Lorentz violating scalar Casimir effect for a D -dimensional sphere

• Published in: Physical review. D 2020-07, Vol.102 (1), p.1, Article 015027
• Main Authors: Martín-Ruiz, A., Escobar, C. A., Escobar-Ruiz, A. M., Franca, O. J.
• Format: Article
• Language: English
• Subjects: Broken symmetry; Codification; Green's functions; Invariants; Scalars; Symmetry
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.102.015027

We investigate the Casimir effect, due to the confinement of a scalar field in a D-dimensional sphere, with Lorentz symmetry breaking. The Lorentz-violating part of the theory is described by an additional term λ ( u ⋅ ∂ ϕ ) 2 in the scalar field Lagrangian, where the parameter λ and the background vector u μ codify the breakdown of Lorentz symmetry. We compute, as a function of D > 2 , the Casimir stress by using Green's function techniques for two specific choices of the vector u μ . In the timelike case, uμ = ( 1 , 0 , … , 0 ) , the Casimir stress can be factorized as the product of the Lorentz invariant result times the factor ( 1 + λ ) − 1/2. For the radial spacelike case, uμ = ( 0 , 1 , 0 , … , 0 ) , we obtain an analytical expression for the Casimir stress which nevertheless does not admit a factorization in terms of the Lorentz invariant result. For the radial spacelike case we find that there exists a critical value λc = λc ( D ) at which the Casimir stress transits from a repulsive behavior to an attractive one for any D > 2. The physically relevant case D = 3 is analyzed in detail where the critical value λc|D=3 = 0.0025 was found. As in the Lorentz symmetric case, the force maintains the divergent behavior at positive even integer values of D.