Related papers: Physically Sound Hamiltonian Formulation of the Dy…
We argue that the results for the vacuum forces on a slab and on an atom embedded in a magnetodielectric medium near a mirror, obtained using a recently suggested Lorentz-force approach to the Casimir effect, are equivalent to the…
For the Casimir piston filled with an inhomogeneous medium, the Casimir energy is regularized and expressed with cylinder kernel coefficients by using the first-order perturbation theory. When the refraction index of the medium is smoothly…
A new method based on the Monte-Carlo calculation on the lattice is proposed to study the Casimir effect in the compact lattice U(1) theory with Wilson action. We have studied the standard Casimir problem with two parallel plane surfaces…
We calculate the Casimir forces in two configurations, namely, three parallel dielectric slabs and a dielectric slab between two perfectly conducting plates, where the dielectric materials are dispersive and inhomogeneous in the direction…
A simple model is introduced in which the cosmological constant is interpreted as a true Casimir effect on a scalar field filling the universe (e.g. $\mathbf{R} \times \mathbf{T}^p\times \mathbf{T}^q$, $\mathbf{R} \times \mathbf{T}^p\times…
We show that the statement in F. Sorge [Class. Quant. Grav. 36, no.23, 235006 (2019)] that the Casimir effect receives second order corrections due to gravity is not consistent. We remark especially on the tracing of the proper time…
Vacuum fluctuations are a fundamental and irremovable property of a quantized electromagnetic field. These fluctuations are the cause of the Casimir effect -- mutual attraction of two electrically neutral metallic plates in vacuum in the…
We analyze the dynamical Casimir effect for a massless scalar field confined between two concentric spherical shells which impose on the field mixed boundary conditions. We thus complement a previous result [Phys. Rev. A \textbf{78}, 032521…
We develop the formalism for canonical reduction of $(1+1)$--dimensional gravity coupled with a set of point particles by eliminating constraints and imposing coordinate conditions. The formalism itself is quite analogous to the…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
The interaction between a polarizable particle and a reflecting wall is examined. A macroscopic approach is adopted in which the averaged force is computed from the Maxwell stress tensor. The particular case of a perfectly reflecting wall…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
The cosmological constant appearing in the Wheeler-De Witt equation is considered as an eigenvalue of the associated Sturm-Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study such a…
We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the…
In this paper we study an optomechnical system enclosed by an optical cavity with one mirror attached to a spring as a closed quantum system. We provide a different angle of studying the phenomenons related to the dynamical Casimir effect…
We calculate the Casimir energy for scalar fields in interaction with finite-width mirrors, described by nonlocal interaction terms. These terms, which include quantum effects due to the matter fields inside the mirrors, are approximated by…
Nonlinear terms in the equations of motion can induce secularly growing loop corrections to correlation functions. Recently such corrections were shown to affect the particle production by a nonuniformly moving ideal mirror. We extend this…
We study the vacuum fluctuations of a quantum scalar field in the presence of a thin and inhomogeneous flat mirror, modeled with a delta potential. Using Heat-Kernel techniques, we evaluate the Euclidean effective action perturbatively in…
We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as…
The Casimir effect is a crucial prediction of Quantum Field Theory which has fascinating connections with open questions in fundamental physics. The ideal formula written by Casimir does not describe real experiments and it has to be…