The Casimir pressure regularization in two-dimensional field models

A method for Casimir pressure calculation with the help of the regular part of the Green surface function is considered in the two-dimensional case. Also, a method for the approximate calculation of the regular part of the Green surface function using a Born-type series is suggested. It is tested for a problem for which the exact solution is known.     

The correspondence between Casimir pressure and energy in one-dimensional field models

We propose a method of calculation of Casimir pressure using the Green function for one-dimensional case. This method yields the renormalized pressure if an external field is absent, otherwise it permits us to calculate the dependence of pressure at one boundary on the other boundary’s coordinate. The calculated pressure permits one to obtain the Casimir energy for the systems under consideration.     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both fiat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimlr effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet and Neumann boundary conditions are also discussed.