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.

Accepted for publication in Physical Review D

References in corpus (14)

• Discreteness of Space from the Generalized Uncertainty Principle
• Tunable Casimir repulsion with three dimensional topological insulators
• Polymer Quantum Mechanics and its Continuum Limit
• Effect of finite temperature and uniaxial anisotropy on the Casimir effect with three-dimensional topological insulators
• The propagator in polymer quantum field theory
• Local effects of the quantum vacuum in Lorentz-violating electrodynamics
• Casimir effect between ponderable media as modeled by the standard model extension
• Quantum gravity and the Coulomb potential
• Polymer quantization, singularity resolution and the 1/r^2 potential
• Diffraction in Time of Polymer Particles
• Polymer-Fourier quantization of the scalar field revisited
• Low Energy Lorentz Violation in Polymer Quantization Revisited
• Casimir effect in a quantum space-time
• Tunneling of Polymer Particles