pinecone/core-2020-05-10-deduplication huggingface dataset:
Conserved Currents, Consistency Relations and Operator Product
  Expansions in the Conformally Invariant O(N) Vector Model

We discuss conserved currents and operator product expansions (OPE's) in the
context of a $O(N)$ invariant conformal field theory. Using OPE's we find
explicit expressions for the first few terms in suitable short-distance limits
for various four-point functions involving the fundamental $N$-component scalar
field $\phi^{\alpha}(x)$, $\alpha=1,2,..,N$. We propose an alternative
evaluation of these four-point functions based on graphical expansions.
Requiring consistency of the algebraic and graphical treatments of the
four-point functions we obtain the values of the dynamical parameters in either
a free theory of $N$ massless fields or a non-trivial conformally invariant
$O(N)$ vector model in $2<d<4$, up to next-to-leading order in a $1/N$
expansion. Our approach suggests an interesting duality property of the
critical $O(N)$ invariant theory. Also, solving our consistency relations we
obtain the next-to-leading order in $1/N$ correction for $C_{T}$ which
corresponds to the normalisation of the energy momentum tensor two-point
function.Comment: 45 pages Latex + 2 uuencoded PostScript figures, DAMTP 94/1
On Galilei Invariance in Quantum Mechanics and the Bargmann
  Superselection Rule

We reinvestigate Bargmann's superselection rule for the overall mass of $n$
particles in ordinary quantum mechanics with Galilei invariant interaction
potential. We point out that in order for mass to define a superselection rule
it should be considered as a dynamical variable. We present a minimal extension
of the original dynamics in which mass it treated as dynamical variable. Here
the classical symmetry group turns out to be given by an $\reals$-extension of
the Galilei group which formerly appeared only at the quantum level. There is
now no obstruction to implement an action of the classical symmetry group on
Hilbert space. We include some critical comments of a general nature on formal
derivations of superselection rules without dynamical context.Comment: 14 Pages, Plain-TeX, no figure
Spinors in non-relativistic Chern-Simons electrodynamics

It is shown that the non-relativistic `Dirac' equation of L\'evy-Leblond, we
used recently to describe a spin $1/2$ field interacting non-relativistically
with a Chern-Simons gauge field, can be obtained by lightlike reduction from
$3+1$ dimensions. This allows us to prove that the system is Schr\"odinger
symmetric. A spinor representation of the Schr\"odinger group is presented.
Static, self-dual solutions, describing spinor vortices are given and shown to
be the non-relativistic limits of the fermionic vortices found by Cho et al.
The construction is extended to external harmonic and uniform magnetic fields.Comment: Plain TEX, 43 page
Multi-particle States from the Effective Action for Local Composite
  Operators: Anharmonic Oscillator

The effective action for the local composite operator $\Phi^2(x)$ in the
scalar quantum field theory with $\lambda\Phi^4$ interaction is obtained in the
expansion in two-particle-point-irreducible (2PPI) diagrams up to five-loops.
The effective potential and 2-point Green's functions for elementary and
composite fields are derived. The ground state energy as well as one- and
two-particle excitations are calculated for space-time dimension $n=1$, when
the theory is equivalent to the quantum mechanics of an anharmonic oscillator.
The agreement with the exact spectrum of the oscillator is much better than
that obtained within the perturbation theory.Comment: 15 pages, plain Latex, 4 tared, compressed and uuencoded Postscript
  figure
Generalized Thirring Models

The Thirring model and various generalizations of it are analyzed in detail.
The four-Fermi interaction modifies the equation of state. Chemical potentials
and twisted boundary conditions both result in complex fermionic determinants
which are analyzed. The non-minimal coupling to gravity does deform the
conformal algebra which in particular contains the minimal models. We compute
the central charges, conformal weights and finite size effects. For the gauged
model we derive the partition functions and the explicit expression for the
chiral condensate at finite temperature and curvature. The Bosonization in
compact curved space-times is also investigated.Comment: LaTex 55 pages, 2 figures, extended version of our previous work
  (hep-th/9308067
Survival and Nonescape Probabilities for Resonant and Nonresonant Decay

In this paper we study the time evolution of the decay process for a particle
confined initially in a finite region of space, extending our analysis given
recently (Phys. Rev. Lett. 74, 337 (1995)). For this purpose, we solve exactly
the time-dependent Schroedinger equation for a finite-range potential. We
calculate and compare two quantities: (i) the survival probability S(t), i.e.,
the probability that the particle is in the initial state after a time t; and
(ii) the nonescape probability P(t), i.e., the probability that the particle
remains confined inside the potential region after a time t. We analyze in
detail the resonant and nonresonant decay. In the former case, after a very
short time, S(t) and P(t) decay exponentially, but for very long times they
decay as a power law, albeit with different exponents. For the nonresonant case
we obtain that both quantities differ initially. However, independently of the
resonant and nonresonant character of the initial state we always find a
transition to the ground state of the system which indicates a process of
``loss of memory'' in the decay.Comment: 26 pages, RevTex file, figures available upon request from
  mateos@sysul2.ifisicacu.unam.mx (To be published in Annals of Physics
Classical and quantum many-body description of bremsstrahlung in dense matter (Landau - Pomeranchuk - Migdal effect)

Some considerations about the importance of coherence effects for bremsstrahlung processes in non--equilibrium dense matter (Landau - Pomeranchuk - Migdal - effect) are presented. They are of particular relevance for the application to photon - and di-lepton production from high energy nuclear collisions, to gluon radiation in QCD transport, or parton kinetics and to neutrino and axion radiation from supernova explosion and from hot neutron stars. The soft behavior of the bremsstrahlung from a source described by classical transport models is discussed and pocket correction formulas for the in-matter radiation cross sections are suggested in terms of standard transport coefficients. The radiation rates are also discussed within a non--equilibrium quantum field theory (Schwinger - Kadanoff - Baym - Keldysh) formulation. A classification of diagrams and corresponding resummation in physically meaningful terms is proposed, which considers the finite damping width of all source particles in matter. This way each diagram in this expansion is already free from the infra--red divergences. Both, the correct quasi--particle and quasi--classical limits are recovered from this subset of graphs. Explicit results are given for dense matter in thermal equilibrium. The diagrammatic description may suggest a formulation of a transport theory that includes the propagation of off--shell particles in non--equilibrium dense matter
Temperature Expansions for Magnetic Systems

We derive finite temperature expansions for relativistic fermion systems in
the presence of background magnetic fields, and with nonzero chemical
potential. We use the imaginary-time formalism for the finite temperature
effects, the proper-time method for the background field effects, and zeta
function regularization for developing the expansions. We emphasize the
essential difference between even and odd dimensions, focusing on $2+1$ and
$3+1$ dimensions. We concentrate on the high temperature limit, but we also
discuss the $T=0$ limit with nonzero chemical potential.Comment: 25 pages, RevTe
Wigner transformation for the determinant of Dirac operators

We use the $\zeta$-function regularization and an integral representation of
the complex power of a pseudo differential operator, to give an unambiguous
definition of the determinant of the Dirac operator. We bring this definition
to a workable form by making use of an asymmetric Wigner representation. The
expression so obtained is amenable to several treatments of which we consider
in detail two, the inverse mass expansion and the gradient expansion, with
concrete examples. We obtain explicit closed expressions for the corresponding
Seeley-DeWitt coefficients to all orders. The determinant is shown to be vector
gauge invariant and to posses the correct axial and scale anomalies. The main
virtue of our approach is that it is conceptually simple and systematic and can
be extended naturally to more general problems (bosonic operators,
gravitational fields, etc). In particular, it avoids defining the real and
imaginary parts of the effective action separately. In addition, it does not
reduce the problem to a bosonic one to apply heat kernel nor performs further
analytical rotations of the fields to make the Dirac operator Hermitian. We
illustrate the flexibility of the method by studying some interesting cases.Comment: Plain TeX, 48 page
Transitions toward Quantum Chaos: with Supersymmetry from Poisson to
  Gauss

The transition from arbitrary to chaotic fluctuation properties in quantum
systems is studied in a random matrix model. It is assumed that the Hamiltonian
can be written as the sum of an arbitrary and a chaos producing part. The
Gaussian ensembles are used to model the chaotic part. A closed integral
representation for all correlations in the case of broken time reversal
invariance is derived by employing supersymmetry and the graded eigenvalue
method. In particular, the two level correlation function is expressed as a
double integral. For a correlation index, exact diffusion equations are derived
for all three universality classes which describe the transition to the chaotic
regime from arbitrary initial conditions. As an application, the transition
from Poisson regularity to chaos is discussed. The two level correlation
function becomes a double integral for all values of the transition parameter.Comment: 49 pages, one figure in one postscript fil
The QED(0+1) model and a possible dynamical solution of the strong CP
  problem

The QED(0+1) model describing a quantum mechanical particle on a circle with
minimal electromagnetic interaction and with a potential -M cos(phi - theta_M),
which mimics the massive Schwinger model, is discussed as a prototype of
mechanisms and infrared structures of gauge quantum field theories in positive
gauges. The functional integral representation displays a complex measure, with
a crucial role of the boundary conditions, and the decomposition into theta
sectors takes place already in finite volume. In the infinite volume limit, the
standard results are reproduced for M=0 (massless fermions), but one meets
substantial differences for M not = 0: for generic boundary conditions,
independently of the lagrangean angle of the topological term, the infinite
volume limit selects the sector with theta = theta_M, and provides a natural
"dynamical" solution of the strong CP problem. In comparison with previous
approaches, the strategy discussed here allows to exploit the consequences of
the theta-dependence of the free energy density, with a unique minimum at theta
= theta_M.Comment: 21 pages, Plain Te
Discussing the U(1)-Problem of QED_2 without Instantons

We construct QED_2 with mass and flavor and an extra Thirring term. The
vacuum expectation values are carefully decomposed into clustering states using
the U(1)-axial symmetry of the considered operators and a limiting procedure.
The properties of the emerging expectation functional are compared to the
proposed theta-vacuum of QCD. The massive theory is bosonized to a generalized
Sine-Gordon model (GSG). The structure of the vacuum of QED_2 manifests itself
in symmetry properties of the GSG. We study the U(1)-problem and derive a
Witten-Veneziano-type formula for the masses of the pseudoscalars determined
from a semiclassical approximation.Comment: Accepted for publication in Annals of Physic
Complete zeta-function approach to the electromagnetic Casimir effect
  for spheres and circles

A technique for evaluating the electromagnetic Casimir energy in situations
involving spherical or circular boundaries is presented. Zeta function
regularization is unambiguously used from the start and the properties of
Bessel and related zeta functions are central. Nontrivial results concerning
these functions are given. While part of their application agrees with previous
knowledge, new results like the zeta-regularized electromagnetic Casimir energy
for a circular wire are included.Comment: accepted in Ann. Phy
Zero temperature phase transitions in quantum Heisenberg ferromagnets

The purpose of this work is to understand the zero temperature phases, and
the phase transitions, of Heisenberg spin systems which can have an extensive,
spontaneous magnetic moment; this entails a study of quantum transitions with
an order parameter which is also a non-abelian conserved charge. To this end,
we introduce and study a new class of lattice models of quantum rotors. We
compute their mean-field phase diagrams, and present continuum, quantum
field-theoretic descriptions of their low energy properties in different
regimes. We argue that, in spatial dimension $d=1$, the phase transitions in
itinerant Fermi systems are in the same universality class as the corresponding
transitions in certain rotor models. We discuss implications of our results for
itinerant fermions systems in higher $d$, and for other physical systems.Comment: 45 pages, REVTEX 3.0, 5 EPS figure
Two-Photon Algebra Eigenstates: A Unified Approach to Squeezing

We use the concept of the algebra eigenstates that provides a unified
description of the generalized coherent states (belonging to different sets)
and of the intelligent states associated with a dynamical symmetry group. The
formalism is applied to the two-photon algebra and the corresponding algebra
eigenstates are studied by using the Fock-Bargmann analytic representation.
This formalism yields a unified analytic approach to various types of
single-mode photon states generated by squeezing and displacing
transformations.Comment: To appear in Annals of Physics, REVTeX with AMSsymbols, 27 pages, no
  figures. More information on http://www.technion.ac.il/~brif/science.htm
Exploring Periodic Orbit Expansions and Renormalisation with the Quantum
  Triangular Billiard

A study of the quantum triangular billiard requires consideration of a
boundary value problem for the Green's function of the Laplacian on a trianglar
domain. Our main result is a reformulation of this problem in terms of coupled
non--singular integral equations. A non--singular formulation, via Fredholm's
theory, guarantees uniqueness and provides a mathematically firm foundation for
both numerical and analytic studies. We compare and contrast our reformulation,
based on the exact solution for the wedge, with the standard singular integral
equations using numerical discretisation techniques. We consider in detail the
(integrable) equilateral triangle and the Pythagorean 3-4-5 triangle. Our
non--singular formulation produces results which are well behaved
mathematically. In contrast, while resolving the eigenvalues very well, the
standard approach displays various behaviours demonstrating the need for some
sort of ``renormalisation''. The non-singular formulation provides a
mathematically firm basis for the generation and analysis of periodic orbit
expansions. We discuss their convergence paying particular emphasis to the
computational effort required in comparision with Einstein--Brillouin--Keller
quantisation and the standard discretisation, which is analogous to the method
of Bogomolny. We also discuss the generalisation of our technique to smooth,
chaotic billiards.Comment: 50 pages LaTeX2e. Uses graphicx, amsmath, amsfonts, psfrag and
  subfigure. 17 figures. To appear Annals of Physics, southern sprin
Dissipation and Topologically Massive Gauge Theories in Pseudoeuclidean
  Plane

In the pseudo-euclidean metrics Chern-Simons gauge theory in the infrared
region is found to be associated with dissipative dynamics. In the infrared
limit the Lagrangian of 2+1 dimensional pseudo-euclidean topologically massive
electrodynamics has indeed the same form of the Lagrangian of the damped
harmonic oscillator. On the hyperbolic plane a set of two damped harmonic
oscillators, each other time-reversed, is shown to be equivalent to a single
undamped harmonic oscillator. The equations for the damped oscillators are
proven to be the same as the ones for the Lorentz force acting on two particles
carrying opposite charge in a constant magnetic field and in the electric
harmonic potential. This provides an immediate link with Chern-Simons-like
dynamics of Bloch electrons in solids propagating along the lattice plane with
hyperbolic energy surface. The symplectic structure of the reduced theory is
finally discussed in the Dirac constrained canonical formalism.Comment: 22 pages, LaTe
Point interactions in a strip

We study the behavior of a quantum particle confined to a hard--wall strip of
a constant width in which there is a finite number $ N $ of point
perturbations. Constructing the resolvent of the corresponding Hamiltonian by
means of Krein's formula, we analyze its spectral and scattering properties.
The bound state--problem is analogous to that of point interactions in the
plane: since a two--dimensional point interaction is never repulsive, there are
$ m $ discrete eigenvalues, $ 1\le m\le N $, the lowest of which is
nondegenerate. On the other hand, due to the presence of the boundary the point
interactions give rise to infinite series of resonances; if the coupling is
weak they approach the thresholds of higher transverse modes. We derive also
spectral and scattering properties for point perturbations in several related
models: a cylindrical surface, both of a finite and infinite heigth, threaded
by a magnetic flux, and a straight strip which supports a potential independent
of the transverse coordinate. As for strips with an infinite number of point
perturbations, we restrict ourselves to the situation when the latter are
arranged periodically; we show that in distinction to the case of a
point--perturbation array in the plane, the spectrum may exhibit any finite
number of gaps. Finally, we study numerically conductance fluctuations in case
of random point perturbations.Comment: a LaTeX file, 38 pages, to appear in Ann. Phys.; 12 figures available
  at request from tater@ujf.cas.c
Gravitational waves propagating into Friedmann--Robertson--Walker
  universes

We consider space-times with two isometries which represent gravitational
waves with distinct wavefronts which propagate into exact
Friedmann-Robertson-Walker (FRW) universes. The geometry of possible wavefronts
is analysed in detail in all three types of FRW models. In the spatially flat
and open universes, the wavefronts can be planar or cylindrical; in the closed
case they are toroidal. Exact solutions are given which describe gravitational
waves propagating into the FRW universes with a fluid with a stiff equation of
state. It is shown that the plane-fronted waves may include impulsive or step
(shock) components, while the cylindrical waves in the spatially flat and open
universes and the toroidal waves in closed universes may contain steps. In
general, wavefronts may exist which have an arbitrary finite degree of
smoothness. In all cases, the waves are backscattered. The head-on collision of
such waves is also briefly mentioned.Comment: 26 pages, LaTeX, 8 figures not included. To be published in the
  November issue of Annals of Physic
A general algebraic model for molecular vibrational spectroscopy

We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational
excitations in molecular systems exhibiting high degree of symmetry. A
systematic procedure is proposed to establish the relation between the
algebraic and configuration space formulations, leading to new interactions in
the algebraic model. This approach incorporates the full power of group
theoretical techniques and provides reliable spectroscopic predictions. We
illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules.Comment: 35 pages TEX, submitted to Annals of Physics (N.Y.
Extended Two--Particle Green's Functions and Optical Potentials for
  Two--Particle Scattering by Many--Body Targets

An extension of the fermionic particle--particle propagator is presented,
that possesses similar algebraic properties to the single--particle Green's
function. In particular, this extended two--particle Green's function satisfies
Dyson's equation and its self energy has the same analytic structure as the the
self energy of the single--particle Green's function. For the case of a system
interacting by one--particle potentials only, the two--particle self energy
takes on a particularly simple form, just like the common self energy does. The
new two--particle self energy also serves as a well behaved optical potential
for the elastic scattering of a two--particle projectile by a many--body
target. Due to its analytic structure, the two--particle self energy avoids
divergences that appear with effective potentials derived by other means.Comment: 17 pages of LaTeX, no figures, submitted to Annals of Physics (N. Y.
Transport equations including many-particle correlations for an
  arbitrary quantum system. General formalism

We present a new method to derive transport equations for quantum
many-particle systems. This method uses an equation-of-motion technique and is
applicable to systems with bosons and fermions, arbitrary interactions and
time-dependent external fields. Using a cluster expansion of the r-particle
density matrices the infinite hierarchy of equations of motion for
many-particle expectation values is transposed into an equivalent one in terms
of correlations. This new hierarchy permits a systematic breaking of the
hierarchy at any order. Diagrams are derived for these transport equations. In
a second paper the method is tested for exactly soluble electron-phonon models
in one dimension.Comment: 19 pages, 14 Postscript figures, uses RevTeX, to be published in:
  Annals of Physics (N.Y.
Inclusion of Quantum Fluctuations in Wave Packet Dynamics

We discuss a method by which quantum fluctuations can be included in
microscopic transport models based on wave packets that are not energy
eigenstates. By including the next-to-leading order term in the cumulant
expansion of the statistical weight, which corresponds to the wave packets
having Poisson energy distributions, we obtain a much improved global
description of the quantum statistical properties of the many-body system. In
the case of atomic nuclei, exemplified by 12C and 40Ca, the standard
liquid-drop results are reproduced at low temperatures and a phase
transformation to a fragment gas occurs as the temperature is raised. The
treatment can be extended to dynamical scenarios by means of a Langevin force
emulating the transitions between the wave packets. The general form of the
associated transport coefficients is derived and it is shown that the
appropriate microcanonical equilibrium distribution is achieved in the course
of the time evolution. Finally, invoking Fermi's golden rule, we derive
specific expressions for the transport coefficients and verify that they
satisfy the fluctuation-dissipation theorem.Comment: uuencoded revtex body and 8 ps figures (16 pages total