The Casimir Energy for Lorentz-Violating Scalar Field in Sphere

Abstract

Abstract: In the present article, the Casimir energy was computed for the massless and Lorentz-violating scalar field, confined in a sphere with Dirichlet and Neumann boundary conditions. In 3+1 space-time dimensions, four violated directions to break the Lorentz symmetry are likely, according to which we presented the Casimir energy regarding all possible directions for the Lorentz violation and discussed the pure contribution to the Lorentz violation in a language of graphs. In the details of the calculation, a simple method was developed based on the direct mode summation and the sum-over-modes were performed via the contour integration in a complex plane of eigenfrequencies. The obtained result for all cases of Lorentz symmetry breaking was consistent with the expected physical basis. Keywords: Casimir energy, Lorentz-violating sphere scalar field. PACS No: 11.10.z; 11.10.Gh; 11.25.Db; 11.15.Bt