# Scalar models of formally interacting non-standard quantum fields in Minkowski space-time

## TL;DR

This paper explores algebraic quantum field theory in non-standard frameworks like hyperfunction theories, constructing models of interacting scalar fields and analyzing their properties to advance understanding of non-trivial quantum field theories.

## Contribution

It introduces model theories of formally interacting scalar fields within hyperfunction frameworks, analyzing their characteristic properties and mimicking non-trivial Lagrangian structures.

## Key findings

- Constructed models of formally interacting neutral scalar fields.
- Analyzed two-point functions and characteristic properties.
- Demonstrated local redefinitions mimic non-trivial interactions.

## Abstract

For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework of non-standard theories like hyperfunction or ultra-hyperfunction quantum field theory. For this purpose model theories of formally interacting neutral scalar fields are constructed and some of their characteristic properties like two-point functions are discussed. The formal self-couplings are obtained from local normally-ordered analytic redefinitions of the free scalar quantum field, mimicking a non-trivial structure of the resulting Lagrangians and equations of motion.