pinecone/core-2020-05-10-deduplication huggingface dataset:
Scalar Matter Coupled to Quantum Gravity in the Causal Approach: Finite
  One-Loop Calculations and Perturbative Gauge Invariance

Quantum gravity coupled to scalar massive matter fields is investigated
within the framework of causal perturbation theory. One-loop calculations
include matter loop graviton self-energy and matter self-energy and yield
ultraviolet finite and cutoff-free expressions. Perturbative gauge invariance
to second order implies the usual Slavnov-Ward identities for the graviton
self-energy in the loop graph sector and generates the correct quartic
graviton-matter interaction in the tree graph sector. The mass zero case is
also discussed.Comment: 37 pages, latex, no figures, some typos corrected, section 3 modifie
Symmetries and conservation laws in histories-based theories

Symmetries are defined in histories-based theories paying special attention
to the class of history theories admitting quasitemporal structure (a
generalization of the concept of `temporal sequences' of `events' using partial
semigroups) and logic structure for `single-time histories'. Symmetries are
classified into orthochronous (those preserving the `temporal order' of
`events') and nonorthochronous. A straightforward criterion for physical
equivalence of histories is formulated in terms of orthochronous symmetries;
this criterion covers various notions of physical equivalence of histories
considered by Gell-Mann and Hartle as special cases. In familiar situations, a
reciprocal relationship between traditional symmetries (Wigner symmetries in
quantum mechanics and Borel-measurable transformations of phase space in
classical mechanics) and symmetries defined in this work is established. In a
restricted class of theories, a definition of conservation law is given in the
history language which agrees with the standard ones in familiar situations; in
a smaller subclass of theories, a Noether type theorem (implying a connection
between continuous symmetries of dynamics and conservation laws) is proved. The
formalism evolved is applied to histories (of particles, fields or more general
objects) in general curved spacetimes. Sharpening the definition of symmetry so
as to include a continuity requirement, it is shown that a symmetry in our
formalism implies a conformal isometry of the spacetime metric.Comment: 54 pages. Accepted for publication in Annals of Physics. Several
  typos corrected. This paper is a combined version of gr-qc/9812018 and
  gr-qc/9905028 with several modification
Extended Gauge Theories in Euclidean Space with Higher Spin Fields

The extended Yang-Mills gauge theory in Euclidean space is a renormalizable
(by power counting) gauge theory describing a local interacting theory of
scalar, vector, and tensor gauge fields (with maximum spin 2). In this article
we study the quantum aspects and various generalizations of this model in
Euclidean space. In particular the quantization of the pure gauge model in a
common class of covariant gauges is performed. We generalize the pure gauge
sector by including matter fermions in the adjoint representation of the gauge
group and analyze its N=1 and N=2 supersymmetric extensions. We show that the
maximum half-integer spin contained in these fermion fields in dimension 4 is
3/2. Moreover we develop an extension of this theory so as to include internal
gauge symmetries and the coupling to bosonic matter fields. The spontaneous
symmetry breaking of the extended gauge symmetry is also analyzed.Comment: LaTeX, 36 pages, section 4 expanded, new section 7 and new references
  added, to appear in Annals of Physic
Two-dimensional gravitational anomalies, Schwinger terms and dispersion relations

We are dealing with two-dimensional gravitational anomalies, specifically with the Einstein anomaly and the Weyl anomaly, and we show that they are fully determined by dispersion relations independent of any renormalization procedure (or ultraviolet regularization). The origin of the anomalies is the existence of a superconvergence sum rule for the imaginary part of the relevant formfactor. In the zero mass limit the imaginary part of the formfactor approaches a $\delta$-function singularity at zero momentum squared, exhibiting in this way the infrared feature of the gravitational anomalies. We find an equivalence between the dispersive approach and the dimensional regularization procedure. The Schwinger terms appearing in the equal time commutators of the energy momentum tensors can be calculated by the same dispersive method. Although all computations are performed in two dimensions the method is expected to work in higher dimensions too
Mass and Spin Renormalization in Lorentz Electrodynamics

A new, relativistically covariant, massive Lorentz Electrodynamics (LED) is
presented in which the bare particle has a finite positive bare rest mass and
moment of inertia. The particle's electromagnetic self-interaction renormalizes
its mass and spin. Most crucially, the renormalized particle is a soliton:
after any scattering process its rest mass and spin magnitude are dynamically
restored to their pre-scattering values. This guarantees that ``an electron
remains an electron,'' poetically speaking. A renormalization flow study of the
limit of vanishing bare rest mass is conducted for this model. This limit
yields a purely electromagnetic classical field theory with ultra-violet cutoff
at about the electron's Compton wavelength! The renormalized limit model
matches the empirical electron data as orderly as one can hope for at the level
of Lorentz theory. In particular, no superluminal equatorial gyration speeds
occur.Comment: LaTeX, 70 pages, 2 eps figures, submitted; a small computational
  blunder in Eq. (10.25)ff of earlier version has been correcte
Locally Anisotropic Kinetic Processes and Thermodynamics in Curved
  Spaces

The kinetic theory is formulated with respect to anholonomic frames of
reference on curved spacetimes. By using the concept of nonlinear connection we
develop an approach to modelling locally anisotropic kinetic processes and, in
corresponding limits, the relativistic non-equilibrium thermodynamics with
local anisotropy. This lead to a unified formulation of the kinetic equations
on (pseudo) Riemannian spaces and in various higher dimensional models of
Kaluza-Klein type and/or generalized Lagrange and Finsler spaces. The
transition rate considered for the locally anisotropic transport equations is
related to the differential cross section and spacetime parameters of
anisotropy. The equations of states for pressure and energy in locally
anisotropic thermodynamics are derived. The obtained general expressions for
heat conductivity, shear and volume viscosity coefficients are applied to
determine the transport coefficients of cosmic fluids in spacetimes with
generic local anisotropy. We emphasize that such locally anisotropic structures
are induced also in general relativity if we are modelling physical processes
with respect to frames with mixed sets of holonomic and anholonomic basis
vectors which naturally admits an associated nonlinear connection structure.Comment: version 2, 46 pages, latex 209, minor changes, accepted to Annals of
  Physics (NY
Semiclassical trace formulas in terms of phase space path integrals

Semiclassical trace formulas are examined using phase space path integrals.
Our main concern in this paper is the Maslov index of the periodic orbit, which
seems not fully understood in previous works. We show that the calculation of
the Maslov index is reduced to a classification of connections on a vector
bundle over $S^{1}$ with structure group $Sp(2n,R)$. We derive a formula for
the index of the n-repetition, and show that a Bohr-Sommerfeld type
quantization condition including quadratic fluctuation around the orbit is
derived using this formula.Comment: 59pages 8figures, typos correcte
Quantum Coherence of the Ground State of a Mesoscopic Ring

We discuss the phase coherence properties of a mesoscopic normal ring coupled
to an electric environment via Coulomb interactions. This system can be mapped
onto the Caldeira-Leggett model with a flux dependent tunneling amplitude. We
show that depending on the strength of the coupling between the ring and the
environment the free energy can be obtained either by a Bethe ansatz approch
(for weak coupling) or by using a perturbative expression which we derive here
(in the case of strong coupling). We demonstrate that the zero-point
fluctuations of the environment can strongly suppress the persistent current of
the ring below its value in the absence of the environment. This is an
indication that the equilibrium fluctuations in the environment disturb the
coherence of the wave functions in the ring. Moreover the influence of quantum
fluctuations can induce symmetry breaking seen in the polarization of the ring
and in the flux induced capacitance.Comment: 30 pages, 9 figure
On electrodynamics of rapidly moving sources

Rapidly moving sources create pairs in the vacuum and lose energy. In
consequence of this, the velocity of a charged body cannot approach the speed
of light closer than a certain limit which depends only on the coupling
constant. The vacuum back-reaction secures the observance of the conservation
laws. A source can lose up to 50% of energy and charge because of the vacuum
instability.Comment: 52 pages including 6 figures. Latex 2.09. Figures by METAFONT, 300
  DPI. Keep all files in a separate director
Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice
  Strips

We present exact calculations of the zero-temperature partition function
(chromatic polynomial) $P$ for the $q$-state Potts antiferromagnet on
triangular lattice strips of arbitrarily great length $L_x$ vertices and of
width $L_y=3$ vertices and, in the $L_x \to \infty$ limit, the exponent of the
ground-state entropy, $W=e^{S_0/k_B}$. The strips considered, with their
boundary conditions ($BC$) are (a) $(FBC_y,PBC_x)=$ cyclic, (b)
$(FBC_y,TPBC_x)=$ M\"obius, (c) $(PBC_y,PBC_x)=$ toroidal, and (d)
$(PBC_y,TPBC_x)=$ Klein bottle, where $F$, $P$, and $TP$ denote free, periodic,
and twisted periodic. Exact calculations of $P$ and $W$ are also given for
wider strips, including (e) cyclic, $L_y=4$, and (f) $(PBC_y,FBC_x)=$
cylindrical, $L_y=5,6$. Several interesting features are found, including the
presence of terms in $P$ proportional to $\cos(2\pi L_x/3)$ for case (c). The
continuous locus of points ${\cal B}$ where $W$ is nonanalytic in the $q$ plane
is discussed for each case and a comparative discussion is given of the
respective loci ${\cal B}$ for families with different boundary conditions.
Numerical values of $W$ are given for infinite-length strips of various widths
and are shown to approach values for the 2D lattice rapidly. A remark is also
made concerning a zero-free region for chromatic zeros.Comment: 50 pages, latex, 6 encapsulated postscript figure
Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

Dimensional reduction of generalized gravity theories or string theories
generically yields dilaton fields in the lower-dimensional effective theory.
Thus at the level of D=4 theories, and cosmology many models contain more than
just one scalar field (e.g. inflaton, Higgs, quintessence). Our present work is
restricted to two-dimensional gravity theories with only two dilatons which
nevertheless allow a large class of physical applications.
  The notions of factorizability, simplicity and conformal simplicity, Einstein
form and Jordan form are the basis of an adequate classification. We show that
practically all physically motivated models belong either to the class of
factorizable simple theories (e.g. dimensionally reduced gravity, bosonic
string) or to factorizable conformally simple theories (e.g. spherically
reduced Scalar-Tensor theories). For these theories a first order formulation
is constructed straightforwardly. As a consequence an absolute conservation law
can be established.Comment: 23 pages, 1 tabl
Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random
  Matrices

We consider $m$ spinless Fermions in $l > m$ degenerate single-particle
levels interacting via a $k$-body random interaction with Gaussian probability
distribution and $k <= m$ in the limit $l$ to infinity (the embedded $k$-body
random ensembles). We address the cases of orthogonal and unitary symmetry. We
derive a novel eigenvalue expansion for the second moment of the Hilbert-space
matrix elements of these ensembles. Using properties of the expansion and the
supersymmetry technique, we show that for $2k > m$, the average spectrum has
the shape of a semicircle, and the spectral fluctuations are of Wigner-Dyson
type. Using a generalization of the binary correlation approximation, we show
that for $k << m << l$, the spectral fluctuations are Poissonian. This is
consistent with the case $k = 1$ which can be solved explicitly. We construct
limiting ensembles which are either fully integrable or fully chaotic and show
that the $k$-body random ensembles lie between these two extremes. Combining
all these results we find that the spectral correlations for the embedded
ensembles gradually change from Wigner-Dyson for $2k > m$ to Poissonian for $k
<< m << l$.Comment: 44 pages, 3 postscript figures, revised version including a new proof
  of one of our main claim
Fokker-Planck and Langevin Equations from Forward--Backward Path
  Integral

Starting from a forward--backward path integral of a point particle in a bath
of harmonic oscillators, we derive the Fokker-Planck and Langevin equations
with and without inertia. Special emphasis is placed upon the correct operator
order in the time evolution operator. The crucial step is the evaluation of a
Jacobian with a retarded time derivative by analytic regularization.Comment: Author Information under
  http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
  paper (including all PS fonts) at
  http://www.physik.fu-berlin.de/~kleinert/31
Casimir Effect for a Dielectric Wedge

The Casimir effect is considered for a wedge with opening angle $\alpha $,
with perfectly conducting walls, when the interior region is filled with an
isotropic and nondispersive medium with permittivity $\epsilon $ and
permeability $\mu $. The electromagnetic energy-momentum tensor in the bulk is
calculated, together with the surface stress on the walls. A discussion is
given on the possibilities for measuring the influence of the medium, via the
Casimir-Polder force.Comment: 12 pages, LaTeX. Minor typos corrected. To appear in Annals of
  Physics 291 (2001) 1 (July issue
Gravitating Self-dual Chern-Simons Solitons

Self-dual solitons of Chern-Simons Higgs theory are examined in curved
spacetime. We derive duality transformation of the Einstein Chern-Simons Higgs
theory within path integral formalism and study various aspects of dual
formulation including derivation of Bogomolnyi type bound. We find all possible
rotationally-symmetric soliton configurations carrying magnetic flux and
angular momentum when underlying spatial manifolds of these objects comprise a
cone, a cylinder, and a two sphere.Comment: 38 pages, 8 figures (Pslatex files are included in the text.) Two
  references are added. To appear in Annals of Physic
Wigner quasi-distribution function for charged particles in classical
  electromagnetic fields

A gauge-invariant Wigner quasi-distribution function for charged particles in
classical electromagnetic fields is derived in a rigorous way. Its relation to
the axial gauge is discussed, as well as the relation between the kinetic and
canonical momenta in the Wigner representation. Gauge-invariant quantum analogs
of Hamilton-Jacobi and Boltzmann kinetic equations are formulated for arbitrary
classical electromagnetic fields in terms of the "slashed" derivatives and
momenta, introduced for this purpose. The kinetic meaning of these slashed
quantities is discussed. We introduce gauge-invariant conditional moments and
use them to derive a kinetic momentum continuity equation. This equation
provides us with a hydrodynamic representation for quantum transport processes
and a definition of the "collision force". The hydrodynamic equation is applied
for the rotation part of the electron motion. The theory is illustrated by its
application in three examples. These are: Wigner quasi-distribution function
and equations for an electron in a magnetic field and harmonic potential;
Wigner quasi-distribution function for a charged particle in periodic systems
using the kq representation; two Wigner quasi-distribution functions for
heavy-mass polaron in an electric field.Comment: 47 pages; accepted for publication in Annals of Physic
Short-range correlations in semi-exclusive electron scattering
  experiments

One-nucleon emission electron scattering experiments are studied with a model
that considers short--range correlations up to the first order in the number of
correlation lines. The proper normalization of the many-body wave functions
requires the evaluation of two- and three-point diagrams, the last ones usually
neglected in the literature. When all these diagrams are included the effects
of the short-range correlations are rather small. The results of our
calculations are compared with experimental data taken on $^{16}$O.Comment: 24 pages, 16 figures, 1 tabl
Strong coupling theory for tunneling and vibrational relaxation in
  driven bistable systems

A study of the dynamics of a tunneling particle in a driven bistable
potential which is moderately-to-strongly coupled to a bath is presented. Upon
restricting the system dynamics to the Hilbert space spanned by the M lowest
energy eigenstates of the bare static potential, a set of coupled non-Markovian
master equations for the diagonal elements of the reduced density matrix,
within the discrete variale representation, is derived. The resulting dynamics
is in good agreement with predictions of ab-initio real-time path integral
simulations. Numerous results, analytical as well as numerical, for the quantum
relaxation rate and for the asymptotic populations are presented. Our method is
particularly convenient to investigate the case of shallow, time-dependent
potential barriers and moderate-to-strong damping, where both a semi-classical
and a Redfield-type approach are inappropriate.Comment: 37 pages, 23 figure
New Approach to Quantum Field Theory for Arbitrary Observers in
  Electromagnetic Backgrounds

A reformulation of fermionic QFT in electromagnetic backgrounds is presented
which uses methods analogous to those of conventional multiparticle quantum
mechanics. Emphasis is placed on the (Schr\"odinger picture) states of the
system, described in terms of Slater determinants of Dirac states, and not on
the field operator $\hat{\psi}(x)$ (which is superfluous in this approach). The
vacuum state `at time $\tau$' is defined as the Slater determinant of a basis
for the span of the negative spectrum of the `first quantized' Hamiltonian
$\hat{H}(\tau)$, thus providing a concrete realisation of the Dirac Sea. The
general S-matrix element of the theory is derived in terms of time-dependent
Bogoliubov coefficients, demonstrating that the S-matrix follows directly from
the definition of inner product between Slater determinants. The process of
`Hermitian extension', inherited directly from conventional multiparticle
quantum mechanics, allows second quantized operators to be defined without
appealing to a complete set of orthonormal modes, and provides an extremely
straightforward derivation of the general expectation value of the theory. The
concept of `radar time', advocated by Bondi in his work on k-calculus, is used
to generalise the particle interpretation to an arbitrarily moving observer. A
definition of particle results, which depends {\it only} on the observer's
motion and the background present, not on any choice of coordinates or gauge,
or of the particle detector. We relate this approach to conventional methods by
comparing and contrasting various derivations. Our particle definition can be
viewed as a generalisation to arbitrary observers of Gibbons' approach.Comment: 36 pages, 3 figure
Group theoretical approach to the intertwined Hamiltonians

We show that the finite difference B\"acklund formula for the Schr\"odinger
Hamiltonians is a particular element of the transformation group on the set of
Riccati equations considered by two of us in a previous paper. Then, we give a
group theoretical explanation to the problem of Hamiltonians related by a first
order differential operator. A generalization of the finite difference
algorithm relating eigenfunctions of {\emph three} different Hamiltonians is
found, and some illustrative examples of the theory are analyzed, finding new
potentials for which one eigenfunction and its corresponding eigenvalue is
exactly known
Exact Conservation Laws of the Gradient Expanded Kadanoff-Baym Equations

It is shown that the Kadanoff-Baym equations at consistent first-order
gradient approximation reveal exact rather than approximate conservation laws
related to global symmetries of the system. The conserved currents and
energy-momentum tensor coincide with corresponding Noether quantities in the
local approximation. These exact conservations are valid, provided a
Phi-derivable approximation is used to describe the system, and possible memory
effects in the collision term are also consistently evaluated up to first-order
gradients.Comment: 26 pages, feynman.package for diagrams, submitted to Annals of
  Physic
Pair Production and Vacuum Polarization of Arbitrary Spin Particles with
  EDM and AMM

The exact solutions of the wave equation for arbitrary spin particles with
electric dipole and magnetic moments in the constant and uniform
electromagnetic field were found. The differential probability of pair
production of particles by an external electromagnetic field has been
calculated on the basis of the exact solutions. We have also estimated the
imaginary part of the constant and uniform electromagnetic field. The nonlinear
corrections to the Maxwell Lagrangian have been calculated taking into account
the vacuum polarization of arbitrary spin particles. The role of electric
dipole and magnetic moments of arbitrary spin particles in instability of the
vacuum is discussed.Comment: 18 pages, LaTeX, accepted for publication in Ann.Phys.(USA
A Convergent Iterative Solution of the Quantum Double-well Potential

We present a new convergent iterative solution for the two lowest quantum
wave functions $\psi_{ev}$ and $\psi_{od}$ of the Hamiltonian with a quartic
double well potential $V$ in one dimension. By starting from a trial function,
which is by itself the exact lowest even or odd eigenstate of a different
Hamiltonian with a modified potential $V+\delta V$, we construct the Green's
function for the modified potential. The true wave functions, $\psi_{ev}$ or
$\psi_{od}$, then satisfies a linear inhomogeneous integral equation, in which
the inhomogeneous term is the trial function, and the kernel is the product of
the Green's function times the sum of $\delta V$, the potential difference, and
the corresponding energy shift. By iterating this equation we obtain successive
approximations to the true wave function; furthermore, the approximate energy
shift is also adjusted at each iteration so that the approximate wave function
is well behaved everywhere. We are able to prove that this iterative procedure
converges for both the energy and the wave function at all $x$.Comment: 76 pages, Latex, no figure, 1 tabl