Related papers: Boundary conditions at spatial infinity for fields…
We present explicitly another example of a temperature inversion symmetry in the Casimir effect for a nonsymmetric boundary condition. We also give an interpretation for our result.
We have constructed a quantum field theory in a finite box, with periodic boundary conditions, using the hypothesis that particles living in a finite box are created and/or annihilated by the creation and/or annihilation operators,…
We compute the first radiative correction to the Casimir energy in the $(d+1)$-dimensional $\lambda|\phi|^{4}$ model submitted to quasi-periodic boundary conditions in one spatial direction. Our results agree with the ones found in the…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
The Wightman function and the vacuum expectation values of the field squared and of the energy-momentum tensor are obtained, for a massive scalar field with an arbitrary curvature coupling parameter, in the region between two infinite…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
Casimir forces of massive fermionic Dirac fields are calculated for parallel plates geometry in spatial space with dimension d and imposing bag model boundary conditions.It is shown that in the range of ma>>1 where m is mass of fields…
This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the…
The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.
Hamilton's principle does not formally apply to systems whose boundary conditions lie outside configuration space, but extensions are possible using certain "natural" boundary conditions that allow action extremization. With the single…
The Casimir forces on two parallel plates in conformally flat domain wall background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary…
We show that under certain boundary conditions on the matter fields and on the fluctuations of the background metric the gravity-matter system can be coupled to the boundary of space-time through the stress-energy tensor. The connection of…
We study the Casimir problem as the limit of a conventional quantum field theory coupled to a smooth background. The Casimir energy diverges in the limit that the background forces the field to vanish on a surface. We show that this…
In this paper we consider estimating the number of solutions to multiplicative equations in finite fields when the variables run through certain sets with high additive structure. In particular, we consider estimating the multiplicative…
We consider a system consisting of a quantum, massless, real scalar field, in the presence of nonlinear mirrors: infinite parallel planes, upon which the field satisfies nonlinear boundary conditions. The latter are implemented by…
We have developed an exact, general method to compute Casimir interactions between a finite number of compact objects of arbitrary shape and separation. Here, we present details of the method for a scalar field to illustrate our approach in…
In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of…
We discuss corrections to the Casimir effect at finite temperature and effective field theory. Recently, it has been shown that effective field theories can reproduce radiative corrections to the Casimir energy calculated in full QED. We…
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…