Casimir energy and topological mass for a massive scalar field with Lorentz violation

Abstract

A Lorentz symmetry violation aether-type theoretical model is considered to investigate the Casimir effect and the generation of topological mass associated with self-interacting massive scalar fields obeying Dirichlet, Newman, and mixed boundary conditions on two large and parallel plates. By adopting the path integral approach, we find the effective potential at one-and two-loop corrections, which provides both the energy density and the topological mass when taken in the ground state of the scalar field. We then analyze how these quantities are affected by the Lorentz symmetry violation and compare the results with previous ones found in literature.

The Lorentz-violating real scalar field at thermal equilibrium

“…In order to find the effects of the Lorentz symmetry breaking terms on our model, we firstly looked for the particle spectrum of the theory, given explicitly in Eq. (18), from which we conclude that there should be specific bounds over the values of the κ μν coefficients in order to have a real positive energy that is also bounded from below. Then, we assumed that the magnitude of the constant tensor components are very small, i.e.…”

“…The first term in the above expression is divergent and represent the vacuum energy, which has been analyzed recently in connection with the Casimir energy in Refs. [15][16][17][18]. Since we are interested only in studying thermal properties, we will disregard that term from now on.…”

“…where p 0 is the free particle energy, given by (18). The first term in (72), is ultraviolet divergent but linear in the inverse temperature β.…”

“…The effects of Lorentz violation has been widely investigated in several different scenarios. It is worth mentioning recent studies on the statistical mechanics in LV background [10][11][12][13][14], the Casimir effect [15][16][17][18][19][20], the Bose-Einstein condensation [21][22][23][24][25], QED sector [26][27][28][29][30], LV theories with boundary conditions [31][32][33][34], Chern-Simons-like terms [35][36][37][38][39], scattering processes [40][41][42][43][44], geometrical correspondences [45,46], supersymmetric LV models [47][48][49][50][51], as well as many others interesting subjects (see also [52] and references therein for a more exhaustive list of related papers).…”

The Lorentz-violating real scalar field at thermal equilibrium

“…The first term in the above expression is divergent and represent the vacuum energy, which has been analyzed recently in connection with the Casimir energy in Refs. [11,12,13,14]. Since we are interested only in studying thermal properties, we will disregard that term from now on.…”