at specific q values
- Applicable at high, high, and low energy scales depending on q

## Abstract

We show how to deal with the generalized q-Schr\"odinger and q-Klein-Gordon fields in a variety of scenarios. These q-fields are meaningful at very high energies (TeVs) for for $q=1.15$, high ones (GeVs) for $q=1.001$, and low energies (MeVs)for $q=1.000001$ [Nucl. Phys. A {\bf 948} (2016) 19, Nucl. Phys. A {\bf 955} (2016) 16]. We develop here the quantum field theory (QFT) for the q-Schr\"odinger and q-Klein-Gordon fields, showing that both reduce to the customary Schr\"odinger and Klein-Gordon QFTs for q close to unity. Further, we analyze the q-Klein-Gordon field for $2q-1=n$ (n integer $\ge 2$) and analytically compute the self-energy and the propagator up to second order.