Casimir effect in polymer scalar field theory

Abstract

In this paper, we study the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance $L$, due to the presence of a minimal length $\lambda$ arising from a background independent (polymer) quantization scheme. To this end, we polymer-quantize the classical Klein-Gordon Hamiltonian for a massive scalar field confined between the plates and obtain the energy spectrum. The minimal length scale of the theory introduces a natural cutoff for the momenta in the plane parallel to the plates and a maximum number of discrete modes between the plates. The zero-point energy is calculated by summing over the modes, and by assuming $\lambda \ll L$, we expressed it as an expansion in powers of $1/N$, being $N=L/\lambda$ the number of points between the plates. Closed analytical expressions are obtained for the Casimir energy in the cases of small and large scalar mass limits.

arXiv commentAccepted for publication in Physical Review D

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Cited by in corpus (2)

• Quantum Groups and Polymer Quantum Mechanics
• Scalar Casimir effect for a conducting cylinder in a Lorentz violating background