A pseudo-bosonic Klein-Gordon field with finite two-points function

TL;DR

This paper introduces a new class of pseudo-bosonic Klein-Gordon fields in 1+1 dimensions, highlighting a subclass with finite two-point functions, which contrasts with standard fields and could impact quantum field theory.

Contribution

It presents a novel class of pseudo-bosonic Klein-Gordon fields derived from non-Hermitian quantum mechanics, with a specific subclass exhibiting finite two-point functions.

Findings

Existence of a subclass with finite two-point functions

Contrasts with standard Klein-Gordon fields

Potential implications for quantum field theory

Abstract

We introduce a class of pseudo-bosonic Klein-Gordon fields in 1+1 dimensions and we discuss some of their properties. This work originates from non Hermitian quantum mechanics and deformed canonical commutation relations. We show that, within this class of fields, there exist a specific subclass with the interesting feature of having finite equal space-time two-points function, contrarily to what happens for {\em standard} Klein-Gordon fields. This, in our opinion, is a relevant aspect of our proposal which is a good motivation to undertake a deeper analysis of this (and related) quantum fields.