pinecone/core-2020-05-10-deduplication huggingface dataset:
Symmetry, Duality and Anholonomy of Point Interactions in One Dimension

We analyze the spectral structure of the one dimensional quantum mechanical
system with point interaction, which is known to be parametrized by the group
U(2). Based on the classification of the interactions in terms of symmetries,
we show, on a general ground, how the fermion-boson duality and the spectral
anholonomy recently discovered can arise. A vital role is played by a hidden
su(2) formed by a certain set of discrete transformations, which becomes a
symmetry if the point interaction belongs to a distinguished U(1) subfamily in
which all states are doubly degenerate. Within the U(1), there is a particular
interaction which admits the interpretation of the system as a supersymmetric
Witten model.Comment: 47 pages, 5 figures (with 7 EPS files); corrected typo
Retarded versus time-nonlocal quantum kinetic equations

The finite duration of the collisions in Fermionic systems as expressed by
the retardation time in non-Markovian Levinson-type kinetic equations is
discussed in the quasiclassical limit. We separate individual contributions
included in the memory effect resulting in (i) off-shell tails of the Wigner
distribution, (ii) renormalization of scattering rates and (iii) of the
single-particle energy, (iv) collision delay and (v) related non-local
corrections to the scattering integral. In this way we transform the Levinson
equation into the Landau-Silin equation extended by the non-local corrections
known from the theory of dense gases. The derived nonlocal kinetic equation
unifies the Landau theory of quasiparticle transport with the classical kinetic
theory of dense gases. The space-time symmetry is discussed versus
particle-hole symmetry and a solution is proposed which transforms these two
exclusive pictures into each other.Comment: slightly revised, 19 page
Algebraic Aspects of the Background Field Method

We discuss some algebraic properties of the background field method. We
introduce an extra gauge-fixing term for the background gauge field right at
the beginning in the action in such a way that BRST invariance is preserved.
The background effective action is considered and it is shown to satisfy both
the Slavnov-Taylor identities and the Ward identities. This allows to prove the
background equivalence theorem by means of the standard techniques. We show
that the Legendre transform W_{bg} of the background gauge invariant action
gives the same physical amplitudes as the original one we started with.
Moreover, we point out that W_{bg} cannot in general be derived from a
classical action by the Gell-Mann-Low formula. Finally, we show that the BRST
doublet generated from the background field does not modify the anomaly of the
original underlying gauge theory. The proof is algebraic and makes no use of
arguments based on power-counting
Relativity of pure states entanglement

Entanglement of any pure state of an N times N bi-partite quantum system may
be characterized by the vector of coefficients arising by its Schmidt
decomposition. We analyze various measures of entanglement derived from the
generalized entropies of the vector of Schmidt coefficients. For N >= 3 they
generate different ordering in the set of pure states and for some states their
ordering depends on the measure of entanglement used. This odd-looking property
is acceptable, since these incomparable states cannot be transformed to each
other with unit efficiency by any local operation. In analogy to special
relativity the set of pure states equivalent under local unitaries has a causal
structure so that at each point the set splits into three parts: the 'Future',
the 'Past' and the set of noncomparable states.Comment: 18 pages 7 figure
Scarring and the statistics of tunnelling

We show that the statistics of tunnelling can be dramatically affected by
scarring and derive distributions quantifying this effect. Strong deviations
from the prediction of random matrix theory can be explained quantitatively by
modifying the Gaussian distribution which describes wavefunction statistics.
The modified distribution depends on classical parameters which are determined
completely by linearised dynamics around a periodic orbit. This distribution
generalises the scarring theory of Kaplan [Phys. Rev. Lett. {\bf 80}, 2582
(1998)] to describe the statistics of the components of the wavefunction in a
complete basis, rather than overlaps with single Gaussian wavepackets. In
particular it is shown that correlations in the components of the wavefunction
are present, which can strongly influence tunnelling-rate statistics. The
resulting distribution for tunnelling rates is tested successfully on a
two-dimensional double-well potential.Comment: 20 pages, 4 figures, submitted to Ann. Phy
Neutrino Self-Energy and Index of Refraction in Strong Magnetic Field: A
  New Approach

The Ritus' $E_{p}$ eigenfunction method is extended to the case of spin-1
charged particles in a constant electromagnetic field and used to calculate the
one-loop neutrino self-energy in the presence of a strong magnetic field.From
the obtained self-energy, the neutrino dispersion relation and index of
refraction in the magnetized vacuum are determined within the field range
$m_{e}^{2}\ll eB\ll M_{W}^{2}$. The propagation of neutrinos in the magnetized
vacuum is anisotropic due to the dependence of the index of refraction on the
angle between the directions of the neutrino momentum and the external field.
Possible cosmological implications of the results are discussed.Comment: latex, 26 pages, 1 figure. Discussion section redon
Semiclassical Symmetries

Essential properties of semiclassical approximation for quantum mechanics are
viewed as axioms of an abstract semiclassical mechanics. Its symmetry
properties are discussed. Semiclassical systems being invariant under Lie
groups are considered. An infinitesimal analog of group relation is written.
Sufficient conditions for reconstructing semiclassical group transformations
(integrability of representation of Lie algebra) are discussed. The obtained
results may be used for mathematical proof of Poincare invariance of
semiclasical Hamiltonian field theory and for investigation of quantum
anomalies.Comment: LaTeX, 33 page
Minimal Coupling in Koopman-von Neumann Theory

Classical mechanics (CM), like quantum mechanics (QM), can have an
operatorial formulation. This was pioneered by Koopman and von Neumann (KvN) in
the 30's. They basically formalized, via the introduction of a classical
Hilbert space, earlier work of Liouville who had shown that the classical time
evolution can take place via an operator, nowadays known as the Liouville
operator. In this paper we study how to perform the coupling of a point
particle to a gauge field in the KvN version of CM. So we basically implement
at the classical operatorial level the analog of the minimal coupling of QM. We
show that, differently than in QM, not only the momenta but also other
variables have to be coupled to the gauge field. We also analyze in details how
the gauge invariance manifests itself in the Hilbert space of KvN and indicate
the differences with QM. As an application of the KvN method we study the
Landau problem proving that there are many more degeneracies at the classical
operatorial level than at the quantum one. As a second example we go through
the Aharonov-Bohm phenomenon showing that, at the quantum level, this
phenomenon manifests its effects on the spectrum of the quantum Hamiltonian
while at the classical level there is no effect whatsoever on the spectrum of
the Liouville operator.Comment: 38+1 pages, 2 figures, Latex; one reference change
Non-Equilibrium Statistical Mechanics of Classical Lattice $\phi^4$
  Field Theory

Classical $\phi^4$ theory in weak and strong thermal gradients is studied on
the lattice in (1+1) dimensions. Classical $\phi^4$ theory in weak and strong
thermal gradients is studied on the lattice in (1+1) dimensions. The steady
state physics of the theory is investigated from first principles and
classified into dynamical regimes. We derive the bulk properties associated
with thermal transport, and explore in detail the non-equilibrium statistical
mechanics of the theory as well as connections to equilibrium and irreversible
thermodynamics. Linear response predictions are found to be valid for systems
quite far from equilibrium and are seen to eventually break down simultaneously
with local equilibrium.Comment: 28 pages, 20 fig
Axial anomaly and topological charge in lattice gauge theory with
  Overlap Dirac operator

An explicit, detailed evaluation of the classical continuum limit of the
axial anomaly/index density of the overlap Dirac operator is carried out in the
infinite volume setting, and in a certain finite volume setting where the
continuum limit involves an infinite volume limit. Our approach is based on a
novel power series expansion of the overlap Dirac operator. The correct
continuum expression is reproduced when the parameter $m_0$ is in the physical
region $0<m_0<2$. This is established for a broad range of continuum gauge
fields. An analogous result for the fermionic topological charge, given by the
index of the overlap Dirac operator, is then established for a class of
topologically non-trivial fields in the aforementioned finite volume setting.
Problematic issues concerning the index in the infinite volume setting are also
discussed.Comment: Latex, 33 pages. v6: shortened and (hopefully) more succinct version,
  to appear in Ann.Phy
Functional Callan-Symanzik Equation for the Coulomb Gas

A non-perturbative scheme, based on the functional generalization of the
Callan-Symanzik equation is developed to treat the Coulomb interaction in an
electron gas. The one-particle irreducible vertex functions are shown to
satisfy an evolution equation whose initial condition is given by means of the
classical action and the final point corresponds to the physical system. This
equation is truncated by expanding it in momenta and excitation energies,
leaving the electric charge as an arbitrary, not necesseraly small parameter.
Exact coupled partial differential equations up to first order in the
frequencies and excitation energies are derived. The numerical integration of
these eqations is left to a later stage. Nevertheless, in order to demonstrate
the relation with the perturbation expansion the one-loop Lindhard function and
screening are reproduced in the independent mode approximation of the evolution
equation.Comment: 16 page
Covariant Thermodynamics of Quantum Systems: Passivity, Semipassivity,
  and the Unruh Effect

According to the Second Law of Thermodynamics, cycles applied to
thermodynamic equilibrium states cannot perform work (passivity property of
thermodyamic equilibrium states). In the presence of matter this can hold only
in the rest frame of the matter, as moving matter drives, e.g., windmills and
turbines. If, however, a homogeneous and stationary state has the property that
no cycle can perform more work than an ideal windmill, then it can be shown
that there is some inertial frame where the state is a thermodynamic
equilibrium state. This provides a covariant characterization of thermodynamic
equilibrium states.
  In the absence of matter, cycles should perform work only when driven by
nonstationary inertial forces caused by the observer's motion. If a pure state
of a relativistic quantum field theory behaves this way, it satisfies the
spectrum condition and exhibits the Unruh effect.Comment: 22 page
Effective action for scalar fields in two-dimensional gravity

We consider a general two-dimensional gravity model minimally or nonminimally
coupled to a scalar field. The canonical form of the model is elucidated, and a
general solution of the equations of motion in the massless case is reviewed.
In the presence of a scalar field all geometric fields (zweibein and Lorentz
connection) are excluded from the model by solving exactly their Hamiltonian
equations of motion. In this way the effective equations of motion and the
corresponding effective action for a scalar field are obtained. It is written
in a Minkowskian space-time and does not include any geometric variables. The
effective action arises as a boundary term and is nontrivial both for open and
closed universes. The reason is that unphysical degrees of freedom cannot be
compactly supported because they must satisfy the constraint equation. As an
example we consider spherically reduced gravity minimally coupled to a massless
scalar field. The effective action is used to reproduce the Fisher and Roberts
solutions
Electromagnetic transition form factors and dilepton decay rates of
  nucleon resonances

Relativistic, kinematically complete phenomenological expressions for the
dilepton decay rates of nucleon resonances with arbitrary spin and parity are
derived in terms of the magnetic, electric, and Coulomb transition form
factors. The dilepton decay rates of the nucleon resonances with masses below 2
GeV are estimated using the extended vector meson dominance model for the
transition form factors. The model provides a unified description of the photo-
and electroproduction data, the vector meson decays, and the dilepton decays of
the nucleon resonances. The constraints on the transition form factors from the
quark counting rules are taken into account. The parameters of the model are
fixed by fitting the available photo- and electroproduction data and using
results of the multichannel partial-wave analysis of the $\pi N$ scattering.
Where experimental data are not available, predictions of the non-relativistic
quark models are used as an input. The vector meson coupling constants of the
magnetic, electric, and Coulomb types are determined. The dilepton widths and
the dilepton spectra from decays of nucleon resonances with masses below 2 GeV
are calculated.Comment: An error in the code is found and fixed. Numerical results for the
  spin-half nucleon resonances changed. A few misprints are removed from the
  text. 56 pages including 7 tables and 27 eps figures, REVTe
Supersymmetry-based Approach to Quantum Particle Dynamics

We present the N=2 supersymmetric formulation for the classical and quantum
dynamics of a nonrelativistic charged particle on a curved surface in the
presence of a perpendicular magnetic field. For a particle moving on a
constant-curvature surface in a constant magnetic field, our Hamiltonian
possesses the shape-invariance property in addition. On the surface of a sphere
and also on the hyperbolic plane, we exploit the supersymmetry and
shape-invariance properties to obtain complete solutions to the corresponding
quantum mechanical problems.Comment: revtex, 24pages, no figur
Exact solutions to Pauli-Villars-regulated field theories

We present a new class of quantum field theories which are exactly solvable.
The theories are generated by introducing Pauli-Villars fermionic and bosonic
fields with masses degenerate with the physical positive metric fields. An
algorithm is given to compute the spectrum and corresponding eigensolutions. We
also give the operator solution for a particular case and use it to illustrate
some of the tenets of light-cone quantization. Since the solutions of the
solvable theory contain ghost quanta, these theories are unphysical. However,
we also discuss how perturbation theory in the difference between the masses of
the physical and Pauli-Villars particles could be developed, thus generating
physical theories. The existence of explicit solutions of the solvable theory
also allows one to study the relationship between the equal-time and light-cone
vacua and eigensolutions.Comment: 20 pages, REVTeX; minor corrections to normalization
Gauge Theoretical Construction of Non-compact Calabi-Yau Manifolds

We construct the non-compact Calabi-Yau manifolds interpreted as the complex
line bundles over the Hermitian symmetric spaces. These manifolds are the
various generalizations of the complex line bundle over CP^{N-1}. Imposing an
F-term constraint on the line bundle over CP^{N-1}, we obtain the line bundle
over the complex quadric surface Q^{N-2}. On the other hand, when we promote
the U(1) gauge symmetry in CP^{N-1} to the non-abelian gauge group U(M), the
line bundle over the Grassmann manifold is obtained. We construct the
non-compact Calabi-Yau manifolds with isometries of exceptional groups, which
we have not discussed in the previous papers. Each of these manifolds contains
the resolution parameter which controls the size of the base manifold, and the
conical singularity appears when the parameter vanishes.Comment: LaTeX2e, 27 pages, no figures, typos correcte
Functional Closure of Schwinger-Dyson Equations in Quantum
  Electrodynamics, Part 1: Generation of Connected and One-Particle Irreducible
  Feynman Diagrams

Using functional derivatives with respect to free propagators and
interactions we derive a closed set of Schwinger-Dyson equations in quantum
electrodynamics. Its conversion to graphical recursion relations allows us to
systematically generate all connected and one-particle irreducible Feynman
diagrams for the $n$-point functions and the vacuum energy together with their
correct weights.Comment: Author Information under
  http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of
  paper also at http://www.physik.fu-berlin.de/~kleinert/32
Ground states of quantum antiferromagnets in two dimensions

We explore the ground states and quantum phase transitions of
two-dimensional, spin S=1/2, antiferromagnets by generalizing lattice models
and duality transforms introduced by Sachdev and Jalabert (Mod. Phys. Lett. B
4, 1043 (1990), http://onsager.physics.yale.edu/p32.pdf). The `minimal' model
for square lattice antiferromagnets is a lattice discretization of the quantum
non-linear sigma model, along with Berry phases which impose quantization of
spin. With full SU(2) spin rotation invariance, we find a magnetically ordered
ground state with Neel order at weak coupling, and a confining paramagnetic
ground state with bond charge (e.g. spin Peierls) order at strong coupling. We
study the mechanisms by which these two states are connected in intermediate
coupling. We extend the minimal model to study different routes to
fractionalization and deconfinement in the ground state, and also generalize it
to cases with a uniaxial anisotropy (the spin symmetry group is then U(1)). For
the latter systems, fractionalization can appear by the pairing of vortices in
the staggered spin order in the easy-plane; however, we argue that this route
does not survive the restoration of SU(2) spin symmetry. For SU(2) invariant
systems we study a separate route to fractionalization associated with the
Higgs phase of a complex boson measuring non-collinear, spiral spin
correlations: we present phase diagrams displaying competition between magnetic
order, bond charge order, and fractionalization, and discuss the nature of the
quantum transitions between the various states. A strong check on our methods
is provided by their application to S=1/2 frustrated antiferromagnets in one
dimension: here, our results are in complete accord with those obtained by
bosonization and by the solution of integrable models.Comment: 44 pages, 19 figures; SS web page: http://pantheon.yale.edu/~subir
  (v2) updated discussion of literatur
Faster-than-c signals, special relativity, and causality

Motivated by the recent attention on superluminal phenomena, we investigate
the compatibility between faster-than-c propagation and the fundamental
principles of relativity and causality. We first argue that special relativity
can easily accommodate -- indeed, does not exclude -- faster-than-c signalling
at the kinematical level. As far as causality is concerned, it is impossible to
make statements of general validity, without specifying at least some features
of the tachyonic propagation. We thus focus on the Scharnhorst effect
(faster-than-c photon propagation in the Casimir vacuum), which is perhaps the
most plausible candidate for a physically sound realization of these phenomena.
We demonstrate that in this case the faster-than-c aspects are ``benign'' and
constrained in such a manner as to not automatically lead to causality
violations.Comment: Plain LaTeX2E; 25 pages; 4 embedded figures (LaTeX pictures). V2:
  Some discussion clarified, minor rearrangements, references updated, no
  change in physics conclusions. To appear in Annals of Physic
Renormalization Group Method Applied to Kinetic Equations: roles of
  initial values and time

The so-called renormalization group (RG) method is applied to derive kinetic
and transport equations from the respective microscopic equations. The derived
equations include Boltzmann equation in classical mechanics, Fokker-Planck
equation, a rate equation in a quantum field theoretical model. Utilizing the
formulation of the RG method which elucidates the important role played by the
choice of the initial conditions, the general structure and the underlying
assumptions in the derivation of kinetic equations in the RG method is
clarified. It is shown that the present formulation naturally leads to the
choice for the initial value of the microscopic distribution function at
arbitrary time $t_0$ to be on the averaged distribution function to be
determined. The averaged distribution function may be thought as an integral
constant of the solution of microscopic evolution equation; the RG equation
gives the slow dynamics of the would-be initial constant, which is actually the
kinetic equation governing the averaged distribution function. It is further
shown that the averaging as given above gives rise to a coarse-graining of the
time-derivative which is expressed with the initial time $t_0$, thereby leads
to time-irreversible equations even from a time-reversible equation. It is
shown that a further reduction of Boltzmann equation to fluid dynamical
equations and the adiabatic elimination of fast variables in Fokker-Planck
equation are also performed in a unified way in the present method.Comment: The detailed derivations are added to section 5 (fluiddynamical limit
  of Boltzmann equation) and to Appendix B (Adiabatic elimination of fast
  variables in Fokker-Planck equation) which is moved to the text as a section.
  Other minor corrections are made all over the text including typo
Quantum Mechanics and Stochastic Mechanics for compatible observables at
  different times

Bohm Mechanics and Nelson Stochastic Mechanics are confronted with Quantum
Mechanics in presence of non-interacting subsystems. In both cases, it is shown
that correlations at different times of compatible position observables on
stationary states agree with Quantum Mechanics only in the case of product wave
functions. By appropriate Bell-like inequalities it is shown that no classical
theory, in particular no stochastic process, can reproduce the quantum
mechanical correlations of position variables of non interacting systems at
different times.Comment: Plain Te
Nahm Transform and Moduli Spaces of CPn Models on the Torus

There is a Nahm transform for two-dimensional gauge fields which establishes
a one-to-one correspondence between the orbit space of U(N) gauge fields with
topological charge k defined on a torus and that of U(k) gauge fields with
charge N on the dual torus. The main result of this paper is to show that a
similar duality transform cannot exist for CPn instantons. This fact
establishes a significative difference between 4-D gauge theories and CPn
models. The result follows from the global analysis of the moduli space of
instantons based on a complete and explicit parametrization of all self-dual
solutions on the two-dimensional torus. The boundary of the space of regular
instantons is shown to coincide with the space of singular instantons. This
identification provides a new approach to analyzing the role of overlapping
instantons in the infrared sector of CPn sigma models.Comment: 28 pages, 5 eps-figure