What question did this study set out to answer?

The central aim is to introduce and analyze pseudo-bosonic Klein–Gordon fields and their properties, especially focusing on their finite two-point functions.

March 8, 2026Open Access

A pseudo-bosonic Klein–Gordon field with finite two-point function

Key Points

The central aim is to introduce and analyze pseudo-bosonic Klein–Gordon fields and their properties, especially focusing on their finite two-point functions.
Introduction of a class of pseudo-bosonic Klein–Gordon fields in 1+1 dimensions
Discussion of properties based on non-Hermitian quantum mechanics
Examination of deformed canonical commutation relations within the fields
Identification of a subclass of pseudo-bosonic Klein–Gordon fields with finite equal space-time two-point functions
Contradiction with the behavior of ordinary Klein–Gordon fields regarding two-point functions
Call for deeper analysis of the proposed quantum fields due to their unique properties

Abstract

Abstract We introduce a class of pseudo-bosonic Klein–Gordon fields (KGFs) in 1+1 dimensions, and we discuss some of their properties. This approach originates from non-Hermitian quantum mechanics and deformed canonical commutation relations (CCRs). We show that, within this class of fields, there exists a specific subclass with the quite interesting property of having finite equal space-time two-point function, contrarily to what happens for ordinary KGFs. 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.

A pseudo-bosonic Klein–Gordon field with finite two-point function

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Abstract

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