pinecone/core-2020-05-10-deduplication huggingface dataset:
Exact Construction of the Electromagnetic Current Operator for
  Relativistic Composite Systems

The electromagnetic current operator of a composite system must be a
relativistic vector operator satisfying current conservation, cluster
separability and the condition that interactions between the constituents do
not renormalize the total electric charge. Assuming that these interactions are
described in the framework of relativistic quantum mechanics of systems with a
fixed number of particles we explicitly construct the current operators
satisfying the above properties in cases of two and three particles and prove
that solutions exist for any number of particles. The consideration is
essentially based on the method of packing operators in the point form of
relativistic dynamics developed by Sokolov. Using the method developed by
Sokolov and Shatny we also construct the current operators in the instant and
front forms and prove that the corresponding results are physically equivalent.
The paper is self-contained what makes it possible for the reader to learn
both, relativistic quantum mechanics of systems with a fixed number of
particles and the problem of constructing the electromagnetic current operator
for such systems.Comment: (lev@nusun.jinr.dubna.su), 100 pages LaTe
QUANTUM DISSIPATION AND QUANTUM NOISE

We derive the exact action for a damped mechanical system ( and the special
case of the linear oscillator) from the path integral formulation of the
quantum Brownian motion problem developed by Schwinger and by Feynman and
Vernon. The doubling of the phase-space degrees of freedom for dissipative
systems and thermal field theories is discussed and the initial values of the
doubled variables are related to quantum noise effects.Comment: This is a Tex file; To be published in Annals of Phys. (N.Y.) 238,
  200 (1995
Finite Temperature and Density Effects in Planar Q.E.D

The behavior of finite temperature planar electrodynamics is investigated. We
calculate the static as well as dynamic characteristic functions using real
time formalism. The temperature and density dependence of dielectric and
permeability functions, plasmon frequencies and their relation to the screening
length is determined. The radiative correction to the fermion mass is also
calculated. We also calculate the temperature dependence of the electron
(anyon) magnetic moment. Our results for the gyromagnetic ratio go smoothly to
the known result at zero temperature, $g=2$, in accordance with the general
expectation.Comment: 24 pages, LaTe
Resummations in Hot Scalar Electrodynamics

The gauge-boson sector of perturbative scalar electrodynamics is investigated
in detail as a testing ground for resummation methods in hot gauge theories. It
also serves as a simple non-trivial reference system for the non-Abelian gluon
plasma. The complete next-to-leading order contributions to the polarization
tensor are obtained within the resummation scheme of Braaten and Pisarski. The
simpler scheme proposed recently by Arnold and Espinosa is shown to apply to
static quantities only, whereas Braaten-Pisarski resummation turns out to need
modification for collective phenomena close to the light-cone. Finally, a
recently proposed resummation of quasi-particle damping contributions is
assessed critically.Comment: 53 p. LaTeX, 7 figs. (2 in LaTeX, 5 EPS appended as uu-encoded file),
  ITP-UH-01/94 & DESY 94-03
Calculation and Interpretation of Hadron Correlation Functions in
  Lattice QCD

Several new developments in the calculation and interpretation of hadron
density-density correlation functions are presented. The asymptotic behavior of
correlation functions is determined from a tree diagram path integral. A method
is developed to use this behavior to correct for leading image contributions on
a finite periodic spatial lattice and to correct for the finite temporal extent
of the lattice. Equal time correlation functions are shown to determine a sum
of the ground state rms radius plus a polarization correction, and it is shown
how to extract the hadron polarizability from unequal time correlation
functions. Image-corrected correlation functions calculated in quenched lattice
QCD are presented and used to determine the size of the pion and nucleon.Comment: 39 pages with 9 figures, TeX, MIT-CTP-210
A renormalization group approach to the chiral transition

A methodology is given to test the QCD N_f=2 chiral transition, presently conjectured to be second order. Scaling forms for the correlation length, susceptibilities and equation of state are given which account for finite lattice spacing. Confirmation by lattice simulation would provide a large set of consistency checks for establishing that the transition is second order. Further corrections from finite volume effects and higher dimensional operator mixing are given. The implications of scaling corrections in finite temperature lattice QCD studies are examined with emphasis on tests for the believed second order chiral transition within the realistic setting of finite lattice spacing effects
An Alternative Perturbative Expansion in Quantum Mechanics. Scaling and
  cut-off Resummation

An alternative perturbative expansion in quantum mechanics which allows a
full expression of the scaling arbitrariness is introduced. This expansion is
examined in the case of the anharmonic oscillator and is conveniently resummed
using a method which consists in introducing an energy cut-off that is
carefully removed as the order of the expansion is increased. We illustrate
this technique numerically by computing the asymptotic behavior of the ground
state energy of the anharmonic oscillator for large couplings, and show how the
exploitation of the scaling arbitrariness substantially improves the
convergence of this perturbative expansion.Comment: 16 pages, tex file, report RU93-3-
On the Quantum Baker's Map and its Unusual Traces

The quantum baker's map is the quantization of a simple classically chaotic
system, and has many generic features that have been studied over the last few
years. While there exists a semiclassical theory of this map, a more rigorous
study of the same revealed some unexpected features which indicated that
correction terms of the order of log(h) had to be included in the periodic
orbit sum. Such singular semiclassical behaviour was also found in the simplest
traces of the quantum map. In this note we study the quantum mechanics of a
baker's map which is obtained by reflecting the classical map about its edges,
in an effort to understand and circumvent these anomalies. This leads to a real
quantum map with traces that follow the usual Gutzwiller-Tabor like
semiclassical formulae. We develop the relevant semiclassical periodic orbit
sum for this map which is closely related to that of the usual baker's map,
with the important difference that the propagators leading to this sum have no
anomalous traces.Comment: 23 pages, LaTex. The 3 Figs. may be obtained from the author
Localization Properties in One Dimensional Disordered Supersymmetric
  Quantum Mechanics

A model of localization based on the Witten Hamiltonian of supersymmetric
quantum mechanics is considered. The case where the superpotential $\phi(x)$ is
a random telegraph process is solved exactly. Both the localization length and
the density of states are obtained analytically. A detailed study of the low
energy behaviour is presented. Analytical and numerical results are presented
in the case where the intervals over which $\phi(x)$ is kept constant are
distributed according to a broad distribution. Various applications of this
model are considered.Comment: 43 pages, plain TEX, 8 figures not included, available upon request
  from the Authors
On Schroedinger Equations with Concentrated Nonlinearities

Schr\"odinger equations with nonlinearities concentrated in some regions of
space are good models of various physical situations and have interesting
mathematical properties. We show that in the semiclassical limit it is possible
to separate the relevant degrees of freedom by noticing that in the regions
where the nonlinearities are effective all states are suppressed but the
metastable ones (resonances). In this way the description of the nonlinear
regions is reduced to ordinary differential equations weakly coupled to
standard Schr\"odinger equations valid in the linear regions. The idea is
illustrated through the study of a prototype equation recently proposed for
resonant tunneling of electrons through a double barrier heterostructure and
for which nonlinear oscillations have been numerically predicted.Comment: 24 pages with figures, compressed and uuencoded ps fil
Polarization rotation effects due to parity violation in atoms

We present a study of parity (P) violating polarization rotations of atoms in external electric fields. Five different types of rotations are identified and the consequences of time reversal invariance (T) are discussed. The role played by Zeldovich's electric dipole moment of unstable states is elucidated. To calculate the effects, we use the standard model of elementary particle physics where P violation in atoms is due to the exchange of the Z boson between the quarks in the nucleus and the atomic electrons. We consider in detail hydrogen-like systems in n=2 states, especially ^1_1H, ^4_2He^+, and ^{12}_6C^{5+}. We discuss ways to obtain in some cases large enhancement factors for the P-violating polarization rotations and show that e.g. for ^1_1H one could in principle observe rotations as large as a few percent, where for a statistically significant result one would need a total of 10^{15} polarized atoms. We point out that some of our P-violating polarization rotations are very sensitive to the nuclear spin-dependent part of the P-violating Hamiltonian which receives a contribution from the polarized strange quark density in polarized nuclei
Energy Theorem for 2+1 dimensional gravity

We prove a positive energy theorem in 2+1 dimensional gravity for open
universes and any matter energy-momentum tensor satisfying the dominant energy
condition. We consider on the space-like initial value surface a family of
widening Wilson loops and show that the energy-momentum of the enclosed
subsystem is a future directed time-like vector whose mass is an increasing
function of the loop, until it reaches the value $1/4G$ corresponding to a
deficit angle of $2\pi$. At this point the energy-momentum of the system
evolves, depending on the nature of a zero norm vector appearing in the
evolution equations, either into a time-like vector of a universe which closes
kinematically or into a Gott-like universe whose energy momentum vector, as
first recognized by Deser, Jackiw and 't Hooft is space-like.
  This treatment generalizes results obtained by Carroll, Fahri, Guth and Olum
for a system of point-like spinless particle, to the most general form of
matter whose energy-momentum tensor satisfies the dominant energy condition.
The treatment is also given for the anti de Sitter 2+1 dimensional gravity.Comment: (Revtex), 24 pages,MIT-CTP#2324 snd IFUP-TH-33/9
The classification of diagrams in perturbation theory

The derivation of scattering equations connecting the amplitudes obtained
from diagrammatic expansions is of interest in many branches of physics. One
method for deriving such equations is the classification-of-diagrams technique
of Taylor. However, as we shall explain in this paper, there are certain points
of Taylor's method which require clarification. Firstly, it is not clear
whether Taylor's original method is equivalent to the simpler
classification-of-diagrams scheme used by Thomas, Rinat, Afnan and Blankleider
(TRAB). Secondly, when the Taylor method is applied to certain problems in a
time-dependent perturbation theory it leads to the over-counting of some
diagrams. This paper first restates Taylor's method, in the process uncovering
reasons why certain diagrams might be double-counted in the Taylor method. It
then explores how far Taylor's method is equivalent to the simpler TRAB method.
Finally, it examines precisely why the double-counting occurs in Taylor's
method, and derives corrections which compensate for this double-counting.Comment: 50 pages, RevTeX. Major changes from original version. Thirty figures
  available upon request to phdrp@pippin.cc.flinders.edu.au. Accepted for
  publication in Annals of Physic
The structure of the invariant charge in massive theories with one
  coupling

Invariance under finite renormalization group (RG) transformations is used to
structure the invariant charge in models with one coupling in the 4 lowest
orders of perturbation theory. In every order there starts a RG-invariant,
which is uniquely continued to higher orders. Whereas in massless models the
RG-invariants are power series in logarithms, there is no such requirement in a
massive model. Only, when one applies the Callan-Symanzik (CS) equation of the
respective theories, the high-energy behavior of the RG-invariants is
restricted. In models, where the CS-equation has the same form as the
RG-equation, the massless limit is reached smoothly, i.e. the beta-functions
are constants in the asymptotic limit and the RG-functions starting the new
invariant tend to logarithms. On the other hand in the spontaneously broken
models with fermions the CS-equation contains a beta-function of a physical
mass. As a consequence the beta-functions depend on the normalization point
also in the asymptotic region and a mass independent limit does not exist
anymore.Comment: 35 pages (1 figure available upon request), Plain TeX, BUTP 93-26 (1
  more macro included
Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

By resorting to the Fock--Bargmann representation, we incorporate the quantum
Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions.
The main tool is the realization of the $q$--WH algebra in terms of finite
difference operators. The physical relevance of our study relies on the fact
that coherent states (CS) are indeed formulated in the space of entire analytic
functions where they can be rigorously expressed in terms of theta functions on
the von Neumann lattice. The r\^ole played by the finite difference operators
and the relevance of the lattice structure in the completeness of the CS system
suggest that the $q$--deformation of the WH algebra is an essential tool in the
physics of discretized (periodic) systems. In this latter context we define a
quantum mechanics formalism for lattice systems.Comment: 22 pages, TEX file, DFF188/9/93 Firenz
Behavior of Friedmann-Robertson-Walker Cosmological Models in
  Scalar-Tensor Gravity

We analyze solutions to Friedmann-Robertson-Walker cosmologies in Brans-Dicke
theory, where a scalar field is coupled to gravity. Matter is modelled by a
$\gamma$-law perfect fluid, including false-vacuum energy as a special case.
Through a change of variables, we reduce the field equations from fourth order
to second order, and they become equivalent to a two-dimensional dynamical
system. We then analyze the entire solution space of this dynamical system, and
find that many qualitative features of these cosmologies can be gleaned,
including standard non-inflationary or extended inflationary expansion, but
also including bifurcations of stable or unstable expansion or contraction,
noninflationary vacuum-energy dominated models, and several varieties of
``coasting," ``bouncing," ``hesitating," and ``vacillating" universes. It is
shown that inflationary dogma, which states that a universe with curvature and
dominated by inflationary matter will always approach a corresponding
flat-space solution at late times, does not hold in general for the
scalar-tensor theory, but rather that the occurence of inflation depends upon
the initial energy of the scalar field relative to the expansion rate. In the
case of flat space ($k=0$), the dynamical system formalism generates some
previously known exact power-law solutions.Comment: Slight stylistic changes and some references added. This version to
  be published in {\sl Annals of Physics
Quantisation of second class systems in the Batalin-Tyutin formalism

We review the Batalin-Tyutin approach of quantising second class systems
which consists in enlarging the phase space to convert such systems into first
class. The quantisation of first class systems, it may be mentioned, is already
well founded. We show how the usual analysis of Batalin-Tyutin may be
generalised, particularly if one is dealing with nonabelian theories. In order
to gain a deeper insight into the formalism we have considered two specific
examples of second class theories-- the massive Maxwell theory (Proca model)
and its nonabelian extension. The first class constraints and the involutive
Hamiltonian are explicitly constructed. The connection of our Hamiltonian
approach with the usual Lagrangian formalism is elucidated. For the Proca model
we reveal the importance of a boundary term which plays a significant role in
establishing an exact identification of the extra fields in the Batalin-Tyutin
approach with the St\"uckelberg scalar. Some comments are also made concerning
the corresponding identification in the nonabelian example.Comment: 26 pages, Latex file, e-mail shila@saha.ernet.in SINP-TNP/94-
Constraint Correlation Dynamics of SU(N) Gauge Theories

A constraint correlation dynamics up to 4-point Green functions is proposed
for SU(N) gauge theories which reduces the N-body quantum field problem to the
two-body level. The resulting set of nonlinear coupled equations fulfills all
conservation laws including fermion number, linear and angular momenta as well
as the total energy. Apart from the conservation laws in the space-time degrees
of freedom the Gauss law is conserved as a quantum expectation value
identically for all times. The same holds for the Ward identities as generated
by commutators of Gauss operators. The constraint dynamical equations are
highly non-perturbative and thus applicable also in the strong coupling regime,
as e.g. low-energy QCD problems.Comment: 26 pages, LATEX, UGI-94-0
Conjectures on Non-Local Effects in String Black Holes

We consider modifications to general relativity by the non-local (classical
and quantum) string effects for the case of a D-dimensional Scwarzschild black
hole. The classical non-local effects do not alter the spacetime topology (the
horizon remains unshifted, at least perturbatively). We suggest a simple
analytic continuation of the perturbative result into the non-perturbative
domain, which eliminates the black hole singularity at the origin and yields an
ultraviolet-finite theory of quantum gravity. We investigate the quantum non-
local effects (including massive modes) and argue that the inclusion of these
back reactions resolves the problem of the thermal spectrum in the semi-
classical approach of field quantization in a black hole background, through
the bootstrap condition. The density of states for both the quantum and thermal
interpretation of the WKB formula are finally shown to differ quant- itatively
when including the non-local effects.Comment: 16 pages, REVTE
Potential scattering on R$^{3}$ x S$^{1}$

In this paper we consider non-relativistic quantum mechanics on a space with an additional internal compact dimension, i.e. R^3\otimes S^1 instead of R^3. More specifically we study potential scattering for this case and the analyticity properties of the forward scattering amplitude, T_{nn}(K), where K^2 is the total energy and the integer n denotes the internal excitation of the incoming particle. The surprising result is that the analyticity properties which are true in R^3 do not hold in R^3\otimes S^1. For example, T_{nn}(K), is \underline{not} analytic in K for ImK>0, for n such that (|n|/R)>\mu, where R is the radius of S^1, and \mu^{-1} is the exponential range of the potential, V(r,\phi)=O(e^{-\mu r}) for large r. We show by explicit counterexample that T_{nn}(K) for n\neq0, can have singularities on the physical energy sheet. We also discuss the motivation for our work, and briefly the lesson it teaches us
Signatures of Confinement in Axial Gauge QCD

A comparative dynamical study of axial gauge QED and QCD is presented.
Elementary excitations associated with particular field configurations are
investigated. Gluonic excitations analogous to linearly polarized photons are
shown to acquire infinite energy. Suppression of this class of excitations in
QCD results from quantization of the chromelectric flux and is interpreted as a
dual Meissner effect, i.e. as expulsion from the QCD vacuum of chromo-electric
fields which are constant over significant distances. This interpretation is
supported by a comparative evaluation of the interaction energy of static
charges in the axial gauge representation of QED and QCD.Comment: 22 pages (no figures
Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron
  Transport in Chaotic Microstructures

We study the ensemble-averaged conductance as a function of applied magnetic
field for ballistic electron transport across few-channel microstructures
constructed in the shape of classically chaotic billiards. We analyse the
results of recent experiments, which show suppression of weak localization due
to magnetic field, in the framework of random-matrix theory. By analysing a
random-matrix Hamiltonian for the billiard-lead system with the aid of
Landauer's formula and Efetov's supersymmetry technique, we derive a universal
expression for the weak-localization contribution to the mean conductance that
depends only on the number of channels and the magnetic flux. We consequently
gain a theoretical understanding of the continuous crossover from orthogonal
symmetry to unitary symmetry arising from the violation of time-reversal
invariance for generic chaotic systems.Comment: 49 pages, latex, 9 figures as tar-compressed uuencoded fil
A Renormalization Group Flow Approach to Decoupling and Irrelevant
  Operators

Using Wilson-Polchinski renormalization group equations, we give a simple new
proof of decoupling in a $\phi^4$-type scalar field theory involving two real
scalar fields (one is heavy with mass $M$ and the other light). Then, to all
orders in perturbation theory, it is shown that effects of virtual heavy
particles up to the order $1/M^{2N_0}$ can be systematically incorporated into
light-particle theory via effective local vertices of canonical dimension at
most $4+2N_0$. The couplings for vertices of dimension $4+2N$ are of order
$1/M^{2N}$ and are systematically calculable. All this is achieved through
intuitive dimensional arguments without resorting to complicated graphical
arguments or convergence theorems.Comment: 26 pages, LaTeX, 1 figure Revised version to appear in Annals of
  Physics (Title was changed. Renormalization conditions on heavy fields were
  changed to physical ones.
SDG fermion-pair algebraic SO(12) and Sp(10) models and their boson
  realizations

It is shown how the boson mapping formalism may be applied as a useful
many-body tool to solve a fermion problem. This is done in the context of
generalized Ginocchio models for which we introduce S-, D-, and G-pairs of
fermions and subsequently construct the sdg-boson realizations of the
generalized Dyson type. The constructed SO(12) and Sp(10) fermion models are
solved beyond the explicit symmetry limits. Phase transitions to rotational
structures are obtained, also in situations where there is no underlying SU(3)
symmetry.Comment: 25 LaTeX pages, 4 uuencoded postscript figures included, Preprint
  IFT/8/94 & STPHY-TH/94-