Related papers: On the Interpretation of the 'Extra' Variables in …
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
Hurwitz transformations are defined as specific automorphisms of a Cayley-Dickson algebra. These transformations generate quadratic and nonquadratic forms. We investigate here the Hurwitz transformations corresponding to Cayley-Dickson…
In "extended phase space" approach to quantum geometrodynamics numerical solutions to Schrodinger equation corresponding to various choice of gauge conditions are obtained for the simplest isotropic model. The "extended phase space"…
The real coordinates separating geodesic Hamilton-Jacobi equation on three-dimensional Minkowski space in several cases cannot be defined in the whole space. We show through an example how to naturally extend them to complex variables…
The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing…
A discrete Hubbard-Stratonovich transformation is presented for systems with an orbital degeneracy $N$ and a Hubbard Coulomb interaction without multiplet effects. An exact transformation is obtained by introducing an external field which…
In this paper we propose some Hamiltonian characterizing the interaction of the two-level atom and both the single radiation mode and external field, which might be a generalization of that of Sch{\"o}n and Cirac (quant-ph/0212068). We…
We study the dynamics of electroweak phase transition in a simple extension of the Standard Model where the Higgs sector is extended by adding an $SU(2)_L$-triplet with hypercharge Y=2. By making random scans over the parameters of the…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
The properties of an electron in a typical solid are modified by the interaction with the crystal ions, leading to the formation of a quasiparticle: the polaron. Such polarons are often described using the Fr\"ohlich Hamiltonian, which…
We discuss three Hamiltonians, each with a central-field part $H_{0}$ and a PT-symmetric perturbation $igz$. When $H_{0}$ is the isotropic Harmonic oscillator the spectrum is real for all $g$ because $H$ is isospectral to $H_{0}+g^{2}/2$.…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
The existence of a second Higgs doublet in Nature could lead to a cosmological first order electroweak phase transition and explain the origin of the matter-antimatter asymmetry in the Universe. We explore the parameter space of such a…
Superfield methods can be used to determine the precise way the self-dual five-form couples to the metric in the first non-trivial $\alpha'$ corrections to type IIB supergravity. We explicitly compute the exact tensor structure of these…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to $1/|x|^2$. The additional spatial…
The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the…
The evolution of polar perturbations on a spherical background spacetime is analyzed. The matter content is assumed to be a massless scalar field.This provides a nontrivial dynamics to the background and the linearized equations of motion…
We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by…
In a generalized Heisenberg/Schroedinger picture, the unitary representations of the Lorentz group may, for a massive relativistic particle, be used to attribute to waves an extra wavelength that is longer than the de Broglie wavelength.…