Singularities of the Casimir Energy for Quantum Field Theories with Lifshitz Dimensions

Abstract

We study the singularities that the Casimir energy of a scalar field in spacetimes with Lifshitz dimensions exhibits, and provide expressions of the energy in terms of multidimensional zeta functions for the massless case. Using the zeta-regularization method, we found that when the 4-dimensional spacetime has Lifshitz dimensions, then for specific values of the critical exponents, the Casimir energy is singular, in contrast to the non-Lifshitz case. Particularly we found that when the value of the critical exponent is $z=2$, the Casimir energy is singular, while for $z\ge 3$ the Casimir energy is regular. In addition, when flat extra dimensions are considered, the critical exponents of the Lifshitz dimensions affect drastically the Casimir energy, introducing singularities that are absent in the non-Lifshitz case. We also discuss the Casimir energy in the context of braneworld models and the perspective of Lifshitz dimensions in such framework.

Major Revision, Similar to Journal Version

References in corpus (10)

• Quantum Gravity at a Lifshitz Point
• Non-relativistic holography
• Lorentz symmetry breaking as a quantum field theory regulator
• Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect
• Constructing Lifshitz solutions from AdS
• Advance and prospects in constraining the Yukawa-type corrections to Newtonian gravity from the Casimir effect
• Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments
• $f(R)$ theory and geometric origin of the dark sector in Horava-Lifshitz gravity
• On the effective potential for Horava-Lifshitz-like theories with the arbitrary critical exponent
• Lifshitz fermionic theories with z=2 anisotropic scaling

Cited by in corpus (1)

• The Horava-Lifshitz Modifications of the Casimir effect at finite temperature revisted