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 4He^{4}He Quenches Produce Fuzzy, Transient Vortices

We examine the Zurek scenario for the production of vortices in quenches of liquid $^{4}He$ 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 ($T_{em} \approx 10^6 GeV$) 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