196 research outputs found
Finite temperature regularization
We present a non-perturbative regularization scheme for Quantum Field
Theories which amounts to an embedding of the originally unregularized theory
into a spacetime with an extra compactified dimensions of length L ~
Lambda^{-1} (with Lambda an ultraviolet cutoff), plus a doubling in the number
of fields, which satisfy different periodicity conditions and have opposite
Grassmann parity. The resulting regularized action may be interpreted, for the
fermionic case, as corresponding to a finite-temperature theory with a
supersymmetry, which is broken because of the boundary conditions. We test our
proposal in a perturbative calculation (the vacuum polarization graph for a
D-dimensional fermionic theory) and in a non-perturbative one (the chiral
anomaly).Comment: 17 pages, LaTeX fil
Bispectral KP Solutions and Linearization of Calogero-Moser Particle Systems
A new construction using finite dimensional dual grassmannians is developed
to study rational and soliton solutions of the KP hierarchy. In the rational
case, properties of the tau function which are equivalent to bispectrality of
the associated wave function are identified. In particular, it is shown that
there exists a bound on the degree of all time variables in tau if and only if
the wave function is rank one and bispectral. The action of the bispectral
involution, beta, in the generic rational case is determined explicitly in
terms of dual grassmannian parameters. Using the correspondence between
rational solutions and particle systems, it is demonstrated that beta is a
linearizing map of the Calogero-Moser particle system and is essentially the
map sigma introduced by Airault, McKean and Moser in 1977.Comment: LaTeX, 24 page
Constraining the parameters of binary systems through time-dependent light deflection
A theory is derived relating the configuration of the cores of active
galaxies, specifically candidates for presumed super-massive black hole
binaries (SMBHBs), to time-dependent changes in images of those galaxies. Three
deflection quantities, resulting from the monopole term, mass quadrupole term,
and spin dipole term of the core, are examined. The resulting observational
technique is applied to the galaxy 3C66B. This technique is found to under
idealized circumstances surpass the technique proposed by Jenet et al. in
accuracy for constraining the mass of SMBHB candidates, but is exceeded in
accuracy and precision by Jenet's technique under currently-understood likely
conditions. The technique can also under favorable circumstances produce
results measurable by currently-available astronomical interferometry such as
very-long baseline-interferometry (VLBI).Comment: 15 pages, 2 figures, accepted in General Relativity & Gravitatio
Functional Integral Construction of the Thirring model: axioms verification and massless limit
We construct a QFT for the Thirring model for any value of the mass in a
functional integral approach, by proving that a set of Grassmann integrals
converges, as the cutoffs are removed and for a proper choice of the bare
parameters, to a set of Schwinger functions verifying the Osterwalder-Schrader
axioms. The corresponding Ward Identities have anomalies which are not linear
in the coupling and which violate the anomaly non-renormalization property.
Additional anomalies are present in the closed equation for the interacting
propagator, obtained by combining a Schwinger-Dyson equation with Ward
Identities.Comment: 55 pages, 9 figure
Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction
The matrix version of the -KdV hierarchy has been recently
treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian
symmetry reduction applied to a Poisson submanifold in the dual of the Lie
algebra . Here a
series of extensions of this matrix Gelfand-Dickey system is derived by means
of a generalized Drinfeld-Sokolov reduction defined for the Lie algebra
using the natural
embedding for any positive integer. The
hierarchies obtained admit a description in terms of a matrix
pseudo-differential operator comprising an -KdV type positive part and a
non-trivial negative part. This system has been investigated previously in the
case as a constrained KP system. In this paper the previous results are
considerably extended and a systematic study is presented on the basis of the
Drinfeld-Sokolov approach that has the advantage that it leads to local Poisson
brackets and makes clear the conformal (-algebra) structures related to
the KdV type hierarchies. Discrete reductions and modified versions of the
extended -KdV hierarchies are also discussed.Comment: 60 pages, plain TE
A conjecture on Exceptional Orthogonal Polynomials
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of
Sturm-Liouville problems and generalize in this sense the classical families of
Hermite, Laguerre and Jacobi. They also generalize the family of CPRS
orthogonal polynomials. We formulate the following conjecture: every
exceptional orthogonal polynomial system is related to a classical system by a
Darboux-Crum transformation. We give a proof of this conjecture for codimension
2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this
analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The
classification includes all cases known to date plus some new examples of
X2-Laguerre and X2-Jacobi polynomials
Restructuring of colloidal aggregates in shear flow: Coupling interparticle contact models with Stokesian dynamics
A method to couple interparticle contact models with Stokesian dynamics (SD)
is introduced to simulate colloidal aggregates under flow conditions. The
contact model mimics both the elastic and plastic behavior of the cohesive
connections between particles within clusters. Owing to this, clusters can
maintain their structures under low stress while restructuring or even breakage
may occur under sufficiently high stress conditions. SD is an efficient method
to deal with the long-ranged and many-body nature of hydrodynamic interactions
for low Reynolds number flows. By using such a coupled model, the restructuring
of colloidal aggregates under stepwise increasing shear flows was studied.
Irreversible compaction occurs due to the increase of hydrodynamic stress on
clusters. Results show that the greater part of the fractal clusters are
compacted to rod-shaped packed structures, while the others show isotropic
compaction.Comment: A simulation movie be found at
http://www-levich.engr.ccny.cuny.edu/~seto/sites/colloidal_aggregates_shearflow.htm
Quantum and Classical Integrable Systems
The key concept discussed in these lectures is the relation between the
Hamiltonians of a quantum integrable system and the Casimir elements in the
underlying hidden symmetry algebra. (In typical applications the latter is
either the universal enveloping algebra of an affine Lie algebra, or its
q-deformation.) A similar relation also holds in the classical case. We discuss
different guises of this very important relation and its implication for the
description of the spectrum and the eigenfunctions of the quantum system.
Parallels between the classical and the quantum cases are thoroughly discussed.Comment: 59 pages, LaTeX2.09 with AMS symbols. Lectures at the CIMPA Winter
School on Nonlinear Systems, Pondicherry, January 199
Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments
A large number of treatments of the meson spectrum have been tried that
consider mesons as quark - anti quark bound states. Recently, we used
relativistic quantum "constraint" mechanics to introduce a fully covariant
treatment defined by two coupled Dirac equations. For field-theoretic
interactions, this procedure functions as a "quantum mechanical transform of
Bethe-Salpeter equation". Here, we test its spectral fits against those
provided by an assortment of models: Wisconsin model, Iowa State model,
Brayshaw model, and the popular semi-relativistic treatment of Godfrey and
Isgur. We find that the fit provided by the two-body Dirac model for the entire
meson spectrum competes with the best fits to partial spectra provided by the
others and does so with the smallest number of interaction functions without
additional cutoff parameters necessary to make other approaches numerically
tractable. We discuss the distinguishing features of our model that may account
for the relative overall success of its fits. Note especially that in our
approach for QCD, the resulting pion mass and associated Goldstone behavior
depend sensitively on the preservation of relativistic couplings that are
crucial for its success when solved nonperturbatively for the analogous
two-body bound-states of QED.Comment: 75 pages, 6 figures, revised content
Consequences of vacuum polarization on electromagnetic waves in a Lorentz-symmetry breaking scenario
The propagation of electromagnetic waves in a Lorentz-symmetry violating
scenario where there is a region of polarized vacuum is studied. It turns out
that the photon field acquires an interesting polarization state, possibly
useful to set up upper bounds in Lorentz-violating models at laboratory scales.Comment: Latex, 4 pages. To appear in PL
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