201 research outputs found
Vacuum polarization on the spinning circle
Vacuum polarization of a massive scalar field in the background of a
two-dimensional version of a spinning cosmic string is investigated. It is
shown that when the `radius of the universe' is such that spacetime is globally
hyperbolic the vacuum fluctuations are well behaved, diverging though on the
`chronology horizon'. Naive use of the formulae when spacetime is nonglobally
hyperbolic leads to unphysical results. It is also pointed out that the set of
normal modes used previously in the literature to address the problem gives
rise to two-point functions which do not have a Hadamard form, and therefore
are not physically acceptable. Such normal modes correspond to a locally (but
not globally) Minkowski time, which appears to be at first sight a natural
choice of time to implement quantization.Comment: 3 pages, no figures, REVTeX4, published versio
Path integrals on a flux cone
This paper considers the Schroedinger propagator on a cone with the conical
singularity carrying magnetic flux (``flux cone''). Starting from the operator
formalism and then combining techniques of path integration in polar
coordinates and in spaces with constraints, the propagator and its path
integral representation are derived. "Quantum correction" in the Lagrangian
appears naturally and no a priori assumption is made about connectivity of the
configuration space.Comment: LaTeX file, 9 page
On the scattering amplitude in the Aharonov-Bohm gauge field
A general expression for the scattering amplitude of nonrelativistic spinless
particles in the Aharonov-Bohm gauge potential is obtained within the time
independent formalism. The result is valid also in the backward and forward
directions as well as for any choice of the boundary conditions on the wave
function at the flux tube position.Comment: 18 pages, plain TE
Aspects of classical and quantum motion on a flux cone
Motion of a non-relativistic particle on a cone with a magnetic flux running
through the cone axis (a ``flux cone'') is studied. It is expressed as the
motion of a particle moving on the Euclidean plane under the action of a
velocity-dependent force. Probability fluid (``quantum flow'') associated with
a particular stationary state is studied close to the singularity,
demonstrating non trivial Aharonov-Bohm effects. For example, it is shown that
near the singularity quantum flow departs from classical flow. In the context
of the hydrodynamical approach to quantum mechanics, quantum potential due to
the conical singularity is determined and the way it affects quantum flow is
analysed. It is shown that the winding number of classical orbits plays a role
in the description of the quantum flow. Connectivity of the configuration space
is also discussed.Comment: LaTeX file, 21 pages, 8 figure
Time-dependent quantum scattering in 2+1 dimensional gravity
The propagation of a localized wave packet in the conical space-time created
by a pointlike massive source in 2+1 dimensional gravity is analyzed. The
scattering amplitude is determined and shown to be finite along the classical
scattering directions due to interference between the scattered and the
transmitted wave functions. The analogy with diffraction theory is emphasized.Comment: 15 pages in LaTeX with 3 PostScript figure
Dirac fields in the background of a magnetic flux string and spectral boundary conditions
We study the problem of a Dirac field in the background of an Aharonov-Bohm
flux string. We exclude the origin by imposing spectral boundary conditions at
a finite radius then shrinked to zero. Thus, we obtain a behaviour of
eigenfunctions which is compatible with the self-adjointness of the radial
Hamiltonian and the invariance under integer translations of the reduced flux.
After confining the theory to a finite region, we check the consistency with
the index theorem, and evaluate its vacuum fermionic number and Casimir energy.Comment: 9 pages, 1 figure Two references added To be published in
International Journal of Modern Physics
Negative Energy Densities in Extended Sources Generating Closed Timelike Curves in General Relativity with and without Torsion
Near a spinning point particle in (2+1)-dimensional gravity (or near an
infinitely thin, straight, spinning string in 3+1 dimensions) there is a region
of space-time with closed timelike curves. Exact solutions for extended sources
with apparently physically acceptable energy-momentum tensors, have produced
the same exterior space-time structure. Here it is pointed out that in the case
with torsion, closed timelike curves appear only for spin densities so high
that the spin energy density is higher than the net effective energy density.
In models without torsion, the presence of closed time-like curves is related
to a heat flow of unphysical magnitude. This corroborates earlier arguments
against the possibility of closed timelike curves in space-time geometries
generated by physical sources.Comment: (to be published in Phys. Rev. D), 5 pages, REVTEX 3.0, NORDITA 93/62
A (Sept. 10/Revised Nov. 1, 1993
Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional -function potential case
One-dimensional -function potential is discussed in the framework
of Green's function formalism without invoking perturbation expansion. It is
shown that the energy-dependent Green's function for this case is crucially
dependent on the boundary conditions which are provided by self-adjoint
extension method. The most general Green's function which contains four real
self-adjoint extension parameters is constructed. Also the relation between the
bare coupling constant and self-adjoint extension parameter is derived.Comment: LATEX, 13 page
Pauli-Lubanski scalar in the Polygon Approach to 2+1-Dimensional Gravity
In this paper we derive an expression for the conserved Pauli-Lubanski scalar
in 't Hooft's polygon approach to 2+1-dimensional gravity coupled to point
particles. We find that it is represented by an extra spatial shift in
addition to the usual identification rule (being a rotation over the cut). For
two particles this invariant is expressed in terms of 't Hooft's phase-space
variables and we check its classical limit.Comment: Some errors are corrected and a new introduction and discussion are
added. 6 pages Latex, 4 eps-figure
SO(10) Cosmic Strings and Baryon Number Violation
SO(10) cosmic strings formed during the phase transition Spin(10)
SU(5) are studied. Two types of strings ---
one effectively Abelian and one non-Abelian --- are constructed and the string
solutions are calculated numerically. The non-Abelian string can catalyze
baryon number violation via the ``twisting'' of the scalar field which causes
mixing of leptons and quarks in the fermion multiplet. The non-Abelian string
is also found to have the lower energy possibly for the entire range of the
parameters in the theory. Scattering of fermions in the fields of the strings
is analyzed, and the baryon number violation cross section is calculated. The
role of the self-adjoint parameters is discussed and the values are computed.Comment: LaTex (RevTex), 36 pages, 6 figures (available upon request),
MIT-CTP#215
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