79 research outputs found
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
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