pinecone/core-2020-05-10-deduplication huggingface dataset:
A Covariant Generalization of the Real-Time Green's Functions Method in
  the Theory of Kinetic Equations

A generalized quantum kinetic equation (RKE) of the Kadanoff-Baym type is
obtained on the basis of the Heisenberg equations of motion where the time
evolution and space translation are separated from each other by means of the
covariant method. The same approach is used also for a covariant modification
of the real-time Green's functions method based on the Wigner representation.
The suggested approach does not contain arbitrariness' elements and
uncertainties which often arise from derivation of RKE on the basis of the
motion equations of the Kadanoff-Baym type for the correlation functions in the
case of systems with inner degrees of freedom. Possibilities of the proposed
method are demonstrated by examples of derivation of RKE of the Vlasov type and
collision integrals of the Boltzmann-Uehling-Uhlenbeck (BUU) type in the frame
of the $\sigma \omega$ -version of quantum hadrodynamics, for the simplest case
of spin saturated nuclear matter without antinuclear component. Here, the
quasiparticle approximation in a covariant performance is used. A
generalization of the method for the description of strong non-equilibrium
states based on the non-equilibrium statistical operator is then proposed as
well.Comment: Published in Annals Phys. 277 (1999) 19
On the Effective Potential for Local Composite Operators

We show that the effective potential for local composite operators is a
useful object in studing dynamical symmetry breaking by calculating the
effective potential for the local composite operators $\bar{\psi} \psi$ and
$\phi^2$ in the Gross-Neveu (GN) and O(N) models, respectively. Since the
effective potential for local composite operators can be calculated by using
the Cornwall-Jackiw-Tomboulis (CJT) effective potential in theory with
additional bare mass terms, we show that divergences in the effective potential
for local composite operators are the same as in the CJT effective potential.
We compare the results obtained with the results give by the auxiliary field
method.Comment: 17 pages, LaTeX, the analysis of the O(N) model with finite cut-off
  have been reconsidered and the corresponding important reference have been
  adde
Uniform approximations for non-generic bifurcation scenatios including
  bifurcations of ghost orbits

Gutzwiller's trace formula allows interpreting the density of states of a
classically chaotic quantum system in terms of classical periodic orbits. It
diverges when periodic orbits undergo bifurcations, and must be replaced with a
uniform approximation in the vicinity of the bifurcations. As a characteristic
feature, these approximations require the inclusion of complex ``ghost
orbits''. By studying an example taken from the Diamagnetic Kepler Problem,
viz. the period-quadrupling of the balloon-orbit, we demonstrate that these
ghost orbits themselves can undergo bifurcations, giving rise to non-generic
complicated bifurcation scenarios. We extend classical normal form theory so as
to yield analytic descriptions of both bifurcations of real orbits and ghost
orbit bifurcations. We then show how the normal form serves to obtain a uniform
approximation taking the ghost orbit bifurcation into account. We find that the
ghost bifurcation produces signatures in the semiclassical spectrum in much the
same way as a bifurcation of real orbits does.Comment: 56 pages, 21 figure, LaTeX2e using amsmath, amssymb, epsfig, and
  rotating packages. To be published in Annals of Physic
Systematics of the Quadrupole-Quadrupole Interaction and Convergence
  Properties

Our main concern in this work is to show how higher shell admixtures affect
the spectrum of a Q.Q interaction. We first review how, in the valence space,
the familiar SU(3) result for the energy spectrum can be obtained using a
coordinate space Q.Q interaction rather than the Elliott one which is symmetric
in r and p. We then reemphasize that the Elliott spectrum goes as L(L+1) where
L is the orbital angular momentum. While in many cases this is compatible with
the rotational formula which involves I(I+1), where I is the total angular
momentum, there are cases, e.g. odd-odd nuclei, where there is disagreement.
Finally, we consider higher shell admixtures and devise a scheme so as to
obtain results, with the Q.Q interaction, which converge as the model spaces
are increased. We consider not only ground state rotational bands but also
those that involve intruder states.Comment: 13 pages, Revtex, to appear in Annals of Physic
Decomposition of Resonant Scatterers by Surfaces of Section

Scattering on the energy shell is viewed here as the relation between the
bound states of the Hamiltonian, restricted to sections on leads that are
asymptotically independent, far away from the interaction region. The
decomposition is achieved by sectioning this region and adding new leads, thus
generating two new scatterers. So a resonant scatterer, whose $\bS$-matrix has
sharp energy peaks, can be resolved into a pair of scatterers with smooth
energy dependence. The resonant behaviour is concentrated in a spectral
determinant obtained from a dissipative section map. The semiclassical limit of
this theory coincides with the orbit resummation previously proposed by
Georgeot and Prange. A numerical example for a semiseparable scatterer is
investigated, revealing the accurate portrayal of the Wigner time delay by the
spectral determinant.Comment: 23 latex pages including 12 ps figure
Motion of Quantized Vortices as Elementary Objects

The general local, nondissipative equations of motion for a quantized vortex
moving in an uncharged laboratory superfluid are derived from a relativistic,
co-ordinate invariant framework, having vortices as its elementary objects in
the form of stable topological excitations. This derivation is carried out for
a pure superfluid with isotropic gap at the absolute zero of temperature, on
the level of a hydrodynamic, collective co-ordinate description. In the
formalism, we use as fundamental ingredients that particle number as well as
vorticity are conserved, and that the fluid is perfect. No assumptions are
involved as regards the dynamical behaviour of the order parameter. The
interaction of the vortex with the background fluid, representing the Magnus
force, and with itself via phonons, giving rise to the hydrodynamic vortex
mass, are separated. For a description of the motion of the vortex in a dense
laboratory superfluid like helium II, two limits have to be considered: The
nonrelativistic limit for the superfluid background is taken, and the motion of
the vortex is restricted to velocities much less than the speed of sound. The
canonical structure of vortex motion in terms of the collective co-ordinate is
used for the quantization of this motion.Comment: 25 pages, 4 figures, published versio
The ``Mixed'' Green's Function Approach to Quantum Kinetics with Initial
  Correlations

A method for deriving quantum kinetic equations with initial correlations is
developed on the basis of the nonequilibrium Green's function formalism. The
method is applicable to a wide range of correlated initial states described by
nonequilibrium statistical thermodynamics. Initial correlations and the
real-time evolution are treated by a unified technique employing many-component
``mixed'' Green's functions. The Dyson equation for the mixed Green's function
leads to a set of equations for real-time Green's functions and new (cross)
components linking initial correlations with dynamical processes. These
equations are used to formulate a generalized Kadanoff-Baym ansatz for
correlated initial states. A non-Markovian short-time kinetic equation is
derived within the T-matrix approximation for the self-energies. The properties
of the memory kernels in this equation are considered in detail in Born
approximation for the T-matrices. The kinetic equation is demonstrated to
conserve the total energy of the system. An explicit expression for the
time-dependent correlation energy is obtained.Comment: 50 pages, 3 figure
Variational approximations for correlation functions in quantum field
  theories

Applying the time-dependent variational principle of Balian and V\'en\'eroni,
we derive variational approximations for multi-time correlation functions in
$\Phi^4$ field theory. We assume first that the initial state is given and
characterized by a density operator equal to a Gaussian density matrix. Then,
we study the more realistic situation where only a few expectation values are
given at the initial time and we perform an optimization with respect to the
initial state. We calculate explicitly the two-time correlation functions with
two and four field operators at equilibrium in the symmetric phase.Comment: 60 pages, Latex, to be published in Annals of Physic
Noether Currents for Bosonic Branes

We consider a relativistic brane propagating in Minkowski spacetime described
by any action which is local in its worldvolume geometry. We examine the
conservation laws associated with the Poincar\'e symmetry of the background
from a worldvolume geometrical point of the view. These laws are exploited to
explore the structure of the equations of motion. General expressions are
provided for both the linear and angular momentum for any action depending on
the worldvolume extrinsic curvature. The conservation laws are examined in
perturbation theory. It is shown how non-trivial solutions with vanishing
energy-momentum can be constructed in higher order theories. Finally,
subtleties associated with boundary terms are examined in the context of the
brane Einstein-Hilbert action.Comment: 33 pages, Latex. Published in Annals of Physics 279, 126, 200
Finite Volume Effects in Self Coupled Geometries

By integrating the pressure equation at the surface of a self coupled
curvilinear boundary, one may obtain asymptotic estimates of energy shifts,
which is especially useful in lattice QCD studies of nonrelativistic bound
states. Energy shift expressions are found for periodic (antiperiodic) boundary
conditions on antipodal points, which require Neumann (Dirichlet) boundary
conditions for even parity states and Dirichlet (Neumann) boundary conditions
for odd parity states. It is found that averaging over periodic and
antiperiodic boundary conditions is an effective way of removing the asymptotic
energy shifts from the boundary. Asymptotic energy shifts from boxes with self
coupled walls are also considered and shown to be effectively antipodal. The
energy shift equations are illustrated by the solution of the bounded harmonic
oscillator and hydrogen atoms.Comment: 17 pages LaTeX, to appear in Ann. Phy
Renormalization of chiral perturbation theory to order p^6

The renormalization of chiral perturbation theory is carried out to
next-to-next-to-leading order in the meson sector. We calculate the divergent
part of the generating functional of Green functions of quark currents to
O(p^6) for chiral SU(n), involving one- and two-loop diagrams. The
renormalization group equations for the renormalized low-energy constants of
O(p^6) are derived. We compare our results with previous two-loop calculations
in chiral perturbation theory.Comment: 43 pages, LaTeX2e, 1 figur
Quantum mechanics of an electron in a homogeneous magnetic field and a
  singular magnetic flux tube

The eigenvalue problem of the Hamiltonian of an electron confined to a plane
and subjected to a perpendicular time-independent magnetic field which is the
sum of a homogeneous field and an additional field contributed by a singular
flux tube, i.e. of zero width, is investigated. Since both a direct approach
based on distribution-valued operators and a limit process starting from a
non-singular flux tube, i.e. of finite size, fail, an alternative method is
applied leading to consistent results. An essential feature is quantum
mechanical supersymmetry at g=2 which imposes, by proper representation, the
correct choice of "boundary conditions". The corresponding representation of
the Hilbert space in coordinate space differs from the usual space of
square-integrable 2-spinors, entailing other unusual properties. The analysis
is extended to $g\ne 2$ so that supersymmetry is explicitly broken. Finally,
the singular Aharonov-Bohm system with the same amount of singular flux is
analysed by making use of the fact that the Hilbert space must be the same.Comment: 23 pages, LaTeX, minor change
Topological Field Theory and Quantum Holonomy Representations of Motion
  Groups

Canonical quantization of abelian BF-type topological field theory coupled to
extended sources on generic d-dimensional manifolds and with curved line
bundles is studied. Sheaf cohomology is used to construct the appropriate
topological extension of the action and the topological flux quantization
conditions, in terms of the Cech cohomology of the underlying spatial manifold,
as required for topological invariance of the quantum field theory. The
wavefunctions are found in the Hamiltonian formalism and are shown to carry
multi-dimensional representations of various topological groups of the space.
Expressions for generalized linking numbers in any dimension are thereby
derived. In particular, new global aspects of motion group presentations are
obtained in any dimension. Applications to quantum exchange statistics of
objects in various dimensionalities are also discussed.Comment: 45 pages LaTe
Quantization and renormalization of the manifest left-right symmetric
  model of electroweak interactions

Quantization and renormalization of the left-right symmetric model is the
main purpose of the paper. First the model at tree level with a Higgs sector
containing one bidoublet and two triplets is precisely discussed. Then the
canonical quantization and Faddeev-Popov Lagrangian are carried out ('t Hooft
gauge). The BRST symmetry is discussed. Subsequently the on mass shell
renormalization is performed and, as a test of consistency, the renormalization
of the ZNiNj vertex is analyzed.Comment: 74 pages, 65 Postscript figures, submitted to Annals of Physic
High Density QCD and Instantons

Instantons generate strong non-perturbative interactions between quarks. In
the vacuum, these interactions lead to chiral symmetry breaking and generate
constituent quark masses on the order of 300-400 MeV. The observation that the
same forces also provide attraction in the scalar diquark channel leads to the
prediction that cold quark matter is a color superconductor, with gaps as large
as $\sim$~100 MeV. We provide a systematic treatment of color superconductivity
in the instanton model. We show that the structure of the superconductor
depends on the number of flavors. In the case of two flavors, we verify the
standard scenario and provide an improved calculation of the mass gap. For
three flavors, we show that the ground state is color-flavor locked and
calculate the chiral condensate in the high density phase. We show that as a
function of the strange quark mass, there is a sharp transition between the two
phases. Finally, we go beyond the mean field approximation and investigate the
role of instanton-anti-instanton molecules, which -- besides superconducting
gap formation -- provide a competitive mechanism for chiral restoration at
finite density.Comment: 44 pages ReVTeX, incl. 23 eps/ps-figures, slightly revised version
  accepted for publication in Ann. of Phy
P-matrix and J-matrix approaches. Coulomb asymptotics in the harmonic
  oscillator representation of scattering theory

The relation between the R- and P-matrix approaches and the harmonic
oscillator representation of the quantum scattering theory (J-matrix method) is
discussed. We construct a discrete analogue of the P-matrix that is shown to be
equivalent to the usual P-matrix in the quasiclassical limit. A definition of
the natural channel radius is introduced. As a result, it is shown to be
possible to use well-developed technique of R- and P-matrix theory for
calculation of resonant states characteristics, scattering phase shifts, etc.,
in the approaches based on harmonic oscillator expansions, e.g., in nuclear
shell-model calculations. P-matrix is used also for formulation of the method
of treating Coulomb asymptotics in the scattering theory in oscillator
representation.Comment: Revtex, 57 pages including 15 figures; to be published in Annals of
  Physic
Field-dependent symmetries of a non-relativistic fluid model

As found by Bordemann and Hoppe and by Jevicki, a certain non-relativistic
model of an irrotational and isentropic fluid, related to membranes and to
partons, admits a Poincar\'e symmetry. Bazeia and Jackiw associate this
dynamical symmetry to a novel type of ``field dependent'' action on space-time.
The ``Kaluza-Klein type'' framework of Duval et al. is used to explain the
origin of these symmetries and to derive the associated conserved quantities.
In the non-interacting case, the symmetry extends to the entire conformal
group.Comment: 34 pages, LATEX, no figures. Revised version (Rearranged presentation
  and one more example added
Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional
  Extended AdS Supergravity

We investigate systematically the asymptotic dynamics and symmetries of all
three-dimensional extended AdS supergravity models. First, starting from the
Chern-Simons formulation, we show explicitly that the (super)anti-de Sitter
boundary conditions imply that the asymptotic symmetry algebra is the extended
superconformal algebra with quadratic nonlinearies in the currents. We then
derive the super-Liouville action by solving the Chern-Simons theory and obtain
a realization of the superconformal algebras in terms of super-Liouville
fields. Finally, we discuss the possible periodic conditions that can be
imposed on the generators of the algebra and generalize the spectral flow
analysed previously in the context of the $N$-extended linear superconformal
algebras with $N \leq 4$. The $(2+1)$-AdS/2-CFT correspondence sheds a new
light on the properties of the nonlinear superconformal algebras. It also
provides a general and natural interpretation of the spectral flow.Comment: 46 pages,latex2e; added reference
The Role of Energy and a New Approach to Gravitational Waves in General
  Relativity

The energy localization hypothesis of the author that energy is localized in
non-vanishing regions of the energy-momentum tensor implies that gravitational
waves do not carry energy in vacuum. If substantiated, this has significant
implications for current research. Support for the hypothesis is provided by a
re-examination of Eddington's classic calculation of energy loss by a spinning
rod. It is emphasized that Eddington did not monitor the entire Tolman energy
integral, concentrating solely upon the change of the 'kinetic' part of the
energy . The 'quadrupole formula' is thus seen to measure the kinetic energy
change. When the derivative of the missing stress-trace integral is computed,
it is seen to cancel the Eddington term and hence the energy of the rod is
conserved, in support of the localization hypothesis. The issue of initial and
final states is addressed.Comment: 19 Pages, LaTe
1+3 Covariant Cosmic Microwave Background anisotropies II: The almost -
  Friedmann Lemaitre model

This is the second of a series of papers extending the 1+3 covariant and
gauge invariant treatment of kinetic theory to an examination of Cosmic
Microwave Background temperature anisotropies arising from inhomogeneities in
the early universe. The first paper dealt with algebraic issues.
  Here we derive the mode form of the integrated Boltzmann equations, first,
giving a covariant version of the standard derivation using the mode recursion
relations, second, demonstrating the link to the multipole divergence equations
and finally various analytic ways of solving the resulting equations are
discussed.
  A general integral form of solution is obtained for the equations with
Thomson scattering. The covariant Friedmann-Lemaitre multipole form of the
transport equations are found using the covariant and gauge-invariant
generalization of the Peebles and Yu expansion in Thompson scattering time. The
dispersion relations and damping scale are then obtained from the covariant
approach. The equations are integrated to give the covariant and
gauge-invariant equivalent of the canonical scalar sourced anisotropies.
  We carry out a simple treatment of the matter dominated free-streaming
projection, slow decoupling, and tight-coupling cases, with the aim both giving
a unified transparent derivation of this range of results and clarifying the
connection between the more usual approaches (for example that of Hu and
Sugiyama) and the treatment for scalar perturbations (for example the treatment
of Challinor and Lasenby).Comment: To appear in Annals of Physic
The Casimir Energy in a Separable Potential

The Casimir energy is the first-order-in-\hbar correction to the energy of a
time-independent field configuration in a quantum field theory. We study the
Casimir energy in a toy model, where the classical field is replaced by a
separable potential. In this model the exact answer is trivial to compute,
making it a good place to examine subtleties of the problem. We construct two
traditional representations of the Casimir energy, one from the Greens
function, the other from the phase shifts, and apply them to this case. We show
that the two representations are correct and equivalent in this model. We study
the convergence of the Born approximation to the Casimir energy and relate our
findings to computational issues that arise in more realistic models.Comment: 16 pages, 4 EPS figures, REVTeX using BoxedEPS macros; email to
  jaffe@mit.ed
Calculation of Wilson loops in 2-dimensional Yang-Mills theories

The vacuum expectation value of the Wilson loop functional in pure Yang-Mills
theory on an arbitrary two-dimensional orientable manifold is studied. We
consider the calculation of this quantity for the abelian theory in the
continuum case and for the arbitrary gauge group and arbitrary lattice action
in the lattice case. A classification of topological sectors of the theory and
the related classification of the principal fibre bundles over two-dimensional
surfaces are given in terms of a cohomology group. The contribution of
SU(2)-invariant connections to the vacuum expectation value of the Wilson loop
variable is also analyzed and is shown to be similar to the contribution of
monopoles.Comment: 46 pages, Latex, 5 figures included (psfig, epsfig
Path Integrals, BRST Identities and Regularization Schemes in
  Nonstandard Gauges

The path integral of a gauge theory is studied in Coulomb-like gauges. The
Christ-Lee terms of operator ordering are reproduced {\it{within}} the path
integration framework. In the presence of fermions, a new operator term, in
addition to that of Christ-Lee, is discovered. Such kind of terms is found to
be instrumental in restoring the invariance of the effective Lagrangian under a
field dependent gauge transformation, which underlies the BRST symmetry. A
unitary regularization scheme which maintains manifest BRST symmetry and is
free from energy divergences is proposed for a nonabelian gauge field.Comment: 40 pages and 2 figure
Charges from Dressed Matter: Construction

There is a widespread belief in particle physics that there is no
relativistic description of a charged particle. This is claimed to be due to
persistent, long range interactions which distort the in and out going plane
waves and generate infra-red divergences. In this paper we will show that this
is not the case in QED. We construct locally gauge invariant charged fields
which do create in and out Fock states. In a companion paper we demonstrate
that the Green's functions of these fields have a good pole structure
describing particle propagation.Comment: 29 pages, LaTeX, 2 figures, two new references, minor changes,
  version to appear in Annals of Physic