495 research outputs found
Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval
The upper bound for asymptotic behavior of the coefficients of expansion of
the evolution operator kernel in powers of the time interval \Dt was
obtained. It is found that for the nonpolynomial potentials the coefficients
may increase as . But increasing may be more slow if the contributions with
opposite signs cancel each other. Particularly, it is not excluded that for
number of the potentials the expansion is convergent. For the polynomial
potentials \Dt-expansion is certainly asymptotic one. The coefficients
increase in this case as , where is the order of
the polynom. It means that the point \Dt=0 is singular point of the kernel.Comment: 12 pp., LaTe
Some peculiarities in response on filling up the Fermi sphere by quarks
Considering quarks as the quasi-particles of the model Hamiltonian with
four-fermion interaction we study response on the process of filling up the
Fermi sphere by quarks.Comment: 11 pages, 5 figures, minor language improvemen
On duality of Drell-Yan and J/psi production processes
It is studied the model on J/psi production allowing to extract parton
distribution functions (PDFs) from the combined analysis with both data on
Drell-Yan and J/psi production processes. It is shown that this, so attractive
from theoretical point of view, model, can be safely used in the low energy
region E<100 GeV. The significance of gluon contributions to the J/psi
cross-sections is investigated. The obtained results in the high energy region
occur to be rather surprising
Phase diagram and critical properties within an effective model of QCD: the Nambu-Jona-Lasinio model coupled to the Polyakov loop
We investigate the phase diagram of the so-called
Polyakov--Nambu--Jona-Lasinio model at finite temperature and non-zero chemical
potential with three quark flavors. Chiral and deconfinement phase transitions
are discussed and the relevant order-like parameters are analyzed. The results
are compared with simple thermodynamic expectations and lattice data. We
present the phase diagram in the ( plane, paying special attention
to the critical end point: as the strength of the flavor-mixing interaction
becomes weaker, the critical end point moves to low temperatures and can even
disappear.Comment: 46 pages, 11 figures, 3 table
Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions
Recent proofs of the convergence of the linear delta expansion in zero and in
one dimensions have been limited to the analogue of the vacuum generating
functional in field theory. In zero dimensions it was shown that with an
appropriate, -dependent, choice of an optimizing parameter \l, which is an
important feature of the method, the sequence of approximants tends to
with an error proportional to . In the present paper we
establish the convergence of the linear delta expansion for the connected
vacuum function . We show that with the same choice of \l the
corresponding sequence tends to with an error proportional to . The rate of convergence of the latter sequence is governed by
the positions of the zeros of .Comment: 20 pages, LaTeX, Imperial/TP/92-93/5
Resonances and fluctuations in the statistical model
We describe how the study of resonances and fluctuations can help constrain
the thermal and chemical freezeout properties of the fireball created in heavy
ion collisions. This review is based on [1-5].Comment: Proceedings,"Hadronic resonance production in heavy ion and
elementary collisions" UT Austin, March 5-7 201
Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV
This is the second paper on the path integral approach of superintegrable
systems on Darboux spaces, spaces of non-constant curvature. We analyze in the
spaces \DIII and \DIV five respectively four superintegrable potentials,
which were first given by Kalnins et al. We are able to evaluate the path
integral in most of the separating coordinate systems, leading to expressions
for the Green functions, the discrete and continuous wave-functions, and the
discrete energy-spectra. In some cases, however, the discrete spectrum cannot
be stated explicitly, because it is determined by a higher order polynomial
equation.
We show that also the free motion in Darboux space of type III can contain
bound states, provided the boundary conditions are appropriate. We state the
energy spectrum and the wave-functions, respectively
An infinite family of superintegrable Hamiltonians with reflection in the plane
We introduce a new infinite class of superintegrable quantum systems in the
plane. Their Hamiltonians involve reflection operators. The associated
Schr\"odinger equations admit separation of variables in polar coordinates and
are exactly solvable. The angular part of the wave function is expressed in
terms of little -1 Jacobi polynomials. The spectra exhibit "accidental"
degeneracies. The superintegrability of the model is proved using the
recurrence relation approach. The (higher-order) constants of motion are
constructed and the structure equations of the symmetry algebra obtained.Comment: 19 page
On the Divergence of Perturbation Theory. Steps Towards a Convergent Series
The mechanism underlying the divergence of perturbation theory is exposed.
This is done through a detailed study of the violation of the hypothesis of the
Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum
Field Theory. That theorem governs the validity (or lack of it) of the formal
manipulations done to generate the perturbative series in the functional
integral formalism. The aspects of the perturbative series that need to be
modified to obtain a convergent series are presented. Useful tools for a
practical implementation of these modifications are developed. Some resummation
methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure
Chiral Symmetry Breaking in QCD: A Variational Approach
We develop a "variational mass" expansion approach, recently introduced in
the Gross--Neveu model, to evaluate some of the order parameters of chiral
symmetry breakdown in QCD. The method relies on a reorganization of the usual
perturbation theory with the addition of an "arbitrary quark mass , whose
non-perturbative behaviour is inferred partly from renormalization group
properties, and from analytic continuation in properties. The resulting
ansatz can be optimized, and in the chiral limit we estimate the
dynamical contribution to the "constituent" masses of the light quarks
; the pion decay constant and the quark condensate .Comment: 10 pages, no figures, LaTe
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