
In this paper the quantum vacuum energies induced by massive fluctuations of one real scalar field on a configuration of two partially transparent plates are analysed. The physical properties of the infinitely thin plates are characterized by two Dirac-$δ$ potentials. We find that an attractive/repulsive Casimir force arises between the plates when the weights of the $δ$'s have equal/different sign. If some of the plates absorbs fluctuations below some threshold of energy (the corresponding weight is negative) there is the need to set a minimum mass to the scalar field fluctuations to preserve unitarity in the corresponding quantum field theory. Two repulsive $δ$-interactions are compatible with massless fluctuations. The effect of Dirichlet boundary conditions at the endpoints of the interval $(-a,a)$ on a massless scalar quantum field theory defined on this interval is tantamount letting the weights of the repulsive $δ$-interactions to $+\infty$.
Accepted for publication in Phys. Rev. D
High Energy Physics - Theory, Quantum Physics, Física Cuántica, F?sica Cu?ntica, 2290.01 F?sica te?rica altas energ?as, 12 Matemáticas, Física Altas Energías, F?sica Matem?tica, F?sica Altas Energ?as, FOS: Physical sciences, Física Matemática, Mathematical Physics (math-ph), 2212.12 Teoría cuántica de campos, High Energy Physics - Theory (hep-th), 12 Matem?ticas, 2290.01 Física teórica altas energías, 2212.12 Teor?a cu?ntica de campos, Quantum Physics (quant-ph), Mathematical Physics
High Energy Physics - Theory, Quantum Physics, Física Cuántica, F?sica Cu?ntica, 2290.01 F?sica te?rica altas energ?as, 12 Matemáticas, Física Altas Energías, F?sica Matem?tica, F?sica Altas Energ?as, FOS: Physical sciences, Física Matemática, Mathematical Physics (math-ph), 2212.12 Teoría cuántica de campos, High Energy Physics - Theory (hep-th), 12 Matem?ticas, 2290.01 Física teórica altas energías, 2212.12 Teor?a cu?ntica de campos, Quantum Physics (quant-ph), Mathematical Physics
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