TL;DR
This paper investigates the Casimir effect for tachyonic scalar fields in one dimension, calculating the vacuum energy, Casimir energy, and force using Lorentz-invariant methods and comparing results with massive fields.
Contribution
It introduces a Lorentz-invariant approach to compute the Casimir effect for tachyonic fields and derives explicit formulas for energy and force.
Findings
Casimir energy and force depend on the distance for tachyonic fields.
Comparison with massive fields shows differences in Casimir effect behavior.
Renormalized vacuum energy is obtained using Abel-Plana formula.
Abstract
In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square. We consider here only the case of one dimensional, scalar field. In order to describe tachyonic field, we use the absolute synchronization scheme preserving Lorentz invariance. The renormalized vacuum energy is calculated by means of Abel-Plana formula. Finaly, the Casimir energy and Casimir force as the functions of distance are obtained. In order to compare the resulting formula with the standard one, we calculate the Casimir energy and Casimir force for massive, scalar field.
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