Born--Oppenheimer corrections to the effective zero-mode Hamiltonian in SYM theory

We calculate the subleading terms in the Born--Oppenheimer expansion for the effective zero-mode Hamiltonian of N = 1, d=4 supersymmetric Yang--Mills theory with any gauge group. The Hamiltonian depends on 3r abelian gauge potentials A_i, lying in the Cartan subalgebra, and their superpartners (r being the rank of the group). The Hamiltonian belongs to the class of N = 2 supersymmetric QM Hamiltonia constructed earlier by Ivanov and I. Its bosonic part describes the motion over the 3r--dimensional manifold with a special metric. The corrections explode when the root forms \alpha_j(A_i) vanish and the Born--Oppenheimer approximation breaks down.Comment: typos correcte

Remarks on quantization of Pais-Uhlenbeck oscillators

This work is concerned with a quantization of the Pais-Uhlenbeck oscillators from the point of view of their multi-Hamiltonian structures. It is shown that the 2n-th order oscillator with a simple spectrum is equivalent to the usual anisotropic n - dimensional oscillator

Physics of Quark--Gluon Plasma

In this lecture, we give a brief review of what theorists now know, understand, or guess about static and kinetic properties of quark--gluon plasma. A particular attention is payed to the problem of physical observability, i.e. the physical meaningfulness of various characteristics of $QGP$ discussed in the literature.Comment: 35 pages LaTeX, 3 Postscript figures included by epsf.sty are now fixed and printable, uses axodraw.sty included in the package. Some references added and minor stylistic changes made. Lecture at the XXIV ITEP Winter School (Snegiri, February 1996

On the Stability of Coherent States for Pais-Uhlenbeck Oscillator

We have constructed coherent states for the higher derivative Pais-Uhlenbeck Oscillator. In the process we have suggested a novel way to construct coherent states for the oscillator having only negative energy levels. These coherent states have negative energies in general but their coordinate and momentum expectation values and dispersions behave in an identical manner as that of normal (positive energy) oscillator. The coherent states for the Pais-Uhlenbeck Oscillator have constant dispersions and a modified Heisenberg Uncertainty Relation. Moreover, under reasonable assumptions on parameters these coherent states can have positive energies.Comment: Title changed, modified version with no major change in results and conclusions, to appear in Mod.Phys.Lett.

Exceptional points in quantum and classical dynamics

We notice that, when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits a singular behaviour associated with restructuring of classical trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2 -igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies with supersymmetric Yang-Mills dynamics are elucidated.Comment: References added. Final version to be published in J. Phys.

Yang-Mills Integrals

Two results are presented for reduced Yang-Mills integrals with different symmetry groups and dimensions: the first is a compact integral representation in terms of the relevant variables of the integral, the second is a method to analytically evaluate the integrals in cases of low order. This is exhibited by evaluating a Yang-Mills integral over real symmetric matrices of order 3.Comment: LaTeX, 10 pages, references added and minimal change

Analysis of the Rare Bc→Ds,d∗l+l−B_c \to D_{s,d}^{*} l^+ l^- Decays in QCD

The rare $B_c \to D_{s,d}^{*} l^+ l^-$ decays are investigated in the framework of the three point QCD sum rules approach. Considering the gluon condensate corrections to the correlation function, the form factors relevant to these transitions are calculated. The total decay width and branching ratio for these decays are also evaluated. The results for the branching ratios are in good agreement with the quark models.Comment: 20 Pages, 2 Figures and 5 Table

Instantons and fermion condensate in adjoint QCD_2

We show that $QCD_2$ with adjoint fermions involves instantons due to nontrivial $\pi_1[SU(N)/Z_N]~=~Z_N$. At high temperatures, quasiclassical approximation works and the action and the form of effective (with account of quantum corrections) instanton solution can be evaluated. Instanton presents a localized configuration with the size $\propto g^{-1}$. At $N=2$, it involves exactly 2 zero fermion modes and gives rise to fermion condensate $_T$ which falls off $\propto \exp\{-\pi^{3/2} T/g\}$ at high $T$ but remains finite. At low temperatures, both instanton and bosonization arguments also exhibit the appearance of fermion condensate $_{T=0} ~\sim ~g$. For $N>2$, the situation is paradoxical. There are $2(N-1)$ fermion zero modes in the instanton background which implies the absence of the condensate in the massless limit. From the other hand, bosonization arguments suggest the appearance of the condensate for any $N$. Possible ways to resolve this paradox (which occurs also in some 4-dim gauge theories) are discussed.Comment: TPI-MINN-94/6-T. 37 p., 3 fig. Fig.3 and discussion around it are rectified. Bibliography update

Massive Schwinger model and its confining aspects on curved space-time

Using a covariant method to regularize the composite operators, we obtain the bosonized action of the massive Schwinger model on a classical curved background. Using the solution of the bosonic effective action, the energy of two static external charges with finite and large distance separation on a static curved space-time is obtained. The confining behavior of this model is also explicitly discussed.Comment: A disscussion about the infrared regularization and also two references are added. Accepted for publication in Phys. Rev. D (2001