Casimir effect in four simple situations - including a noncommutative two-sphere

We study the vacuum polarization (Casimir) energy in renormalizable, continuum quantum field theory in the presence of a background field, designed to impose Dirichlet boundary conditions on the fluctuating quantum field. In two and three spatial dimensions the Casimir energy diverges as a background field becomes concentrated on the surface on which the Dirichlet boundary condition would eventually hold. This divergence does not affect the force between rigid bodies, but it ...

The Casimir effect is an interesting phenomenon in the sense that it provides us with one of the primitive means of extracting the energy out of the vacuum. Since the original work of Casimir a number of works have appeared in extending the result to the case of more general topological and dynamical configurations of the boundary condition and to the circumstances at finite temperature and gravity. In the studies of the Casimir effects it is common to assume the free electro...

We calculate modifications to the scalar Casimir force between two parallel plates due to space-time non-commutativity. We devise a heuristic approach to overcome the difficulties of describing boundaries in non-commutative theories and predict that boundary corrections are of the same order as non-commutative volume corrections. Further, both corrections have the form of more conventional finite surface effects.

We present a new method to compute quantum energies in presence of a background field. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Our procedure is applied to the study of the Casimir force between rigid bodies induced by a fluctuating real scalar field. We test our method with the classic parallel-plate configuration and study curvature effects quantitatively for the sphere-p...

We develop a method to compute the Casimir effect for arbitrary geometries. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Concentrating on Casimir forces between rigid bodies induced by a fluctuating scalar field, we test our method with the parallel-plate configuration. For the experimentally relevant sphere-plate configuration, we study curvature effects quantitatively and per...

We apply the quasi-local stress-energy tensor formalism to the Casimir effect of a scalar field confined between conducting planes located in a static spacetime. We show that the surface energy vanishes for both Neumann and Dirichlet boundary conditions and consequently the volume Casimir energy reduces to the famous zero point energy of the quantum field, i.e. $E^{vol.}=\sum\frac{\hbar \omega}{2}$. This enables us to reinforce previous results in the literature and extend th...

The Casimir effect arises not only in the presence of material boundaries but also in space with nontrivial topology. In this paper, we choose a topology of the flat $(D+1)$-dimensional spacetime, which causes the helix boundary condition for a Hermitian massless scalar field. Especially, Casimir effect for a massless scalar field on the helix boundary condition is investigated in two and three dimensions by using the zeta function techniques. The Casimir force parallel to th...

The Casimir effect for spherical geometry is calculated using generalized Thermofield Dynamics for the case of scalar field. Casimir force and Casimir pressure are presented. It is found that for high temperatures the Casimir force does change sign.

In this paper we consider a Lorentz-breaking extension of the theory for a real massive scalar quantum field in the region between two large parallel plates, with our manner to break the Lorentz symmetry is CPT-even, aether-like. For this system we calculated the Casimir energy considering different boundary conditions. It turns out to be that the Casimir energy strongly depends on the direction of the constant vector implementing the Lorentz symmetry breaking, as well as on ...

Exact calculations are given for the Casimir energy for various fields in $R\times S^3$ geometry. The Green's function method naturally gives a result in a form convenient in the high-temperature limit, while the statistical mechanical approach gives a form appropriate for low temperatures. The equivalence of these two representations is demonstrated. Some discrepancies with previous work are noted. In no case, even for ${\cal N}=4$ SUSY, is the ratio of entropy to energy fou...