Abstract
We examine the energy of a scalar field in its ground state within -deformed Euclidean space. Specifically, we compute the total vacuum energy of the entire -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 -deformed Euclidean space, we find that the vacuum energy density can assume significant values.
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