Related papers: Relative partition function of Coulomb plus delta …
The Casimir effect describes the attractive force arising due to quantum fluctuations of the vacuum electromagnetic field between closely spaced conducting plates. Traditionally, zeta-regularization is employed in calculations to address…
We derive explicit analytic expressions for the lateral force for two different configurations with corrugations, parallel plates and concentric cylinders. By making use of the multiple scattering formalism, we calculate the force for a…
A streamlined derivation of the Kac-Ward formula for the planar Ising model's partition function is presented and applied in relating the kernel of the Kac-Ward matrices' inverse with the correlation functions of the Ising model's…
The Casimir effect is a fundamental quantum phenomenon induced by the zero-point energy for a quantum field. It is well-known for relativistic fields with a linear dispersion relation, while its existence or absence for nonrelativistic…
The formalism developed in Refs.~\cite{Guo:2023ecc,Guo:2024zal,Guo:2024pvt} that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral is further…
The long-range interaction between two atoms and the long-range interaction between an ion and an electron are compared at small and large intersystem separations. The vacuum dressed atom formalism is applied and found to provide a…
We show that in theory it is possible to obtain a Casimir interaction potential that varies with distance as 1/r. We achieve this by invoking hypothetical particles having a harmonic oscillator interaction potential. The derivation…
We present a useful proposition for discovering extended Laplace-Runge-Lentz vectors of certain quantum mechanical systems. We propose a new family of superintegrable systems and construct their integrals of motion. We solve these systems…
The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the Levi-Civita…
The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector…
A new resummation of the $S$-factor of a composite system of two relativistic spin-1/2 particles of arbitrary masses interacting via a Coulomb-like chromodynamical potential is presented. The analysis is performed in the framework of a…
In this article we consider a piston modelled by a potential in the presence of extra dimensions. We analyze the functional determinant and the Casimir effect for this configuration. In order to compute the determinant and Casimir force we…
The zeta function regularization technique is used to study the finite temperature Casimir effect for a charged and massless scalar field confined between parallel plates and satisfying Dirichlet boundary conditions at the plates. A…
We study derivatives of the shift and penetration factors of collision theory with respect to energy, angular momentum, and charge. Definitive results for the signs of these derivatives are found for the repulsive Coulomb case. In…
In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero point energies of quantum fields are "real''. On the contrary, Casimir effects can be formulated and Casimir forces can be…
The Casimir force between two parallel uncharged closely spaced metallic plates is evaluated in ways alternatives to those usually considered in the literature. In a first approximation we take in account the suppressed quantum numbers of a…
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…
The Casimir-Polder interaction energy between a unipolarizable point atom and a unipolarizable dielectric ring has been limited, until now, to the case when the atom is confined on the axis of symmetry of the ring. We find the generalized…
We bring together two apparently disconnected lines of research (of mathematical and of physical nature, respectively) which aim at the definition, through the corresponding zeta function, of the determinant of a differential operator…
The trace of a function of a Schrodinger operator minus the same for the Laplacian can be expressed in terms of the determinant of its scattering matrix. The naive formula for this determinant is divergent. Using a dispersion relation, we…