Casimir effect in the presence of minimal lengths

Abstract

It is expected that the implementation of minimal length in quantum models leads to a consequent lowering of Planck's scale. In this paper, using the quantum model with minimal length of Kempf et al [3], we examine the effect of the minimal lenght on the Casimir force between parallel plates.

Heuristic derivation of Casimir effect in minimal length theories

“…Working in the outlined scenario, in the present paper we compute GUP-corrections to the Casimir energy for three different geometries: the parallel-plate configuration, the spherical and cylindrical shells. For the first case, we follow a field theoretical treatment first [10][11][12][13] and then a heuristic derivation. The two approaches are found to be consistent as concerns the dependence of the corrective term on the inverse fifth power of the distance between the plates.…”

The exact solutions of a (2 + 1)-dimensional Dirac oscillator under a magnetic field in the presence of a minimal length

“…In this context, many papers were published where a different quantum system in space with Heisenberg algebra was studied. They are: the Abelian Higgs model [15], the thermostatics with minimal length [16], the one-dimensional Hydrogen atom [17], the casimir effect in minimal length theories [18], the effect of minimal lengths on electron magnetism [19], the Dirac oscillator in one and three dimensions [20][21][22][23][24], the solutions of a two-dimensional Dirac equation in presence of an external magnetic field [25], the noncommutative phase space Schrödinger equation [26], Schrödinger equation with Harmonic potential in the presence of a Magnetic Field [27].…”

Influence of a minimal length on the creation of scalar particles

“…This explains why various physical problems are reconsidered by taking into account the minimal length. As example, we cite the harmonic oscillator [24][25][26], the Hydrogen atom [26][27][28][29][30][31][32], the inverse square potential [33], the Dirac oscillator [34], and the resonant scattering by a potential barrier [35,36]. Elsewhere, the influence of the minimal length on the Casimir effect has been communicated in several works [37,38].…”