272 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
Euclidean thermal spinor Green's function in the spacetime of a straight cosmic string
Within the framework of the quantum field theory at finite temperature on a
conical space, we determine the Euclidean thermal spinor Green's function for a
massless spinor field. We then calculate the thermal average of the
energy-momentum tensor of a thermal bath of massless fermions. In the
high-temperature limit, we find that the straight cosmic string does not
perturb the thermal bathComment: 11 pages, latex, no figure
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
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
Topological field theories in n-dimensional spacetimes and Cartan's equations
Action principles of the BF type for diffeomorphism invariant topological
field theories living in n-dimensional spacetime manifolds are presented. Their
construction is inspired by Cuesta and Montesinos' recent paper where Cartan's
first and second structure equations together with first and second Bianchi
identities are treated as the equations of motion for a field theory. In
opposition to that paper, the current approach involves also auxiliary fields
and holds for arbitrary n-dimensional spacetimes. Dirac's canonical analysis
for the actions is detailedly carried out in the generic case and it is shown
that these action principles define topological field theories, as mentioned.
The current formalism is a generic framework to construct geometric theories
with local degrees of freedom by introducing additional constraints on the
various fields involved that destroy the topological character of the original
theory. The latter idea is implemented in two-dimensional spacetimes where
gravity coupled to matter fields is constructed out, which has indeed local
excitations.Comment: LaTeX file, no figure
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
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
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
(2+1)-Gravity with Moving Particles in an Instantaneous Gauge
By defining a regular gauge which is conformal-like and provides
instantaneous field propagation, we investigate classical solutions of
(2+1)-Gravity coupled to arbitrarily moving point-like particles. We show how
to separate field equations from self-consistent motion and we provide a
solution for the metric and the motion in the two-body case with arbitrary
speed, up to second order in the mass parameters.Comment: 16 pages, LaTeX, no figure
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