Numerical Spherically Symmetric Static Solution of the RTG Equations Outside the Matter

There was obtained a numerical external solution for the exact system of the RTG equations with some natural boundary conditions in the static spherically symmetric case. The properties of the solution are discussed.Comment: Plenary talk presented at Workshop on High Energy Physics&Field Theory (Protvino, Russia, 2005

Angular Momentum and Energy-Momentum Densities as Gauge Currents

If we replace the general spacetime group of diffeomorphisms by transformations taking place in the tangent space, general relativity can be interpreted as a gauge theory, and in particular as a gauge theory for the Lorentz group. In this context, it is shown that the angular momentum and the energy-momentum tensors of a general matter field can be obtained from the invariance of the corresponding action integral under transformations taking place, not in spacetime, but in the tangent space, in which case they can be considered as gauge currents.Comment: RevTeX4, 7 pages, no figures. Presentation changes; version to appear in Phys. Rev.

Breaking so(4) symmetry without degeneracy lift

We argue that in the quantum motion of a scalar particle of mass "m" on S^3_R perturbed by the trigonometric Scarf potential (Scarf I) with one internal quantized dimensionless parameter, \ell, the 3D orbital angular momentum, and another, an external scale introducing continuous parameter, B, a loss of the geometric hyper-spherical so(4) symmetry of the free motion can occur that leaves intact the unperturbed {\mathcal N}^2-fold degeneracy patterns, with {\mathcal N}=(\ell +n+1) and n denoting the nodes number of the wave function. Our point is that although the number of degenerate states for any {\mathcal N} matches dimensionality of an irreducible so(4) representation space, the corresponding set of wave functions do not transform irreducibly under any so(4). Indeed, in expanding the Scarf I wave functions in the basis of properly identified so(4) representation functions, we find power series in the perturbation parameter, B, where 4D angular momenta K\in [\ell , {\mathcal N}-1] contribute up to the order \left(\frac{2mR^2B}{\hbar^2}\right)^{{\mathcal N}-1-K}. In this fashion, we work out an explicit example on a symmetry breakdown by external scales that retains the degeneracy. The scheme extends to so(d+2) for any d.Comment: Prepared for the proceedings of the conference "Lie Theory and Its Applications In Physics", June 17-23, 2013, Varna, Bulgari

The Integrability of Pauli System in Lorentz Violating Background

We systematically analyze the integrability of a Pauli system in Lorentz violating background at the non-relativistic level both in two- and three-dimensions. We consider the non-relativistic limit of the Dirac equation from the QED sector of the so-called Standard Model Extension by keeping only two types of background couplings, the vector a_mu and the axial vector b_mu. We show that the spin-orbit interaction comes as a higher order correction in the non-relativistic limit of the Dirac equation. Such an interaction allows the inclusion of spin degree non-trivially, and if Lorentz violating terms are allowed, they might be comparable under special circumstances. By including all possible first-order derivative terms and considering the cases a\ne 0, b\ne 0, and b_0\ne 0 one at a time, we determine the possible forms of constants of motion operator, and discuss the existence or continuity of integrability due to Lorentz violating background.Comment: 19 page

Hamiltonian Cosmological Perturbation Theory

The Hamiltonian approach to cosmological perturbations in general relativity in finite space-time is developed, where a cosmological scale factor is identified with spatial averaging the metric determinant logarithm. This identification preserves the number of variables and leads to a cosmological perturbation theory with the scalar potential perturbations in contrast to the kinetic perturbations in the Lifshitz version which are responsible for the ``primordial power spectrum'' of CMB in the inflationary model. The Hamiltonian approach enables to explain this ``spectrum'' in terms of scale-invariant variables and to consider other topical problem of modern cosmology in the context of quantum cosmological creation of both universes and particles from the stable Bogoliubov vacuum.Comment: 10 pages, text was changed according to the version accepted for publication in Physics Letters

A time-space varying speed of light and the Hubble Law in static Universe

We consider a hypothetical possibility of the variability of light velocity with time and position in space which is derived from two natural postulates. For the consistent consideration of such variability we generalize translational transformations of the Theory of Relativity. The formulae of transformations between two rest observers within one inertial system are obtained. It is shown that equality of velocities of two particles is as relative a statement as simultaneity of two events is. We obtain the expression for the redshift of radiation of a rest source which formally reproduces the Hubble Law. Possible experimental implications of the theory are discussed.Comment: 7 page

"Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions

We develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a constant background electromagnetic field, and use these to show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general constant background field. This explains why the square of a one-loop term appears in the renormalized two-loop Heisenberg-Euler effective action. No integrals need be evaluated, and the explicit form of the background field propagators is not needed. This dramatically simplifies the computation of the renormalized two-loop effective action for scalar QED, and generalizes a previous result obtained for self-dual background fields.Comment: 13 pages; uses axodraw.st

START in a five-dimensional conformal domain

In this paper we give a brief review of the pseudo-Riemannian geometry of the five-dimensional homogeneous space for the conformal group O(4,2). Its topology is described and its relation to the conformally compactified Minkowski space is described. Its metric is calculated using a generalized half-space representation. Compactification via Lie-sphere geometry is outlined. Possible applications to Jaime Keller's START theory may follow by using its predecessor - the 5-optics of Yu. B. Rumer. The point of view of Rumer is given extensively in the last section of the paper. Keywords. Kaluza,Klein, Rumer, conformal symmetry, hyperbolic space, START, fifth dimension, action coordinate, 5-opticsComment: Latex, 13 pages, 3 figures, added sections 3.2. Christoffel symbols and geodesics and 3.3. {\Sigma}- as the space of hyperboloids; accepted for publication in the special volume of AACA in memory of Prof. Jaime Kelle

Discrete Symmetries of Off-Shell Electromagnetism

We discuss the discrete symmetries of the Stueckelberg-Schrodinger relativistic quantum theory and its associated 5D local gauge theory, a dynamical description of particle/antiparticle interactions, with monotonically increasing Poincare-invariant parameter. In this framework, worldlines are traced out through the parameterized evolution of spacetime events, advancing or retreating with respect to the laboratory clock, with negative energy trajectories appearing as antiparticles when the observer describes the evolution using the laboratory clock. The associated gauge theory describes local interactions between events (correlated by the invariant parameter) mediated by five off-shell gauge fields. These gauge fields are shown to transform tensorially under under space and time reflections, unlike the standard Maxwell fields, and the interacting quantum theory therefore remains manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory is achieved by simultaneous reflection of the sense of evolution and the fifth scalar field. Applying this procedure to the classical gauge theory leads to a purely classical manifestation of charge conjugation, placing the CPT symmetries on the same footing in the classical and quantum domains. In the resulting picture, interactions do not distinguish between particle and antiparticle trajectories -- charge conjugation merely describes the interpretation of observed negative energy trajectories according to the laboratory clock.Comment: 26 page

Non-Linear Vibrations in Nuclei

We have perfomed Time Dependant Hartree-Fock (TDHF) calculations on the non linear response of nuclei. We have shown that quadrupole (and dipole) motion produces monopole (and quadrupole) oscillations in all atomic nuclei. We have shown that these findings can be interpreted as a large coupling between one and two phonon states leading to large anharmonicities.Comment: 4 pages, 3 figure