pinecone/core-2020-05-10-deduplication huggingface dataset:
The Higher Derivative Expansion of the Effective Action by the String
  Inspired Method. Part II

We apply the string inspired worldline formalism to the calculation of the
higher derivative expansion of one-loop effective actions in non-Abelian gauge
theory. For this purpose, we have completely computerized the method, using the
symbolic manipulation programs FORM, PERL and M. Explicit results are given to
sixth order in the inverse mass expansion, reduced to a minimal basis of
invariants specifically adapted to the method. Detailed comparisons are made
with other gauge-invariant algorithms for calculating the same expansion. This
includes an explicit check of all coefficients up to fifth order.Comment: 37 pages, LaTeX, 3 figures, typos corrected, to appear in Ann. Phys.
  (N.Y.
The Quantum Aspects of Relativistic Fermion Systems with Particle
  Condensation

A consistent local approach to the study of interacting relativistic fermion
systems with a condensation of bare particles in its ground or vacuum state,
which may has a finite matter density, is developed. The attention is payed to
some of the not so well explored quantum aspects that survive the thermodynamic
limit. A 4-vector local field, called the primary statistical gauge field, and
a statistical blocking parameter are introduced for a consistent treatment of
the problem. The effects of random fluctuations of the fields on local
observables are discussed. It is found that quasiparticle contributions are not
sufficient to saturate local observables. The property of the primary
statistical gauge field are discussed in some detail. Two models for the strong
interaction are then introduced and studied using the general framework
developed. Four possible phases for these models are found. The possibility of
spontaneous CP violation and local fermion creation in two of the four phases
is revealed. The implications of the finding on our understanding of some of
the strong interaction processes are discussed.Comment: 35 pages, 11 figures, RevTeX file, to appear in Ann. Phys. (N.Y.
Convergence properties of the equal-time connected Green function
  approach for temporal gauge SU(2)_{2+1} Yang-Mills theory

The hierarchy of equations of motion for equal-time Green functions in
temporal gauge SU(N) Yang-Mills theory is truncated using an expansion in terms
of connected Green functions. A second hierarchy of constraint equations arises
from Gauss law and can be truncated in a similar way. Within this approximation
scheme we investigate SU(2) Yang-Mills theory on a torus in 2+1 spacetime
dimensions in a finite basis of plane wave states and focus on infrared and
ultraviolet properties of the approach. We study the consequences of restoring
the hierarchy of Gauss law constraints and of different momentum cutoffs for
the 2- and the 3-point functions. In all truncation schemes considered up to
the 4-point level the connected Green function approach is found to be UV
divergent and either violating gauge invariance and/or energy conservation. The
problems associated with adiabatically generating a perturbed ground state are
discussed as well.Comment: 43 pages, LaTeX, 15 PS figure
Reducible systems and embedding procedures in the canonical formalism

We propose a systematic method of dealing with the canonical constrained
structure of reducible systems in the Dirac and symplectic approaches which
involves an enlargement of phase and configuration spaces, respectively. It is
not necessary, as in the Dirac approach, to isolate the independent subset of
constraints or to introduce, as in the symplectic analysis, a series of
lagrange multipliers-for-lagrange multipiers. This analysis illuminates the
close connection between the Dirac and symplectic approaches of treating
reducible theories, which is otherwise lacking. The example of p-form gauge
fields (p=2,3) is analyzed in details.Comment: Latex 23 pages, some corrections and improvements in the text. To
  appear in Annals of Physic
Nonperturbative Stochastic Quantization of the Helix Model

The helix model describes the minimal coupling of an abelian gauge field with
three bosonic matter fields in 0+1 dimensions; it is a model without a global
Gribov obstruction. We perform the stochastic quantization in configuration
space and prove nonperturbatively equivalence with the path integral formalism.
Major points of our approach are the geometrical understanding of separations
into gauge independent and gauge dependent degrees of freedom as well as a
generalization of the stochastic gauge fixing procedure which allows to extract
the equilibrium Fokker-Planck probability distribution of the model.Comment: 43 pages, LaTex, 1 encapsulated Postscript figure (epsbox.sty)
  include
Thermodynamics of a weakly interacting Bose-Einstein gas

The one-loop effective potential for non-relativistic bosons with a delta
function repulsive potential is calculated for a given chemical potential using
functional methods. After renormalization and at zero temperature it reproduces
the standard ground state energy and pressureas function of the particle
density. At finite temperatures it is found necessary to include ring
corrections to the one-loop result in order to satisfy the Goldstone theorem.
It is natural to introduce an effective chemical potential directly related to
the order parameter and which uniformly decreases with increasing temperatures.
This is in contrast to the the ordinary chemical potential which peaks at the
critical temperature. The resulting thermodynamics in the condensed phase at
very low temperatures is found to be the same as in the Bogoliubov
approximation where the degrees of freedom are given by the Goldstone bosons.
At higher temperatures the ring corrections dominate and result in a critical
temperature unaffected by the interaction.Comment: 39 pages, 9 figures, picTex, submitted to Annals of Physics.
  Discussions on renormalization and off-diagonal self energies are made
  clearer in this version. A short derivation of the non-relativistic limit is
  adde
Wigner functions in covariant and single-time formulations

We will establish the connection between the Lorentz covariant and so-called
single-time formulation for the quark Wigner operator. To this end we will
discuss the initial value problem for the Wigner operator of a field theory and
give a discussion of the gauge-covariant formulation for the Wigner operator
including some new results concerning the chiral limit. We discuss the gradient
or semi-classical expansion and the color and spinor decomposition of the
equations of motion for the Wigner operator. The single-time formulation will
be derived from the covariant formulation by taking energy moments of the
equations for the Wigner operator. For external fields we prove that only the
lowest energy moments of the quark Wigner operator contain dynamical
information.Comment: 92 pages, to appear in Annals of Physics (N.Y.
New Fundamental Symmetries of Integrable Systems and Partial Bethe
  Ansatz

We introduce a new concept of quasi-Yang-Baxter algebras. The quantum
quasi-Yang-Baxter algebras being simple but non-trivial deformations of
ordinary algebras of monodromy matrices realize a new type of quantum dynamical
symmetries and find an unexpected and remarkable applications in quantum
inverse scattering method (QISM). We show that applying to quasi-Yang-Baxter
algebras the standard procedure of QISM one obtains new wide classes of quantum
models which, being integrable (i.e. having enough number of commuting
integrals of motion) are only quasi-exactly solvable (i.e. admit an algebraic
Bethe ansatz solution for arbitrarily large but limited parts of the spectrum).
These quasi-exactly solvable models naturally arise as deformations of known
exactly solvable ones. A general theory of such deformations is proposed. The
correspondence ``Yangian --- quasi-Yangian'' and ``$XXX$ spin models ---
quasi-$XXX$ spin models'' is discussed in detail. We also construct the
classical conterparts of quasi-Yang-Baxter algebras and show that they
naturally lead to new classes of classical integrable models. We conjecture
that these models are quasi-exactly solvable in the sense of classical inverse
scattering method, i.e. admit only partial construction of action-angle
variables.Comment: 49 pages, LaTe
Run-away solutions in relativistic spin 1/2 quantum electrodynamics

The existence of run-away solutions in classical and non-relativistic quantum
electrodynamics is reviewed. It is shown that the less singular high energy
behavior of relativistic spin 1/2 quantum electrodynamics precludes an
analogous behavior in that theory. However, a Landau-like anomalous pole in the
photon propagation function or in the electron-massive photon foward scattering
amplitude would generate a new run-away, characterized by an energy scale omega
~ m_e exp (1/alpha). This contrasts with the energy scale omega ~ (m_e/alpha)
associated with the classical and non-relativistic quantum run-aways.Comment: 3 minor changes; 17 pgs, epsf & aps styles,1 eps & 2 embedded ps fig
Oriented Open-Closed String Theory Revisited

String theory on D-brane backgrounds is open-closed string theory. Given the
relevance of this fact, we give details and elaborate upon our earlier
construction of oriented open-closed string field theory. In order to
incorporate explicitly closed strings, the classical sector of this theory is
open strings with a homotopy associative A_\infty algebraic structure. We build
a suitable Batalin-Vilkovisky algebra on moduli spaces of bordered Riemann
surfaces, the construction of which involves a few subtleties arising from the
open string punctures and cyclicity conditions. All vertices coupling open and
closed strings through disks are described explicitly. Subalgebras of the
algebra of surfaces with boundaries are used to discuss symmetries of classical
open string theory induced by the closed string sector, and to write classical
open string field theory on general closed string backgrounds. We give a
preliminary analysis of the ghost-dilaton theorem.Comment: 61 pages, 19 eps figures, phyzzx, BoxedEP
Metaplectic Covariance of the Weyl-Wigner-Groenewold-Moyal Quantization
  and Beyond

The metaplectic covariance for all forms of the Weyl-Wigner-Groenewold-Moyal
quantization is established with different realizations of the inhomogeneous
symplectic algebra. Beyond that, in its most general form $W_{\infty}$
-covariance of this quantization scheme is investigated, and explicit
expressions for the quantum-deformed Hamiltonian vector fields are presented.
In a general basis the structure constants of the $W_{\infty}$-algebra are
obtained and its subalgebras are analyzed.Comment: 20 pages,no figures,to appear in Ann. Phys.(N.Y
A quantum kinetic equation for Fermi-systems including three-body
  correlations

A single-time quantum transport equation, which includes effects beyond the
quasiparticle approximation, is derived for Fermi-systems in the framework of
non-equilibrium real-time Green's functions theory. Ternary correlations are
incorporated in the kinetic description via a cluster expansion for the
self-energies (e.g., the transport vertex and the width) truncated at the level
of three-body scattering amplitudes. A finite temperature/density formulation
of the three-body problem is given. Corresponding three-body equations reduce
to the well-known Faddeev equations in the vacuum limit. In equilibrium the
equation of state contains virial corrections proportional to the third quantum
virial coefficient.Comment: 25 pages, Revtex, 2 figures. Final version to be published in Annals
  of Physics (NY), with minor change
Phase Coherence in Quantum Brownian Motion

The quantum theory of Brownian motion is discussed in the Schwinger version
wherein the notion of a coordinate moving forward in time $x(t)$ is replaced by
two coordinates, $x_+(t)$ moving forward in time and $x_-(t)$ moving backward
in time. The role of the doubling of the degrees of freedom is illustrated for
the case of electron beam two slit diffraction experiments. Interference is
computed with and without dissipation (described by a thermal bath). The notion
of a dissipative interference phase, closely analogous to the Aharonov-Bohm
magnetic field induced phase, is explored.Comment: 12 pages, LaTeX, 2 Figure
A Coupled-Cluster Formulation of Hamiltonian Lattice Field Theory: The
  Non-Linear Sigma Model

We apply the coupled cluster method (CCM) to the Hamiltonian version of the
latticised O(4) non-linear sigma model. The method, which was initially
developed for the accurate description of quantum many-body systems, gives rise
to two distinct approximation schemes. These approaches are compared with each
other as well as with some other Hamiltonian approaches. Our study of both the
ground state and collective excitations leads to indications of a possible
chiral phase transition as the lattice spacing is varied.Comment: 44 Pages, 14 figures. Uses Latex2e, graphicx, amstex and geometry
  package
Hamilton-Jacobi approach to Berezinian singular systems

In this work we present a formal generalization of the Hamilton-Jacobi
formalism, recently developed for singular systems, to include the case of
Lagrangians containing variables which are elements of Berezin algebra. We
derive the Hamilton-Jacobi equation for such systems, analizing the singular
case in order to obtain the equations of motion as total differential equations
and study the integrability conditions for such equations. An example is solved
using both Hamilton-Jacobi and Dirac's Hamiltonian formalisms and the results
are compared.Comment: LaTex, 30 pages, no figure
Renormalization Group Transformation for the Wave Function

The problem considered here is the determination of the hamiltonian of a
first quantized nonrelativistic particle by the help of some measurements of
the location with a finite resolution. The resulting hamiltonian depends on the
resolution of the measuring device. This dependence is reproduced by the help
of a blocking transformation on the wave function. The systems with quadratic
hamiltonian are studied in details. The representation of the renormalization
group in the space of observables is identified.Comment: Final version to appear in Ann. Phy
Magnetoconductance Autocorrelation Function for Few--Channel Chaotic
  Microstructures

Using the Landauer formula and a random matrix model, we investigate the
autocorrelation function of the conductance versus magnetic field strength for
ballistic electron transport through few-channel microstructures with the shape
of a classically chaotic billiard coupled to ideal leads. This function depends
on the total number M of channels and the parameter t which measures the
difference in magnetic field strengths. Using the supersymmetry technique, we
calculate for any value of M the leading terms of the asymptotic expansion for
small t. We pay particular attention to the evaluation of the boundary terms.
For small values of M, we supplement this analytical study by a numerical
simulation. We compare our results with the squared Lorentzian suggested by
semiclassical theory and valid for large M. For small M, we present evidence
for non--analytic behavior of the autocorrelation function at t = 0.Comment: 40 pages, 4 figures, submitted to Annals of Physics (NY
Mirror Maps in Chern-Simons Gauge Theory

We describe mirror symmetry in N=2 superconformal field theories in terms of
a dynamical topology changing process of the principal fiber bundle associated
with a topological membrane. We show that the topological symmetries of
Calabi-Yau sigma-models can be obtained from discrete geometric transformations
of compact Chern-Simons gauge theory coupled to charged matter fields. We
demonstrate that the appearence of magnetic monopole-instantons, which
interpolate between topologically inequivalent vacua of the gauge theory,
implies that the discrete symmetry group of the worldsheet theory is realized
kinematically in three dimensions as the magnetic flux symmetry group. From
this we construct the mirror map and show that it corresponds to the
interchange of topologically non-trivial matter field and gauge degrees of
freedom. We also apply the mirror transformation to the mean field theory of
the quantum Hall effect. We show that it maps the Jain hierarchy into a new
hierarchy of states in which the lowest composite fermions have the same
filling fractions.Comment: 40 pages LaTeX, 4 postscript files, uses psfig.sty; minor textual
  changes, typos corrected, references adde
Structural Aspects of Two-Dimensional Anomalous Gauge Theories

A foundational investigation of the basic structural properties of
two-dimensional anomalous gauge theories is performed. The Hilbert space is
constructed as the representation of the intrinsic local field algebra
generated by the fundamental set of field operators whose Wightman functions
define the model. We examine the effect of the use of a redundant field algebra
in deriving basic properties of the models and show that different results may
arise, as regards the physical properties of the generalized chiral model, in
restricting or not the Hilbert space as representation of the intrinsic local
field algebra. The question referring to considering the vector Schwinger model
as a limit of the generalized anomalous model is also discussed. We show that
this limit can only be consistently defined for a field subalgebra of the
generalized model.Comment: 40 pages. Latex, to appear in Annals of Physic
Time-Dependent Variational Principle for $\phi^4$ Field Theory: RPA
  Approximation and Renormalization (II)

The Gaussian-time-dependent variational equations are used to explored the
physics of $(\phi^4)_{3+1}$ field theory. We have investigated the static
solutions and discussed the conditions of renormalization. Using these results
and stability analysis we show that there are two viable non-trivial versions
of $(\phi^4)_{3+1}$. In the continuum limit the bare coupling constant can
assume $b\to 0^{+}$ and $b\to 0^{-}$, which yield well defined asymmetric and
symmetric solutions respectively. We have also considered small oscillations in
the broken phase and shown that they give one and two meson modes of the
theory. The resulting equation has a closed solution leading to a ``zero mode''
and vanished scattering amplitude in the limit of infinite cutoff.Comment: 29 pages, LaTex file, to appear in Annals of Physic
Polyakov Loop Dynamics in the Center Symmetric Phase

A study of the center symmetric phase of SU(2) Yang Mills theory is
presented. Realization of the center symmetry is shown to result from
non-perturbative gauge fixing. Dictated by the center symmetry, this phase
exhibits already at the perturbative level confinement like properties. The
analysis is performed by investigating the dynamics of the Polyakov loops. The
ultralocality of these degrees of freedom implies significant changes in the
vacuum structure of the theory. General properties of the confined phase and of
the transition to the deconfined phase are discussed. Perturbation theory built
upon the vacuum of ultralocal Polyakov loops is presented and used to
calculate, via the Polyakov loop correlator, the static quark-antiquark
potential.Comment: 45 pages, LaTeX, 8 figure
Monopoles, Polyakov-Loops and Gauge Fixing on the Torus

We consider pure Yang Mills theory on the four torus. A set of non-Abelian
transition functions is presented which encompass all instanton sectors. It is
argued that these transition functions are a convenient starting point for
gauge fixing. In particular, we give an extended Abelian projection with
respect to the Polyakov loop, where $A_0$ is independent of time and in the
Cartan subalgebra. In the non-perturbative sectors such gauge fixings are
necessarily singular. These singularities can be restricted to Dirac strings
joining monopole and anti-monopole like ``defects''.Comment: 24 pages, 4 figures, Latex 2e, some minor improvement
A Canonical Quantization of the Baker's Map

We present here a canonical quantization for the baker's map. The method we
use is quite different from that used in Balazs and Voros (ref.
\QCITE{cite}{}{BV}) and Saraceno (ref. \QCITE{cite}{}{S}). We first construct a
natural ``baker covering map'' on the plane $\QTO{mathbb}{\mathbb{R}}^{2}$. We
then use as the quantum algebra of observables the subalgebra of operators on
$L^{2}(\QTO{mathbb}{\mathbb{R}}) $ generated by $\left\{\exp (2\pi i\hat{x})
,\exp (2\pi i\hat{p}) \right\} $ . We construct a unitary propagator such that
as $\hbar \to 0$ the classical dynamics is returned. For Planck's constant
$h=1/N$, we show that the dynamics can be reduced to the dynamics on an
$N$-dimensional Hilbert space, and the unitary $N\times N$ matrix propagator is
the same as given in ref. \QCITE{cite}{}{BV} except for a small correction of
order $h$. This correction is shown to preserve the classical symmetry $x\to
1-x$ and $p\to 1-p$ in the quantum dynamics for periodic boundary conditions.Comment: 27 pages, 3 figures. Annals of Physics, to appea
Nonlinear Realization of a Dynamical Poincare Symmetry by a
  Field-dependent Diffeomorphism

We consider a description of membranes by (2,1)-dimensional field theory, or
alternatively a description of irrotational, isentropic fluid motion by a field
theory in any dimension. We show that these Galileo-invariant systems, as well
as others related to them, admit a peculiar diffeomorphism symmetry, where the
transformation rule for coordinates involves the fields. The symmetry algebra
coincides with that of the Poincare group in one higher dimension. Therefore,
these models provide a nonlinear representation for a dynamical Poincare group.Comment: Email correspondence to jackiw@mitlns.mit.edu ; 13 pages, 5 eps
  figures; uses BoxedEPS, REVTeX; slightly extended version, title changed,
  typos correcte
Stochastic interpretation of Kadanoff-Baym equations and their relation to Langevin processes

In this more pedagogical study we want to elucidate on stochastic aspects inherent to the (non-)equilibrium real time Green's function description (or `closed time path Green's function' -- CTPGF) of transport equations, the so called `Kadanoff-Baym equations'. As a toy model we couple a free scalar boson quantum field to an exemplaric heat bath with some given temperature T. It will be shown in detail that the emerging transport equations have to be understood as the ensemble average over stochastic equations of Langevin type. This corresponds to the equivalence of the influence functional approach by Feynman and Vernon and the CTP technique. The former, however, gives a more intuitive physical picture. In particular the physical role of (quantum) noise and the connection of its correlation kernel to the Kadanoff-Baym equations will be discussed. The inherent presence of noise and dissipation related by the fluctuation-dissipation theorem guarantees that the modes or particles become thermally populated on average in the long-time limit. For long wavelength modes with momenta much less than the temperature the emerging wave equation do behave nearly as classical. On the other hand, a kinetic transport description can be obtained in the semi-classical particle regime. Including fluctuations, its form resembles that of a phenomenological Boltzmann-Langevin description. However, we will point out some severe discrepancies in comparison to the Boltzmann- Langevin scheme. As a further byproduct we also note how the occurrence of so called pinch singularities is circumvented by a clear physical necessity of damping within the one-particle propagator