arXiv subjects

Nathan Weiss

Publications and source records attributed to Nathan Weiss.

14 recordsLinked to original sources

arXiv1997

Neutrino oscillations in a model with a source and detector

We study the oscillations of neutrinos in a model in which the neutrino is coupled to a localized, idealized source and detector. By varying the spatial and temporal resolution of the source and detector we are able to model the full range of source and detector types ranging from coherent to incoherent. We find that this approach is useful in understanding the interface between the Quantum Mechanical nature of neutrino oscillations on the one hand and the production and detection systems on the other hand. This method can easily be extended to study the oscillations of other particles such as the neutral K and B mesons. We find that this approach gives a reliable way to treat the various ambiguities which arise when one examines the oscillations from a wave packet point of view. We demonstrate that the conventional oscillation formula is correct in the relativistic limit and that several recent claims of an extra factor of 2 in the oscillation length are incorrect. We also demonstrate explicitly that the oscillations of neutrinos which have separated spatially may be "revived" by a long coherent measurement.

hep-ph↗

arXiv1997

Coherent Neutrino Propagation in a Dense Medium

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we have studied the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum $p\sim G_Fρ/\sqrt{2}$. We have studied in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic ``Standard Model'' with two neutrino flavours. For a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos.

hep-ph↗

arXiv1997

Coherent Neutrino Interactions in a Dense Medium

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we study in more detail the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum p \sim (G_Fρ)/\sqrt{2}. We study in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic "Standard Model" with two neutrino flavours. We find that for a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos.

hep-ph↗

arXiv1997

Ising description of the transition region in SU(3) gauge theory at finite temperature

We attempt the numerical construction of an effective action in three dimensions for Ising spins which represent the Wilson lines in the four-dimensional SU(3) gauge theory at finite temperature. For each configuration of the gauge theory, each spin is determined by averaging the Wilson lines over a small neighborhood and then projecting the average to +/-1 according to whether the neighborhood is ordered or disordered. The effective Ising action, determined via the lattice Schwinger-Dyson equations, contains even (two-spin) and odd (one- and three-spin) terms with short range. We find that the truncation to Ising degrees of freedom produces an effective action which is discontinuous across the gauge theory's phase transition. This discontinuity may disappear if the effective action is made more elaborate.

hep-lat↗

arXiv1995

Coherence Effects in Neutrino Oscillations

We study the effect of coherent and incoherent broadening on neutrino oscillations both in vacuum and in the presence of matter (the MSW effect). We show under very general assumptions that it is not possible to distinguish experimentally neutrinos produced in some region of space as wave packets from those produced in the same region of space as plane waves with the same energy distribution.

hep-ph↗

arXiv1995

Mean Field Description of the Fractional Quantum Hall Effect Near $ν=1/(2k+1)$

The nature of Mean Field Solutions to the Equations of Motion of the Chern--Simons Landau--Ginsberg (CSLG) description of the Fractional Quantum Hall Effect (FQHE) is studied. Beginning with the conventional description of this model at some chemical potential $μ_0$ and magnetic field $B$ corresponding to a ``special'' filling fraction $ν=2πρ/eB=1/n$ ($n=1,3,5\cdot \cdot\cdot$) we show that a deviation of $μ$ in a finite range around $μ_0$ does not change the Mean Field solution and thus the mean density of particles in the model. This result holds not only for the lowest energy Mean Field solution but for the vortex excitations as well. The vortex configurations do not depend on $μ$ in a finite range about $μ_0$ in this model. However when $μ-μ_0 < μ_{cr}^-$ (or $μ-μ_0>μ_{cr}^+$) the lowest energy Mean Field solution describes a condensate of vortices (or antivortices). We give numerical examples of vortex and antivortex configurations and discuss the range of $μ$ and $ν$ over which the system of vortices is dilute.

hep-th↗

arXiv1995

Status of the Kazakov--Migdal Model

In this talk I discuss both the present status and some recent work on the Kazakov--Migdal Model which was originally proposed as a soluble, large $N$ realization of QCD. After a brief description of the model and a discussion of its solubility in the large $N$ limit I discuss several of the serious problems with the model which lead to the conclusion that it does {\it not} induce QCD. The model is nonetheless a very interesting example of a Gauge Theory and it is related to some very interesting Matrix Models. I then outline a technique \REF\dmsxyz{\dms}\refend which uses ``Loop Equations'' for solving such models. A Penner--like model is then discussed with two logarithmic singularities. This model is distinguished by the fact that it is exactly and explicitly soluble in spite of the fact that it is not Gaussian. It is shown how to analyze this model using both a technical approach and from a more physical point of view.

hep-th↗

arXiv1995

Kazakov--Migdal Model with Logarithmic Potential and the Double Penner Matrix Model

The Kazakov--Migdal (KM) Model is a U(N) Lattice Gauge Theory with a Scalar Field in the adjoint representation but with no kinetic term for the Gauge Field. This model is formally soluble in the limit $N\rightarrow \infty$ though explicit solutions are available for a very limited number of scalar potentials. A ``Double Penner'' Model in which the potential has two logarithmic singularities provides an example of a explicitly soluble model. We begin by reviewing the formal solution to this Double Penner KM Model. We pay special attention to the relationship of this model to an ordinary (one) matrix model whose potential has two logarithmic singularities (the Double Penner Model). We present a detailed analysis of the large N behavior of this Double Penner Model. We describe the various one cut and two cut solutions and we discuss cases in which ``eigenvalue condensation'' occurs at the singular points of the potential. We then describe the consequences of our study for the KM Model described above. We present the phase diagram of the model and describe its critical regions.

hep-th↗

arXiv1993

Introduction to $Z_N$ Symmetry in $SU_N$ Gauge Theories at Finite Temperatures

There have been several talks at this workshop on the physical interpretation and consequences of the $Z_N$ symmetry which is present in the Euclidean Path Integral formulation of $SU_N$ Gauge Theories at finite temperature. The purpose of this paper is to present an introduction to this subject. After a brief review of Gluodynamics at finite temperature, the nature of the $Z_N$ symmetry in this system is described and its relationship to confinement is discussed. $Z_N$ domain walls and bubbles are then described as is their relationship to the confining--deconfining phase transition. The effect of Fermions is then considered and the presence of metastable extrema of the Effective Potential for the Polyakov--Wilson Line is described. It is then argued that these metastable extrema do not correspond to physically realizable metastable states.

hep-ph↗

arXiv1993

Investigation of Long Baseline Neutrino Oscillations from Experiments at KAON

The proposed KAON factory at the Triumf Laboratory in Vancouver, Canada provides a unique opportunity for high statistics long baseline neutrino oscillation experiments. Several possibilities are under active consideration. In this paper we describe the theoretical expectations for a {\it very} long baseline experiment in which the neutrinos are directed towards, and detected at the Superkamiokande detector in Kamioka, Japan 7200 km away. We find that in the first year this experiment would probe oscillations down to about $Δm^2_0 = 9 \times 10^{-5} eV^2$ for maximal mixing, and if $Δm^2_0 \geq 5 \times 10^{-4} eV^2$ it would be sensitive to $sin^2(2 θ_0) \geq 0.2$. These results are compared with a more modest proposal of a 100 km baseline with a 6300 tonne detector which would probe $Δm^2_0 \geq 1.3 \times 10^{-3} eV^2$ for maximal mixing, and if $Δm^2_0 \geq 0.02 eV^2$ it would be sensitive to $sin^2(2 θ_0) \geq 0.01$. These experiments would either confirm or rule out the entire range of parameters allowed by Kamiokande and IMB to explain the deficit in the ratio of $ν_μ$ to $ν_e$ in current atmospheric neutrino experiments. The Kamiokande experiment would also investigate matter enhanced neutrino oscillations (the MSW effect) down to about $Δm^2 = 3 \times 10^{-4} eV^2$.

hep-ph↗

arXiv1993

Scattering From a Two Dimensional Array of Flux Tubes: A Study of The Validity of Mean Field Theory

Mean Field Theory has been extensively used in the study of systems of anyons in two spatial dimensions. In this paper we study the physical grounds for the validity of this approximation by considering the Quantum Mechanical scattering of a charged particle from a two dimensional array of magnetic flux tubes. The flux tubes are arranged on a regular lattice which is infinitely long in the ``$y$'' direction but which has a (small) finite number of columns in the ``$x$'' direction. Their physical size is assumed to be infinitesimally small. We develop a method for computing the scattering angle as well as the reflection and transmission coefficients to lowest order in the Aharonov--Bohm interaction. The results of our calculation are compared to the scattering of the same particle from a region of constant magnetic field whose magnitude is equal to the mean field of all the flux tubes. For an incident plane wave, the Mean Field approximation is shown to be valid provided the flux in each tube is much less than a single flux quantum. This is precisely the regime in which Mean Field Theory for anyons is expected to be valid. When the flux per tube becomes of order 1, Mean Field Theory is no longer valid.

hep-th↗

arXiv1993

Symmetry and Observables in Induced QCD

We review some of the basic features of the Kazakov-Migdal model of induced QCD. We emphasize the role of $Z_N$ symmetry in determining the observable properties of the model and also argue that it can be broken explicitly without ruining the solvability of induced QCD in the infinite $N$ limit. We outline the sort of critical behavior which the master field must have in order that the model is still solvable. We also review some aspects of the $D=1$ version of the model where the partition function can be obtained analytically. To be published in the Proceedings of "Mathematical Physics, String Theory and Quantum Gravity", Rhakov, Ukraine. October, 1992

hep-th↗

arXiv1992

Induced QCD and Hidden Local ZN Symmetry

We show that a lattice model for induced lattice QCD which was recently proposed by Kazakov and Migdal has a $Z_N$ gauge symmetry which, in the strong coupling phase, results in a local confinement where only color singlets are allowed to propagate along links and all Wilson loops for non-singlets average to zero. We argue that, if this model is to give QCD in its continuum limit, it must have a phase transition. We give arguments to support presence of such a phase transition.

hep-th↗

arXiv1992

Bosonic Chern-Simons Field Theory of Anyon Superconductivity

We study the Quantum Field Theory of nonrelativistic bosons coupled to a Chern--Simons gauge field at nonzero particle density. This field theory is relevant to the study of anyon superconductors in which the anyons are described as {\bf bosons} with a statistical interaction. We show that it is possible to find a mean field solution to the equations of motion for this system which has some of the features of bose condensation. The mean field solution consists of a lattice of vortices each carrying a single quantum of statistical magnetic flux. We speculate on the effects of the quantum corrections to this mean field solution. We argue that the mean field solution is only stable under quantum corrections if the Chern--Simons coefficient $N=2πθ/g^2$ is an integer. Consequences for anyon superconductivity are presented. A simple explanation for the Meissner effect in this system is discussed.

hep-th↗