Zero-Point Energy of a Scalar Field in $q$-Deformed Euclidean Space

TL;DR

This paper investigates the vacuum energy of a scalar field in q-deformed Euclidean space, revealing that the total vacuum energy vanishes for massless fields but can be significant locally.

Contribution

It provides the first calculation of vacuum energy in q-deformed Euclidean space, highlighting differences between total and local vacuum energy behaviors.

Findings

Total vacuum energy vanishes for massless scalar fields.

Local vacuum energy density can be substantial in finite regions.

Results suggest modifications to quantum field theory in q-deformed spaces.

Abstract

We examine the energy of a scalar field in its ground state within $q$-deformed Euclidean space. Specifically, we compute the total vacuum energy of the entire $q$-deformed Euclidean space, originating from the scalar field's ground-state energy. Our results show that, for a massless scalar field, the total vacuum energy vanishes. In contrast, when evaluating the average ground-state energy over finite, localized regions of the $q$-deformed Euclidean space, we find that the vacuum energy density can assume significant values.