280 research outputs found
Non-perturbative quenched propagator beyond the infrared approximation
A new approach to the quenched propagator in QED beyond the IR limit is
proposed. The method is based on evolution equations in the proper time.Comment: 13 pages, 1 figure; Misprint on reference correcte
Defect Production in Slow First Order Phase Transitions
We study the formation of vortices in a U(1) gauge theory following a
first-order transition proceeding by bubble nucleation, in particular the
effect of a low velocity of expansion of the bubble walls. To do this, we use a
two-dimensional model in which bubbles are nucleated at random points in a
plane and at random times and then expand at some velocity .
Within each bubble, the phase angle is assigned one of three discrete values.
When bubbles collide, magnetic `fluxons' appear: if the phases are different, a
fluxon--anti-fluxon pair is formed. These fluxons are eventually trapped in
three-bubble collisions when they may annihilate or form quantized vortices. We
study in particular the effect of changing the bubble expansion speed on the
vortex density and the extent of vortex--anti-vortex correlation.Comment: 13 pages, RevTeX, 15 uuencoded postscript figure
Quantum Superposition Principle and Geometry
If one takes seriously the postulate of quantum mechanics in which physical
states are rays in the standard Hilbert space of the theory, one is naturally
lead to a geometric formulation of the theory. Within this formulation of
quantum mechanics, the resulting description is very elegant from the
geometrical viewpoint, since it allows to cast the main postulates of the
theory in terms of two geometric structures, namely a symplectic structure and
a Riemannian metric. However, the usual superposition principle of quantum
mechanics is not naturally incorporated, since the quantum state space is
non-linear. In this note we offer some steps to incorporate the superposition
principle within the geometric description. In this respect, we argue that it
is necessary to make the distinction between a 'projective superposition
principle' and a 'decomposition principle' that extend the standard
superposition principle. We illustrate our proposal with two very well known
examples, namely the spin 1/2 system and the two slit experiment, where the
distinction is clear from the physical perspective. We show that the two
principles have also a different mathematical origin within the geometrical
formulation of the theory.Comment: 10 pages, no figures. References added. V3 discussion expanded and
new results added, 14 pages. Dedicated to Michael P. Ryan on the occasion of
his sixtieth bithda
Testing cosmological defect formation in the laboratory
Topological defects such as cosmic strings may have been formed at
early-universe phase transitions. Direct tests of this idea are impossible, but
the mechanism can be elucidated by studying analogous processes in
low-temperature condensed-matter systems. Experiments on vortex formation in
superfluid helium and in superconductors have so far yielded somewhat confusing
results. I shall discuss their possible interpretation.Comment: 10 pages. Text of an invited lecture, to be published in Proceedings
of the Second European Conference on Vortex Matter in Superconductors, Crete,
15-25 September 2001. Uses elsart.cls style fil
An Extension to Models for Cosmic String Formation
The canonical Monte-Carlo algorithm for simulating the production of
string-like topological defects at a phase transition is extended by
introducing a distribution of domain sizes. A strong correlation is found
between the fraction in the form of `infinite' string and the variance of the
volume of the regions of constant phase.Comment: Revised version to appear in Phys. Lett. B. Several minor
corrections, including title change. 5 pages Latex with 5 postscript figures
(uuencoded and compressed). Also available through anonymous ftp from
ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at
http://euclid.tp.ph.ic.ac.uk/Papers
Waveforms for Gravitational Radiation from Cosmic String Loops
We obtain general formulae for the plus- and cross- polarized waveforms of
gravitational radiation emitted by a cosmic string loop in transverse,
traceless (synchronous, harmonic) gauge. These equations are then specialized
to the case of piecewise linear loops, and it is shown that the general
waveform for such a loop is a piecewise linear function. We give several simple
examples of the waveforms from such loops. We also discuss the relation between
the gravitational radiation by a smooth loop and by a piecewise linear
approximation to it.Comment: 16 pages, 6 figures, Revte
Non-equilibrium Higgs transition in classical scalar electrodynamics
Real time rearrangement of particle spectra is studied numerically in a U(1)
Gauge+Higgs system, in the unitary gauge and in three spatial dimensions. The
cold system starts from the symmetric phase. Evolution of the partial energy
densities and pressures reveal well-defined equations of state for the
longitudinal and transversal gauge fields very early. Longitudinal modes are
excited more efficiently and thermalize the slowest. Hausdorff-dimension of the
Higgs-defect manifold, eventually seeding vortex excitations is thoroughly
discussed. Scaling dependence of the vortex density on the characteristic time
of the symmetry breaking transition is established.Comment: 17 pages, 7 figures, Replaced with version accepted for publication
in JHE
Scattering off an SO(10) cosmic string
The scattering of fermions from the abelian string arising during the phase
transition induced by the Higgs in the
126 representation is studied. Elastic cross-sections and baryon number
violating cross-sections due to the coupling to gauge fields in the core of the
string are computed by both a first quantised method and a perturbative second
quantised method. The elastic cross-sections are found to be Aharonov-Bohm
type. However, there is a marked asymmetry between the scattering
cross-sections for left and right handed fields. The catalysis cross-sections
are small, depending on the grand unified scale. If cosmic strings were
observed our results could help tie down the underlying gauge group.Comment: 20 page
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.
Cosmic String Cusps with Small-Scale Structure: Their Forms and Gravitational Waveforms
We present a method for the introduction of small-scale structure into
strings constructed from products of rotation matrices. We use this method to
illustrate a range of possibilities for the shape of cusps that depends on the
properties of the small-scale structure. We further argue that the presence of
structure at cusps under most circumstances leads to the formation of loops at
the size of the smallest scales. On the other hand we show that the
gravitational waveform of a cusp remains generally unchanged; the primary
effect of small-scale structure is to smooth out the sharp waveform emitted in
the direction of cusp motion.Comment: RevTeX, 8 pages. Replaced with version accepted for publication by
PR
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