pinecone/core-2020-05-10-deduplication huggingface dataset:
Charges from Dressed Matter: Physics and Renormalisation

Gauge theories are characterised by long range interactions. Neglecting these
interactions at large times, and identifying the Lagrangian matter fields with
the asymptotic physical fields, leads to the infra-red problem. In this paper
we study the perturbative applications of a construction of physical charges in
QED, where the matter fields are combined with the associated electromagnetic
clouds. This has been formally shown, in a companion paper, to include these
asymptotic interactions. It is explicitly demonstrated that the on-shell
Green's functions and S-matrix elements describing these charged fields have,
to all orders in the coupling, the pole structure associated with particle
propagation and scattering. We show in detail that the renormalisation
procedure may be carried out straightforwardly. It is shown that standard
infra-red finite predictions of QED are not altered and it is speculated that
the good infra-red properties of our construction may open the way to the
calculation of previously uncalculable properties. Finally extensions of this
approach to QCD are briefly discussed.Comment: 34 pages, LaTeX, uses FeynMF, 17 figures, very minor wording change,
  version to appear in Annals of Physic
Breaking time reversal symmetry in chaotic driven Rydberg atoms

We consider the dynamics of Rydberg states of the hydrogen atom driven by a
microwave field of elliptical polarization, with a possible additional static
electric field. We concentrate on the effect of a resonant weak field - whose
frequency is close to the Kepler frequency of the electron around the nucleus -
which essentially produces no ionization of the atom, but completely mixes the
various states inside an hydrogenic manifold of fixed principal quantum number.
For sufficiently small fields, a perturbative approach (both in classical and
quantum mechanics) is relevant. For some configurations of the fields, the
classical secular motion (i.e. evolution in time of the elliptical electronic
trajectory) is shown to be predominantly chaotic. Changing the orientation of
the static field with respect to the polarization of the microwave field allows
us to investigate the effect of generalized time-reversal symmetry breaking on
the statistical properties of energy levels.Comment: 26 pages, 11 figures, accepted for publication in Ann. Phys. (N.Y.
Chaos and energy spreading for time-Dependent Hamiltonians, and the
  various Regimes in the theory of Quantum Dissipation

We make the first steps towards a generic theory for energy spreading and
quantum dissipation. The Wall formula for the calculation of friction in
nuclear physics and the Drude formula for the calculation of conductivity in
mesoscopic physics can be regarded as two special results of the general
formulation. We assume a time-dependent Hamiltonian $H(Q,P;x(t))$ with
$x(t)=Vt$, where $V$ is slow in a classical sense. The rate-of-change $V$ is
not necessarily slow in the quantum-mechanical sense. Dissipation means an
irreversible systematic growth of the (average) energy. It is associated with
the stochastic spreading of energy across levels. The latter can be
characterized by a transition probability kernel $P_t(n|m)$ where $n$ and $m$
are level indices. This kernel is the main object of the present study. In the
classical limit, due to the (assumed) chaotic nature of the dynamics, the
second moment of $P_t(n|m)$ exhibits a crossover from ballistic to diffusive
behavior. We define the $V$ regimes where either perturbation theory or
semiclassical considerations are applicable in order to establish this
crossover in the quantal case. In the limit $\hbar\to 0$ perturbation theory
does not apply but semiclassical considerations can be used in order to argue
that there is detailed correspondence, during the crossover time. In the
perturbative regime there is a lack of such correspondence. Namely, $P_t(n|m)$
is characterized by a perturbative core-tail structure that persists during the
crossover time. In spite of this lack of (detailed) correspondence there may be
still a restricted correspondence as far as the second-moment is concerned.
Such restricted correspondence is essential in order to establish the universal
fluctuation-dissipation relation.Comment: 46 pages, 6 figures, 4 Tables. To be published in Annals of Physics.
  Appendix F improve
Spectral determinant on quantum graphs

We study the spectral determinant of the Laplacian on finite graphs
characterized by their number of vertices V and of bonds B. We present a path
integral derivation which leads to two equivalent expressions of the spectral
determinant of the Laplacian either in terms of a V x V vertex matrix or a 2B x
2B link matrix that couples the arcs (oriented bonds) together. This latter
expression allows us to rewrite the spectral determinant as an infinite product
of contributions of periodic orbits on the graph. We also present a
diagrammatic method that permits us to write the spectral determinant in terms
of a finite number of periodic orbit contributions. These results are
generalized to the case of graphs in a magnetic field. Several examples
illustrating this formalism are presented and its application to the
thermodynamic and transport properties of weakly disordered and coherent
mesoscopic networks is discussed.Comment: 33 pages, submitted to Ann. Phy
Classical Supersymmetric Mechanics

We analyse a supersymmetric mechanical model derived from (1+1)-dimensional
field theory with Yukawa interaction, assuming that all physical variables take
their values in a Grassmann algebra B. Utilizing the symmetries of the model we
demonstrate how for a certain class of potentials the equations of motion can
be solved completely for any B. In a second approach we suppose that the
Grassmann algebra is finitely generated, decompose the dynamical variables into
real components and devise a layer-by-layer strategy to solve the equations of
motion for arbitrary potential. We examine the possible types of motion for
both bosonic and fermionic quantities and show how symmetries relate the former
to the latter in a geometrical way. In particular, we investigate oscillatory
motion, applying results of Floquet theory, in order to elucidate the role that
energy variations of the lower order quantities play in determining the
quantities of higher order in B.Comment: 29 pages, 2 figures, submitted to Annals of Physic
The chiral effective pion-nucleon Lagrangian of order p^4

We construct the minimal effective chiral pion-nucleon SU(2) Lagrangian at
fourth order in the chiral expansion. The Lagrangian contains 118 in principle
measurable terms. We develop both the relativistic as well as the heavy baryon
formulation of the effective field theory. For the latter, we also work out
explicitly all 1/m corrections at fourth order. We display all relevant
relations needed to find the linearly independent terms.Comment: 30 pp, LaTeX2e, coefficients of three third order 1/m^2 corrections
  proportional to F_{\mu\nu}^+ corrected in eq.(3.8) and table
The Entropy of Taub-Bolt Solution

A geometrical framework for the definition of entropy in General Relativity
via Noether theorem is briefly recalled and the entropy of Taub-Bolt Euclidean
solutions of Einstein equations is then obtained as an application. The
computed entropy agrees with previously known results, obtained by statistical
methods. It was generally believed that the entropy of Taub-Bolt solution could
not be computed via Noether theorem, due to the particular structure of
singularities of this solution. We show here that this is not true. The Misner
string singularity is, in fact, considered and its contribution to the entropy
is analyzed. As a result, in our framework entropy does not obey the
"one-quarter area law" and it is not directly related to horizons, as sometimes
erroneously suggested in current literature on the subject
Toward the Quantum Design of Multichannel Systems (The Inverse Problem
  Approach)

The multichannel generalization of the theory of spectral, scattering and
decay control is presented. New universal algorithms of construction of complex
quantum systems with given properties are suggested. Particularly,
transformations of interaction matrices leading to the concentration of waves
in a chosen partial channel and spatial localization are shown. The limiting
instructive cases illustrating different phenomena which occur with the
combination of 'incompatible' properties are considered. For example, the
scattering solutions with different resonance widths at the same energy for the
same interaction are revealed. Analogously, a 'paradoxical' coexistence of both
strong reflection and absolute transparency is explained. The case of the
violation of 'natural' asymptotic behavior of partial wave function is
demonstrated : it has a greater damping decrement for the channel with a lower
threshold. Peculiarities of the multichannel periodic structures, bound states
embedded into continuum, resonance tunneling and degeneracy of states are
described.Comment: 22 pages, 6 figure
SU(2,1) Dynamics of Multiple Giant Dipole Resonance Coulomb Excitation

We construct a three-dimensional analytically soluble model of the nonlinear
effects in Coulomb excitation of multiphonon Giant Dipole Resonances (GDR)
based on the SU(2,1) algebra. The full 3-dimensional model predicts further
enhancement of the Double GDR (DGDR) cross sections at high bombarding
energies. Enhancement factors for DGDR measured in thirteen different processes
with various projectiles and targets at different bombarding energies are well
reproduced with the same value of the nonlinearity parameter with the exception
of the anomalous case of $^{136}$Xe which requires a larger value.Comment: 10 pages, 3 Postscript figures, late
Towards a Many-Body Treatment of Hamiltonian Lattice SU(N) Gauge Theory

We develop a consistent approach to Hamiltonian lattice gauge theory, using
the maximal-tree gauge. The various constraints are discussed and implemented.
An independent and complete set of variables for the colourless sector is
determined. A general scheme to construct the eigenstates of the electric
energy operator using a symbolic method is described. It is shown how the
one-plaquette problem can be mapped onto a N-fermion problem. Explicit
solutions for U(1), SU(2), SU(3), SU(4), and SU(5) lattice gauge theory are
shown.Comment: 39 pages, 12 figures, and 2 table
Gauging of 1d-space translations for nonrelativistic matter - geometric
  bags

We develop in a systematic fashion the idea of gauging 1d-space translations
with fixed Newtonian time for nonrelativistic matter (particles and fields). By
starting with a nonrelativistic free theory we obtain its minimal gauge
invariant extension by introducing two gauge fields with a Maxwellian self
interaction. We fix the gauge so that the residual symmetry group is the
Galilei group and construct a representation of the extended Galilei algebra.
The reduced N-particle Lagrangian describes geodesic motion in a
(N-1)-dimensional (Pseudo-) Riemannian space. The singularity of the metric for
negative gauge coupling leads in classical dynamics to the formation of
geometric bags in the case of two or three particles. The ordering problem
within the quantization scheme for $N$-particles is solved by canonical
quantization of a pseudoclassical Schroedinger theory obtained by adding to the
continuum generalization of the point-particle Lagrangian an appropriate
quantum correction. We solve the two-particle bound state problem for both
signs of the gauge coupling. At the end we speculate on the possible physical
relevance of the new interaction induced by the gauge fields.Comment: 28 pages, LaTe
Wilson loops in the adjoint representation and multiple vacua in
  two-dimensional Yang-Mills theory

$QCD_2$ with fermions in the adjoint representation is invariant under
$SU(N)/Z_N$ and thereby is endowed with a non-trivial vacuum structure
(k-sectors). The static potential between adjoint charges, in the limit of
infinite mass, can be therefore obtained by computing Wilson loops in the pure
Yang-Mills theory with the same non-trivial structure. When the (Euclidean)
space-time is compactified on a sphere $S^2$, Wilson loops can be exactly
expressed in terms of an infinite series of topological excitations
(instantons). The presence of k-sectors modifies the energy spectrum of the
theory and its instanton content. For the exact solution, in the limit in which
the sphere is decompactified, a k-sector can be mimicked by the presence of
k-fundamental charges at $\infty$, according to a Witten's suggestion. However
this property neither holds before decompactification nor for the genuine
perturbative solution which corresponds to the zero-instanton contribution on
$S^2$.Comment: RevTeX, 46 pages, 1 eps-figur
Effective Lagrangians in bound state calculations

In order to investigate specific aspects of bound state calculations in a
non-relativistic framework, we consider the energy-levels of a massive scalar
particle, which moves in an external field and interacts in addition with a
massless scalar particle. The discussion includes the following topics:
dimensionally regularized bound-state calculations, ultraviolet finiteness of
bound-state observables and their independence of the off-mass-shell behavior
of Green functions, non-renormalizable interactions, structure of the
non-relativistic two-point function, power counting and matching.Comment: 45 pages, 8 postscript figures, RevTeX styl
The Dislocation Stress Functions From the Double Curl T(3)-Gauge
  Equation: Linearity and a Look Beyond

T(3)-gauge model of defects based on the gauge Lagrangian quadratic in the
gauge field strength is considered. The equilibrium equation of the medium is
fulfilled by the double curl Kroner's ansatz for stresses. The problem of
replication of the static edge dislocation along third axis is analysed under a
special, though conventional, choice of this ansatz. The translational gauge
equation is shown to constraint the functions parametrizing the ansatz (the
stress functions) so that the resulting stress component $\sigma_{3 3}$ is not
that of the edge defect. Another translational gauge equation with the double
curl differential operator is shown to reproduce both the stress functions, as
well as the stress tensors, of the standard edge and screw dislocations.
Non-linear extension of the newly proposed translational gauge equation is
given to correct the linear defect solutions in next orders. New gauge
Lagrangian is suggested in the Hilbert-Einstein form.Comment: 21 pages, LaTeX, no figure
General Relativistic Stars: Linear Equations of State

In this paper Einstein's field equations, for static spherically symmetric
perfect fluid models with a linear barotropic equation of state, are recast
into a 3-dimensional regular system of ordinary differential equations on a
compact state space. The system is analyzed qualitatively, using the theory of
dynamical systems, and numerically. It is shown that certain special solutions
play important roles as building blocks for the solution structure in general.
In particular, these special solutions determine many of the features exhibited
by solutions with a regular center and large central pressure. It is also shown
that the present approach can be applied to more general classes of barotropic
equations of state.Comment: 17 pages, 3 figures, uses ajour.cl
General Relativistic Stars : Polytropic Equations of State

In this paper, the gravitational field equations for static spherically
symmetric perfect fluid models with a polytropic equation of state,
$p=k\rho^{1+1/n}$, are recast into two complementary 3-dimensional {\it
regular} systems of ordinary differential equations on compact state spaces.
The systems are analyzed numerically and qualitatively, using the theory of
dynamical systems. Certain key solutions are shown to form building blocks
which, to a large extent, determine the remaining solution structure. In one
formulation, there exists a monotone function that forces the general
relativistic solutions towards a part of the boundary of the state space that
corresponds to the low pressure limit. The solutions on this boundary describe
Newtonian models and thus the relationship to the Newtonian solution space is
clearly displayed. It is numerically demonstrated that general relativistic
models have finite radii when the polytropic index $n$ satisfies $0\leq n
\lesssim 3.339$ and infinite radii when $n\geq 5$. When $3.339\lesssim n<5$,
there exists a 1-parameter set of models with finite radii and a finite number,
depending on $n$, with infinite radii.Comment: 31 pages, 10 figure
Thermal Photons and Lepton Pairs from Quark Gluon Plasma and Hot
  Hadronic Matter

The formulation of the real and virtual photon production rate from strongly
interacting matter is presented in the framework of finite temperature field
theory. The changes in the hadronic spectral function induced by temperature
are discussed within the ambit of the Walecka type model, gauged linear and
non-linear sigma models, hidden local symmetry approach and QCD sum rule
approach. Possibility of observing the direct thermal photon and lepton pair
from quark gluon plasma has been contrasted with those from hot hadronic matter
with and without medium effects for various mass variation scenarios. At SPS
energies, in-medium effects of different magnitude on the hadronic properties
for the Walecka model, Brown-Rho scaling and Nambu scaling scenarios are
conspicuously visible through the low invariant mass distribution of dilepton
and transverse momentum spectra of photon. However, at RHIC energies the
thermal photon (dilepton) spectra originating from Quark Gluon Plasma
overshines those from hadronic matter for large transverse momentum (invariant
mass) irrespective of the models used for evaluating the finite temperature
effects on the hadronic properties. It is thus expected that both at RHIC and
LHC energies the formation of Quark Gluon Plasma in the initial stages may
indeed turn out to be a realistic scenario.Comment: Text revised, 3 figures adde
Dimensional Transmutation and Dimensional Regularization in Quantum
  Mechanics. II: Rotational Invariance

A thorough analysis is presented of the class of central fields of force that
exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using
dimensional regularization, the two-dimensional delta-function potential and
the $D$-dimensional inverse square potential are studied. In particular, the
following features are analyzed: the existence of a critical coupling, the
boundary condition at the origin, the relationship between the bound-state and
scattering sectors, and the similarities displayed by both potentials. It is
found that, for rotationally symmetric scale-invariant potentials, there is a
strong-coupling regime, for which quantum-mechanical breaking of symmetry takes
place, with the appearance of a unique bound state as well as of a logarithmic
energy dependence of the scattering with respect to the energy.Comment: 29 pages. To appear in Annals of Physic
On G/H geometry and its use in M-theory compactifications

The Riemannian geometry of coset spaces is reviewed, with emphasis on its
applications to supergravity and M-theory compactifications. Formulae for the
connection and curvature of rescaled coset manifolds are generalized to the
case of nondiagonal Killing metrics.
  The example of the N^{010} spaces is discussed in detail. These are a
subclass of the coset manifolds N^{pqr}=G/H = SU(3) x U(1)/U(1) x U(1), the
integers p,q,r characterizing the embedding of H in G. We study the realization
of N^{010} as G/H=SU(3) x SU(2)/U(1) x SU(2) (with diagonal embedding of the
SU(2) \in H into G). For a particular G-symmetric rescaling there exist three
Killing spinors, implying N=3 supersymmetry in the AdS_4 \times N^{010}
compactification of D=11 supergravity. This rescaled N^{010} space is of
particular interest for the AdS_4/CFT_3 correspondence, and its SU(3) x SU(2)
isometric realization is essential for the OSp(4|3) classification of the
Kaluza-Klein modes.Comment: 12 page
Time Evolution in the External Field: the Unitarity Paradox

One of the axioms of quantum field theory is the property of unitarity of the
evolution operator. However, if one considers the quantum electrodynamics in
the external field in the leading order of perturbation theory, one will find
that the evolution transformation is a non-unitary canonical transformation of
creation and annihilation operators. This observation was one of the arguments
for the hypothesis that one should choose different representations of the
canonical commutation relations at different moments of time in the exact
quantum field theory. In this paper the contradiction is analyzed for the case
of a simple quantum mechanical model being an analog of the leading order of
the large-N field theory. On the one hand, this model is renormalized with the
help of the constructive field theory methods; the Hilbert space and unitary
evolution operator are constructed. On the other hand, the leading order of the
evolution transformation in the strong external field is shown to be
non-unitary. Thus, unitarity of evolution in the exact theory is not in
contradiction with non-unitarity of the approximate theory.Comment: 25 pages, LaTex2e, 1 figur
A New Method to Derive Low-Lying N-dimensional Quantum Wave Functions by
  Quadratures Along a Single Trajectory

We present a new method to derive low-lying N-dimensional quantum wave
functions by quadrature along a single trajectory. The N-dimensional
Schroedinger equation is cast into a series of readily integrable first order
ordinary differential equations. Our approach resembles the familiar W.K.B.
approximation in one dimension, but is designed to explore the classically
forbidden region and has a much wider applicability than W.K.B.. The method
also provides a perturbation series expansion and the Green's functions of the
wave equation in N-dimension, all by quadratures along a single trajectory. A
number of examples are given for illustration, including a simple algorithm to
evaluate the Stark effect in closed form to any finite order of the electric
field.Comment: 69 pages, Latex, no figure, no table; more ackowledgment added, typos
  correcte
Multi-boson effects in Bose-Einstein interferometry and the multiplicity
  distribution

Multi-boson symmetrization effects on two-particle Bose-Einstein
interferometry are studied for ensembles with arbitrary multiplicity
distributions. This generalizes the previously studied case of a Poissonian
input multiplicity distribution. In the general case we find interesting
residual correlations which require a modified framework for extracting
information on the source geometry from two-particle correlation measurements.
In sources with high phase-space densities, multi-boson effects modify the
Hanbury Brown-Twiss (HBT) radius parameters and simultaneously generate strong
residual correlations. We clarify their effect on the correlation strength
(intercept parameter) and thus explain a variety of previously reported
puzzling multi-boson symmetrization phenomena. Using a class of analytically
solvable Gaussian source models, with and without space-momentum correlations,
we present a comprehensive overview of multi-boson symmetrization effects on
particle interferometry. For event ensembles of (approximately) fixed
multiplicity, the residual correlations lead to a minimum in the correlation
function at non-zero relative momentum, which can be practically exploited to
search, in a model-independent way, for multi-boson symmetrization effects in
high-energy heavy-ion experiments.Comment: 22 pages ReVTex, including 8 postscript figures. Submitted to Annals
  of Physics (N.Y.