766 research outputs found
Higher Derivative Fermionic Field Equation in the First Order Formalism
The generalized Dirac equation of the third order, describing particles with
spin 1/2 and three mass states, is analyzed. We obtain the first order
generalized Dirac equation in the 24-dimensional matrix form. The mass and spin
projection operators are found which extract solutions of the wave equation
corresponding to pure spin states of particles. The density of the
electromagnetic current is obtained, and minimal and non-minimal (anomalous)
electromagnetic interactions of fermions are considered by introducing three
phenomenological parameters. The Hamiltonian form of the first order equation
has been obtained.Comment: 16 pages, title changed, new section, appendixes, and references
adde
Self-accelerated Universe
It is widely believed that the large redshifts for distant supernovae are
explained by the vacuum energy dominance, or, in other words, by the
cosmological constant in Einstein's equations, which is responsible for the
anti-gravitation effect. A tacit assumption is that particles move along a
geodesic for the background metric. This is in the same spirit as the consensus
regarding the uniform Galilean motion of a free electron. However, there is a
runaway solution to the Lorentz--Dirac equation governing the behavior of a
radiating electron, in addition to the Galilean solution. Likewise, a runaway
solution to the entire system of equations, both gravitation and matter
equations of motion including, may provide an alternative explanation for the
accelerated expansion of the Universe, without recourse to the hypothetic
cosmological constant.Comment: 11 pages; Talk at the 9th Adriatic Meeting, Dubrovnic, Croatia, 4-14
September, 2003, Minor improvement, references added; to appear in ``Progress
in General Relativity and Quantum Cosmology Research'', Nova Science
Publisher
Variational problem for the Frenkel and the Bargmann-Michel-Telegdi (BMT) equations
We propose Lagrangian formulation for the particle with value of spin fixed
within the classical theory. The Lagrangian turns out to be invariant under
non-abelian group of local symmetries. As the gauge-invariant variables for
description of spin we can take either the Frenkel tensor or the BMT vector.
Fixation of spin within the classical theory implies -corrections to
the corresponding equations of motion.Comment: 04 pages, notations changed, misprints correcte
Helicity supersymmetry of dyons
The 'dyon' system of D'Hoker and Vinet consisting of a spin 1/2 particle with
anomalous gyromagnetic ratio 4 in the combined field of a Dirac monopole plus a
Coulomb plus a suitable potential (which arises in the long-range limit
of a self-dual monopole) is studied following Biedenharn's approach to the
Dirac-Coulomb problem: the explicit solution is obtained using the
`Biedenharn-Temple operator', , and the extra two-fold degeneracy is
explained by the subtle supersymmetry generated by the 'Dyon Helicity' or
generalized `Biedenharn-Johnson-Lippmann' operator . The new SUSY
anticommutes with the chiral SUSY discussed previously.Comment: 14 pages, 2 figure
Little Groups of Preon Branes
Little groups for preon branes (i.e. configurations of branes with maximal
(n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,...,11 are
calculated for all massless, and partially for massive orbits. For massless
orbits little groups are semidirect product of d-2 translational group
on a subgroup of (SO(d-2) R-invariance) group. E.g. at d=9
the subgroup is exceptional group. It is also argued, that 11d Majorana
spinor invariants, which distinguish orbits, are actually invariant under
d=2+10 Lorentz group. Possible applications of these results include
construction of field theories in generalized space-times with brane charges
coordinates, different problems of group's representations decompositions,
spin-statistics issues.Comment: LaTeX, 11 page
Canonical and Lie-algebraic twist deformations of -Poincare and contractions to -Galilei algebras
We propose canonical and Lie-algebraic twist deformations of
-deformed Poincare Hopf algebra which leads to the generalized
-Minkowski space-time relations. The corresponding deformed
-Poincare quantum groups are also calculated. Finally, we perform the
nonrelativistic contraction limit to the corresponding twisted Galilean
algebras and dual Galilean quantum groups.Comment: 16 pages, no figures, v3: few changes provided - version for journal,
v2: submitted incidentally, v4: the page numbers for all references in
preprint version are provide
Effective dynamics of an electrically charged string with a current
Equations of motion for an electrically charged string with a current in an
external electromagnetic field with regard to the first correction due to the
self-action are derived. It is shown that the reparametrization invariance of
the free action of the string imposes constraints on the possible form of the
current. The effective equations of motion are obtained for an absolutely
elastic charged string in the form of a ring (circle). Equations for the
external electromagnetic fields that admit stationary states of such a ring are
revealed. Solutions to the effective equations of motion of an absolutely
elastic charged ring in the absence of external fields as well as in an
external uniform magnetic field are obtained. In the latter case, the frequency
at which one can observe radiation emitted by the ring is evaluated. A model of
an absolutely nonstretchable charged string with a current is proposed. The
effective equations of motion are derived within this model, and a class of
solutions to these equations is found.Comment: 14 pages, 3 figures, format changed, minor change
Unitary dynamics of spherical null gravitating shells
The dynamics of a thin spherically symmetric shell of zero-rest-mass matter
in its own gravitational field is studied. A form of action principle is used
that enables the reformulation of the dynamics as motion on a fixed background
manifold. A self-adjoint extension of the Hamiltonian is obtained via the group
quantization method. Operators of position and of direction of motion are
constructed. The shell is shown to avoid the singularity, to bounce and to
re-expand to that asymptotic region from which it contracted; the dynamics is,
therefore, truly unitary. If a wave packet is sufficiently narrow and/or
energetic then an essential part of it can be concentrated under its
Schwarzschild radius near the bounce point but no black hole forms. The quantum
Schwarzschild horizon is a linear combination of a black and white hole
apparent horizons rather than an event horizon.Comment: 26 pages, Latex, no figures; definitive version, to be published in
Nuclear Physics
Klauder's coherent states for the radial Coulomb problem in a uniformly curved space and their flat-space limits
First a set of coherent states a la Klauder is formally constructed for the
Coulomb problem in a curved space of constant curvature. Then the flat-space
limit is taken to reduce the set for the radial Coulomb problem to a set of
hydrogen atom coherent states corresponding to both the discrete and the
continuous portions of the spectrum for a fixed \ell sector.Comment: 10 pages, no figure
From the Mendeleev periodic table to particle physics and back to the periodic table
We briefly describe in this paper the passage from Mendeleev's chemistry
(1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and
particle physics (from 1953 to 2006). We show how the consideration of
symmetries, largely used in physics since the end of the 1920's, gave rise to a
new format of the periodic table in the 1970's. More specifically, this paper
is concerned with the application of the group SO(4,2)xSU(2) to the periodic
table of chemical elements. It is shown how the Madelung rule of the atomic
shell model can be used for setting up a periodic table that can be further
rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative
results are obtained from this nonstandard table.Comment: 15 pages; accepted for publication in Foundations of Chemistry
(special issue to commemorate the one hundredth anniversary of the death of
Mendeleev who died in 1907); version 2: 16 pages; some sentences added;
acknowledgment and references added; misprints correcte
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