Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval Δt\Delta t

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 $n!$. 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 $\Gamma(n \frac{L-2}{L+2})$, where $L$ 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 ($T,\,\mu_B)$ 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, $N$-dependent, choice of an optimizing parameter \l, which is an important feature of the method, the sequence of approximants $Z_N$ tends to $Z$ with an error proportional to ${\rm e}^{-cN}$. In the present paper we establish the convergence of the linear delta expansion for the connected vacuum function $W=\ln Z$. We show that with the same choice of \l the corresponding sequence $W_N$ tends to $W$ with an error proportional to ${\rm e}^{-c\sqrt N}$. The rate of convergence of the latter sequence is governed by the positions of the zeros of $Z_N$.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 $m$, whose non-perturbative behaviour is inferred partly from renormalization group properties, and from analytic continuation in $m$ properties. The resulting ansatz can be optimized, and in the chiral limit $m \to 0$ we estimate the dynamical contribution to the "constituent" masses of the light quarks $M_{u,d,s}$; the pion decay constant $F_\pi$ and the quark condensate $< \bar q q >$.Comment: 10 pages, no figures, LaTe