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We study the singularities that the Casimir energy of a scalar field inspacetimes with Lifshitz dimensions exhibits, and provide expressions of theenergy in terms of multidimensional zeta functions for the massless case. Usingthe zeta-regularization method, we found that when the 4-dimensional spacetimehas 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 $z\geq 3$ the Casimir energy isregular. In addition, when flat extra dimensions are considered, the criticalexponents of the Lifshitz dimensions affect drastically the Casimir energy,introducing singularities that are absent in the non-Lifshitz case. We alsodiscuss the Casimir energy in the context of braneworld models and theperspective of Lifshitz dimensions in such framework.

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