552 research outputs found
Electroweak Vacuum Geometry
We analyse symmetry breaking in the Weinberg-Salam model paying particular
attention to the underlying geometry of the theory. In this context we find two
natural metrics upon the vacuum manifold: an isotropic metric associated with
the scalar sector, and a squashed metric associated with the gauge sector.
Physically, the interplay between these metrics gives rise to many of the
non-perturbative features of Weinberg-Salam theory.Comment: 20 pages. Late
Analytical properties of certain probability distributions
This research has been carried out on Dr Aitken's
suggestion. The first chapter is largely a recapitulation
of known results which I have learnt from Dr Aitken, here
arranged for convenience of reference later in the thesis.The second chapter is the application of these methods
to the deduction of a two-variate GamMa type Distribution.
Dr Aitken pointed out that the variances in a normally
correlated two-variate distribution would give the required
distribution,and chanter II is just the carrying out of that
suggestion. fie also directed me to the papers by Hardy and
by Wishart and Bartlett which give rise to chapter III.
Those two chapters form the centre or core of the thesis
from which the other research radiates in three main directions, of varying interest from the points of view of pure
mathematics and of statistical applications.The first is chapter IV which is purely of mathematical
interest. It contains the most substantial single piece
of research in the thesis. It was perhaps fortunate that
on my first searching Watson's Theory of Bessel Functions
for theorems involving incomplete Gamma functions, I did not
find the paragraph on Hadamadd's paper. The result given
by Watson would have been sufficient for the purposes of
chapter III, but not being satisfied with my own deduction
of it, I sought to find it as a special case of a more
general theorem, and in doing so have been led to discover
a more general result, and incidental results which may be
of great interest in themselves.Secondly, the generalisations in chapters V and VI
are of interest as giving forms for statistical distributions,
but they wilt also be of interest for pure mathematics,
giving, for example; a generalisation to any number of
variables of Mehler s theorem (1866) which has been discussed
by Hardy and Watson and others.The third branch of the thesis is,concerned with the
actual method of fitting a distribution function such as that discussed in chapters II and III. This is discussed
in Chapter IX, and tables to make easy the fitting by the
method suggested there of a type III curve are given in
chapter X.Other parts of the thesis are chapters VII and VIII,
of which. VII is concerned with an attempt, not so far
successful, to extend the theory to all Pearson's types,
instead of type III only. (Similar attempts must have been
made before s see Romanovsky, Biometrika, Vol XVI, parts I
and II, p. 106) And chapter VIII applies a method whit I
learnt from Dr Aitken in application to a normal distribution
to the distribution of chapter II, and deduces simple formal
which may be of great practical significance in dealing with
problems of selection in distributions in which the coefficient
of variation is important and is not smal
A study of global monopole in Lyra geometry
A class of exact static solution around a global monopole resulting from the
breaking of a global S0(3) symmetry is obtained in the context of Lyra
geometry. Our solution is shown to possess an interesting feature like
wormholes space-time. It has been shown that the global monopole exerts no
gravitational force on surrounding non-relativistic matter.Comment: 6 pages, Published in Mod.Phys.Lett.A19:2785-2790,200
Impurity in a Bose-Einstein condensate in a double well
We compare and contrast the mean-field and many-body properties of a
Bose-Einstein condensate trapped in a double well potential with a single
impurity atom. The mean-field solutions display a rich structure of
bifurcations as parameters such as the boson-impurity interaction strength and
the tilt between the two wells are varied. In particular, we study a pitchfork
bifurcation in the lowest mean-field stationary solution which occurs when the
boson-impurity interaction exceeds a critical magnitude. This bifurcation,
which is present for both repulsive and attractive boson-impurity interactions,
corresponds to the spontaneous formation of an imbalance in the number of
particles between the two wells. If the boson-impurity interaction is large,
the bifurcation is associated with the onset of a Schroedinger cat state in the
many-body ground state. We calculate the coherence and number fluctuations
between the two wells, and also the entanglement entropy between the bosons and
the impurity. We find that the coherence can be greatly enhanced at the
bifurcation.Comment: 19 pages, 17 figures. The second version contains minor corrections
and some better figures (thicker lines
Slow Quenches Produce Fuzzy, Transient Vortices
We examine the Zurek scenario for the production of vortices in quenches of
liquid in the light of recent experiments. Extending our previous
results to later times, we argue that short wavelength thermal fluctuations
make vortices poorly defined until after the transition has occurred. Further,
if and when vortices appear, it is plausible that that they will decay faster
than anticipated from turbulence experiments, irrespective of quench rates.Comment: 4 pages, Revtex file, no figures Apart from a more appropriate title,
this paper differs from its predecessor by including temperature, as well as
pressure, quenche
Gravitationally-Induced Quantum Superpopsition Reduction with Large Extra Dimensions
A gravity-driven mechanism (``objective reduction'') proposed to explain
quantum state reduction is analyzed in light of the possible existence of large
extra dimensions in the ADD scenario. By calculating order-of-magnitude
estimates for nucleon superpositions, it is shown that if the mechanism at
question is correct, constraints may be placed on the number and size of extra
dimensions. Hence, measurement of superposition collapse times ({\it e.g.}
through diffraction or reflection experiments) could represent a new probe of
extra dimensions. The influence of a time-dependent gravitational constant on
the gravity-driven collapse scheme with and without the presence of extra
dimensions is also discussed.Comment: 22 pp; 1 postscript figure Expanded version of previous submission To
appear in Phys Rev
Slow Cooling of an Ising Ferromagnet
A ferromagnetic Ising chain which is endowed with a single-spin-flip Glauber
dynamics is investigated. For an arbitrary annealing protocol, we derive an
exact integral equation for the domain wall density. This integral equation
admits an asymptotic solution in the limit of extremely slow cooling. For
instance, we extract an asymptotic of the density of domain walls at the end of
the cooling procedure when the temperature vanishes. Slow annealing is usually
studied using a Kibble-Zurek argument; in our setting, this argument leads to
approximate predictions which are in good agreement with exact asymptotics.Comment: 6 page
Coupling of Gravity to Matter via SO(3,2) Gauge Fields
We consider gravity from the quantum field theory point of view and introduce
a natural way of coupling gravity to matter by following the gauge principle
for particle interactions. The energy-momentum tensor for the matter fields is
shown to be conserved and follows as a consequence of the dynamics in a
spontaneously broken SO(3,2) gauge theory of gravity. All known interactions
are described by the gauge principle at the microscopic level.Comment: 12 latex page
How Efficient Is The Langacker-Pi Mechanism of Monopole Annihilation?
We investigate the dynamics of monopole annihilation by the Langacker-Pi
mechanism. We find taht considerations of causality, flux-tube energetics and
the friction from Aharonov-Bohm scatteering suggest that the monopole
annihilation is most efficient if electromagnetism is spontaneously broken at
the lowest temperature () consistent with not having
the monopoles dominate the energy density of the universe.Comment: 10 page
A nonlinear quantum model of the Friedmann universe
A discussion is given of the quantisation of a physical system with finite
degrees of freedom subject to a Hamiltonian constraint by treating time as a
constrained classical variable interacting with an unconstrained quantum state.
This leads to a quantisation scheme that yields a Schrodinger-type equation
which is in general nonlinear in evolution. Nevertheless it is compatible with
a probabilistic interpretation of quantum mechanics and in particular the
construction of a Hilbert space with a Euclidean norm is possible. The new
scheme is applied to the quantisation of a Friedmann Universe with a massive
scalar field whose dynamical behaviour is investigated numerically.Comment: 11 pages of text + 4 pages for 8 figure
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