pinecone/core-2020-05-10-deduplication huggingface dataset:
The Luttinger-Schwinger Model

We study the Luttinger-Schwinger model, i.e. the (1+1) dimensional model of
massless Dirac fermions with a non-local 4-point interaction coupled to a
U(1)-gauge field. The complete solution of the model is found using the
boson-fermion correspondence, and the formalism for calculating all gauge
invariant Green functions is provided. We discuss the role of anomalies and
show how the existence of large gauge transformations implies a fermion
condensate in all physical states. The meaning of regularization and
renormalization in our well-defined Hilbert space setting is discussed. We
illustrate the latter by performing the limit to the Thirring-Schwinger model
where the interaction becomes local.Comment: 19 pages, Latex, to appear in Annals of Physics, download problems
  fixe
Dynamics as Shadow of Phase Space Geometry

Starting with the generally well accepted opinion that quantizing an
arbitrary Hamiltonian system involves picking out some additional structure on
the classical phase space (the {\sl shadow} of quantum mechanics in the
classical theory), we describe classical as well as quantum dynamics as a
purely geometrical effect by introducing a {\sl phase space metric structure}.
This produces an ${\cal O}(\hbar)$ modification of the classical equations of
motion reducing at the same time the quantization of an arbitrary Hamiltonian
system to standard procedures. Our analysis is carried out in analogy with the
adiabatic motion of a charged particle in a curved background (the additional
metric structure) under the influence of a universal magnetic field (the
classical symplectic structure). This allows one to picture dynamics in an
unusual way, and reveals a dynamical mechanism that produces the selection of
the right set of physical quantum states.Comment: LaTeX (epsfig macros), 30 pages, 1 figur
Dibaryon Condensate in Nuclear Matter and Neutron Stars: Exact Analysis
  in One-Dimensional Models

We investigate dense nuclear matter with a dibaryon Bose-Einstein condensate
as a possible intermediate state before the quark-gluon phase transition. An
exact analysis of this state of matter is presented in a one-dimensional model.
The analysis is based on a reduction of the quantization rules for the N-body
problem to N coupled algebraic transcendental equations. We observe that when
the Fermi momentum approaches the resonance momentum, the one-particle
distribution function increases near the Fermi surface. When the Fermi momentum
is increased beyond the resonance momentum, the equation of state becomes
softer. The observed behavior can be interpreted in terms of formation of a
Bose-Einstein condensate of two-fermion resonances (dibaryons). In cold nuclear
matter, it should occur if 2(m_N + epsilon_F) is greater or equal to m_D, where
m_N and m_D are respectively the nucleon and dibaryon masses and epsilon_F is
the nucleon Fermi energy.Comment: 25 pages, LaTeX, 2 Postscript figures, to appear in Annals of Physic
Self-Adjoint Extensions of the Pauli Equation in the Presence of a
  Magnetic Monopole

We discuss the Hamiltonian for a nonrelativistic electron with spin in the
presence of an abelian magnetic monopole and note that it is not self-adjoint
in the lowest two angular momentum modes. We then use von Neumann's theory of
self-adjoint extensions to construct a self-adjoint operator with the same
functional form. In general, this operator will have eigenstates in which the
lowest two angular momentum modes mix, thereby removing conservation of angular
momentum. However, consistency with the solutions of the Dirac equation limits
the possibilities such that conservation of angular momentum is restored.
Because the same effect occurs for a spinless particle with a sufficiently
attractive inverse square potential, we also study this system. We use this
simpler Hamiltonian to compare the eigenfunctions corresponding to a particular
self-adjoint extension with the eigenfunctions satisfying a boundary condition
consistent with probability conservation.Comment: revised version to be published in Annals of Physics (includes a new
  section comparing the Pauli case to the Dirac case, as well as other
  improvements), 17 pages, LaTex (using RevTex
One-Loop Effective Action on Rotational Spacetime: Zeta-Function
  Regularization and Schwinger Perturbative Expansion

The zeta-function regularization method is used to evaluate the renormalized
effective action for massless conformally coupling scalar field propagating in
a closed Friedman spacetime perturbed by a small rotation. To the second order
of the rotational parameter in the model spacetime the analytic form of the
effective action is obtained with the help of the Schwinger perturbation
formula. After investigating the time evolution of the rotational parameter we
find that the quantum field effect can produce an effect which damps the
cosmological rotational in the early universe.Comment: 15 page
QCD Sum Rules for Skeptics

A new Monte-Carlo based uncertainty analysis is introduced to quantitatively
determine the predictive ability of QCD sum rules. A comprehensive analysis of
ground state rho-meson and nucleon spectral properties is performed. Many of
the findings contradict the conventional wisdom of both practitioners and
skeptics alike. Associations between the phenomenological fit parameters are
particularly interesting as they reveal how the sum rules resolve the spectral
properties. The use of derivative sum rules for the determination of rho-meson
spectral properties is shown to be a very unfavorable approach. Most prior
nucleon sum rule analyses are based on a sum rule which is found to be invalid;
the results are suspect, and should be reevaluated. The ``Ioffe formula'',
argued by many to qualitatively encapsulate a description of the nucleon mass
in terms of the chiral symmetry breaking order parameter is misleading at best.
QCD Sum Rules are found to be self-consistent without contributions from direct
instantons. This implies that instanton effects are adequately accounted for in
the nonperturbative vacuum condensates. This in-depth examination of QCD sum
rule self consistency paints a favorable picture for further quantitative
refinements of the QCD sum rule approach.Comment: 70 page RevTeX Manuscript with 40 embedded figures. Revised
  manuscript accepted for publication. Recent estimates of QCD vacuum
  condensates are used in the analysis. This and related papers may also be
  obtained from http://www.phys.washington.edu/~derek/Publications.htm
Super-Virasoro Anomaly, Super-Weyl Anomaly and the Super-Liouville
  Action for 2D Supergravity

The relation between super-Virasoro anomaly and super-Weyl anomaly in $N=1$
NSR superstring coupled with 2D supergravity is investigated from canonical
theoretical view point. The WZW action canceling the super-Virasoro anomaly is
explicitly constructed. It is super-Weyl invariant but nonlocal functional of
2D supergravity. The nonlocality can be remedied by the super-Liouvlle action,
which in turn recovers the super-Weyl anomaly. The final gravitational
effective action turns out to be local but noncovariant super-Liouville action,
describing the dynamical behavior of the super-Liouville fields. The BRST
invariance of this approach is examined in the superconformal gauge and in the
light-cone gauge.Comment: 45 page
BRST Cohomology and Hilbert Spaces of Non-Abelian Models in the
  Decoupled Path Integral Formulation

The existence of several nilpotent Noether charges in the decoupled
formulation of two-dimensional gauge theories does not imply that all of these
are required to annihilate the physical states. We elucidate this matter in the
context of simple quantum mechanical and field theoretical models, where the
structure of the Hilbert space is known. We provide a systematic procedure for
deciding which of the BRST conditions is to be imposed on the physical states
in order to ensure the equivalence of the decoupled formulation to the
original, coupled one.Comment: 31 pages,Late
Coherent State Quantization of Constraint Systems

A careful reexamination of the quantization of systems with first- and
second-class constraints from the point of view of coherent-state phase-space
path integration reveals several significant distinctions from more
conventional treatments. Most significantly, we emphasize the importance of
using path-integral measures for Lagrange multipliers which ensure that the
quantum system satisfies the quantum constraint conditions. Our procedures
involve no delta-functionals of the classical constraints, no need for gauge
fixing of first-class constraints, no need to eliminate second-class
constraints, no potentially ambiguous determinants, and have the virtue of
resolving differences between canonical and path-integral approaches. Several
examples are considered in detail.Comment: Latex, 38 pages, no figure
Lattice Charge Overlap I: Elastic Limit of Pi and Rho Mesons

Using lattice QCD on a $16^{3}\times 24$ lattice at $\beta=6.0$, we examine
the elastic limit of charge overlap functions in the quenched approximation for
the pion and rho meson; results are compared to previous direct current
insertion calculations. A good signal is seen for the pion, but the electric
and magnetic rho meson results are considerably noisier. We find that the pion
and rho results are characterized by a monopole mass to rho mass ratio of
$0.97(8)$ and $0.73(10)$, respectively. Assuming the functional form of the
electric and magnetic form factors are the same, we also find a rho meson
g-factor of $g=2.25(34)$, consistent with the nonrelativistic quark model.Comment: 19 pages a uuencoded, compressed file (LateX). Uses more
  configurations and computes correlated chi-squareds on fits. Figures still
  w/o label
Neutrino Propagation in a Fluctuating Sun

We adapt to neutrino physics a general formulation for particle propagation in fluctuating media, initially developed for applications to electromagnetism and neutron optics. In leading approximation this formalism leads to the usual MSW effective hamiltonian governing neutrino propagation through a medium. Next-to-leading contributions describe deviations from this description, which arise due to neutrino interactions with fluctuations in the medium. We compute these corrections for two types of fluctuations: ($i$) microscopic thermal fluctuations, and ($ii$) macroscopic fluctuations in the medium's density. While the first of these reproduces standard estimates, which are negligible for applications to solar neutrinos, we find the second can be quite large, since it grows in size with the correlation length of the fluctuation. We consider two models in some detail. For fluctuations whose correlations are extend only over a local region in space of length $\ell$, appreciable effects for MSW oscillations arise if $(\delta n/n)^2 \ell\gsim 100$ m or so. Alternatively, a crude model of helioseismic $p$-waves gives appreciable effects only when $(\delta n/n) \gsim 1\%$. In general the dominant effect is to diminish the quality of the resonance, making the suppression of the ${}^7$Be neutrinos a good experimental probe of fluctuations deep within the sun. Fluctuations can also provide a new mechanism for reducing the solar neutrino flux, giving an energy-independent suppression factor of $\hf$, away from the resonant region, even for small vacuum mixing angles
Locally Anisotropic Gravity and Strings

An introduction into the theory of locally anisotropic spaces (modelled as
vector bundles provided with compatible nonlinear and distinguished linear
connections and metric structures and containing as particular cases different
types of Kaluza--Klein and/or extensions of Lagrange and Finsler spaces) is
presented. The conditions for consistent propagation of closed strings in
locally anisotropic background spaces are analyzed. The connection between the
conformal invariance, the vanishing of the renormalization group beta--function
of the generalized sigma--model and field equations of locally anisotropic
gravity is studied in detail.Comment: 49 pages, Revtex, a short variant is submitted to Nucl. Phys.
A Class of Quantum Integrable Models Associated with the Infra-red Limit
  of Massive Chern-Simons Theory

We study the infra-red limit of non-abelian Chern-Simons gauge theory
perturbed by a non-topological, albeit gauge invariant, mass term. It is shown
that, in this limit, we may construct an infinite class of integrable quantum
mechanical models which, for the case of SU(2) group, are labelled by the
angular momentum eigenvalue. The first non-trivial example in this class is
obtained for the triplet representation and it physically describes the gauge
invariant coupling of a non-abelian Chern-Simons particle with a particle
moving on $S^3$ - the SU(2) group manifold. In addition to this, the model has
a fascinating resemblance to the Landau problem and may be regarded as a
non-abelian and a non-linear generalisation of the same defined on the
three-sphere with the uniform magnetic field replaced by an angular momentum
field. We explicitly solve for some eigenstates of this model in a closed form
in terms of some generalised orthogonal polynomials. In the process, we unravel
some startling connections with Anderson's chain models which are important in
the study of disordered systems in condensed matter physics. We also sketch a
method which allows us, in principle, to find the energy eigenvalues
corresponding to the above eigenstates of the theory if the Lyapunov exponents
of the transfer matrix of the infinite chain model involved are known.Comment: Plain TeX File, 23 Page
The Hamiltonian Structure of Soliton Equations and Deformed W-Algebras

The Poisson bracket algebra corresponding to the second Hamiltonian structure
of a large class of generalized KdV and mKdV integrable hierarchies is
carefully analysed. These algebras are known to have conformal properties, and
their relation to $\cal W$-algebras has been previously investigated in some
particular cases. The class of equations that is considered includes
practically all the generalizations of the Drinfel'd-Sokolov hierarchies
constructed in the literature. In particular, it has been recently shown that
it includes matrix generalizations of the Gelfand-Dickey and the constrained KP
hierarchies. Therefore, our results provide a unified description of the
relation between the Hamiltonian structure of soliton equations and $\cal
W$-algebras, and it comprises almost all the results formerly obtained by other
authors. The main result of this paper is an explicit general equation showing
that the second Poisson bracket algebra is a deformation of the Dirac bracket
algebra corresponding to the $\cal W$-algebras obtained through Hamiltonian
reduction.Comment: 41 pages, plain TeX, no figures. New introduction and references
  added. Version to be published in Annals of Physics (N.Y.
Improved transport equations including correlations for electron-phonon
  systems. Comparison with exact solutions in one dimension

We study transport equations for quantum many-particle systems in terms of
correlations by applying the general formalism developed in an earlier paper to
exactly soluble electron-phonon models. The one-dimensional models considered
are the polaron model with a linear energy dispersion for the electrons and a
finite number of electrons and the same model including a Fermi sea
(Tomonaga-Luttinger model). The inclusion of two-particle correlations shows a
significant and systematic improvement in comparison with the usual
non-Markovian equations in Born approximation. For example, the improved
equations take into account the renormalization of the propagation by the
self-energies to second order in the coupling.Comment: 20 pages, 15 Postscript figures, uses RevTeX, to be published in:
  Annals of Physics (N.Y.
Non-ideal Boson system in the Gaussian approximation

We investigate ground-state and thermal properties of a system of
non-relativistic bosons interacting through repulsive, two-body interactions in
a self-consistent gaussian mean-field approximation wich consists in writing
the variational determined density operator as the most general gaussian
functional of the quantized field operators. Finite temperature results are
obtained in a grand canonical framework. Contact is made with the results of
Lee,Yang and Huang in terms of a particular truncations of the gaussian
approximation. The full gaussian approximation supports a free phase or a
thermodynamically unstable phase when contact forces and a standard
renormalization scheme are used. When applied to a Hamiltonian with zero range
forces interpreted as an effective theory with a high momentum cut-off, the
full gaussian approximation generates a quasi-particle spectrum having an
energy gap.Comment: 28 pages,5 figures to be published in Ann. of Phy
Deconfinement Transition for Quarks on a Line

We examine the statistical mechanics of a 1-dimensional gas of both adjoint
and fundamental representation quarks which interact with each other through
1+1-dimensional U(N) gauge fields. Using large-N expansion we show that, when
the density of fundamental quarks is small, there is a first order phase
transition at a critical temperature and adjoint quark density which can be
interpreted as deconfinement. When the fundamental quark density is comparable
to the adjoint quark density, the phase transition becomes a third order one.
We formulate a way to distinguish the phases by considering the expectation
values of high winding number Polyakov loop operators.Comment: Reported problems with figures fixed; 38 pages, LaTeX, 5 figures,
  epsfi
First Order Vortex Dynamics

A non-dissipative model for vortex motion in thin superconductors is
considered. The Lagrangian is a Galilean invariant version of the
Ginzburg--Landau model for time-dependent fields, with kinetic terms linear in
the first time derivatives of the fields. It is shown how, for certain values
of the coupling constants, the field dynamics can be reduced to first order
differential equations for the vortex positions. Two vortices circle around one
another at constant speed and separation in this model.Comment: 22pages, no figures, tex fil
Phase Operator Problem and Macroscopic Extension of Quantum Mechanics

To find the Hermitian phase operatorof a single-mode electromagnetic field in
quantum mechanics, the Schroedinger representation is extended to a larger
Hilbert space augmented by states with infinite excitation by nonstandard
analysis. The Hermitian phase operator is shown to exist on the extended
Hilbert space. This operator is naturally considered as the controversial limit
of the approximate phase operators on finite dimensional spaces proposed by
Pegg and Barnett. The spectral measure of this operator is a Naimark extension
of the optimal probability operator-valued measure for the phase parameter
found by Helstrom. Eventually, the two promising approaches to the statistics
of the phase in quantum mechanics is unified by means of the Hermitian phase
operator in the macroscopic extension of the Schroedinger representation.Comment: 26 pages, LaTeX, no figures, to appear in Ann. Phys. (N.Y.
Cosmology in Brans-Dicke theory with a scalar potential

We consider the general behaviour of cosmologies in Brans-Dicke theory where
the dilaton is self-interacting via a potential $V(\Phi)$. We show that the
general radiation universe is a two-dimensional dynamical system whereas the
dust or false vacuum universe is three-dimensional. This is in contrast to the
non-interacting dilaton which has uniformly a two-dimensional phase space. We
find the phase spaces in each case and the general behaviour of the
cosmologies.Comment: 28 pages harvmac, 7 figure
Inequivalent Quantizations and Holonomy Factor from the Path-Integral
  Approach

A path-integral quantization on a homogeneous space G/H is proposed based on
the guiding principle `first lift to G and then project to G/H'. It is then
shown that this principle gives a simple procedure to obtain the inequivalent
quantizations (superselection sectors) along with the holonomy factor (induced
gauge field) found earlier by algebraic approaches. We also prove that the
resulting matrix-valued path-integral is physically equivalent to the
scalar-valued path-integral derived in the Dirac approach, and thereby present
a unified viewpoint to discuss the basic features of quantizing on $G/H$
obtained in various approaches so far.Comment: 21 pages, uses Plain Te
Massive Schwinger model within mass perturbation theory

In this article we give a detailed discussion of the mass perturbation theory
of the massive Schwinger model. After discussing some general features and
briefly reviewing the exact solution of the massless case, we compute the
vacuum energy density of the massive model and some related quantities. We
derive the Feynman rules of mass perturbation theory and discuss the exact
$n$-point functions with the help of the Dyson-Schwinger equations. Further we
identify the stable and unstable bound states of the theory and compute some
bound-state masses and decay widths. Finally we discuss scattering processes,
where the resonances and particle production thresholds of the model are
properly taken into account by our methods.Comment: 57 pages, LaTeX, 20 figures, needed macro: psbox.te
CP-Violating Reflection of High Energy Fermions during a first order Phase Transition

We study the high energy behaviour of fermions hitting a general wall caused by a first-order phase transition. The wall profile is introduced through general analytic and non-analytic functions. The reflection coefficient is computed in the high energy limit and its connection with the analytic properties of the wall profile function is shown. The high energy behaviour of the fermions hitting the wall is determined either by the leading singularity, i.e. the closest pole to the real axis, when the profile function is analytic, or by the first non-continuous derivative on the real axis, in the non-analytic case. CP-violating wall profiles are studied and it is shown that the respective symmetry properties of the CP-conserving and CP-violating profile functions plays an important role on the size of the CP asymmetry
Michel theory of symmetry breaking and gauge theories

We extend Michel's theorem on the geometry of symmetry breaking [L. Michel,
{\it Comptes Rendus Acad. Sci. Paris} {\bf 272-A} (1971), 433-436] to the case
of pure gauge theories, i.e. of gauge-invariant functionals defined on the
space ${\cal C}$ of connections of a principal fiber bundle. Our proof follows
closely the original one by Michel, using several known results on the geometry
of ${\cal C}$. The result (and proof) is also extended to the case of gauge
theories with matter fields.Comment: 24 pages. An old paper posted for archival purpose