The last integrable case of kozlov-Treshchev Birkhoff integrable potentials

We establish the integrability of the last open case in the Kozlov-Treshchev classification of Birkhoff integrable Hamiltonian systems. The technique used is a modification of the so called quadratic Lax pair for $D_n$ Toda lattice combined with a method used by M. Ranada in proving the integrability of the Sklyanin case.Comment: 13 page

Reduction and Realization in Toda and Volterra

We construct a new symplectic, bi-hamiltonian realization of the KM-system by reducing the corresponding one for the Toda lattice. The bi-hamiltonian pair is constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper we also review the important work of Moser on the Toda and KM-systems.Comment: 17 page

Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case

The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function [2,3] we arrive at the complete ${\cal O}(\alpha_s^4)$ expression for the Adler function and, as a direct consequence, at the complete ${\cal O}(\alpha_s^4)$ correction to the $e^+ e^-$ annihilation into hadrons in a general gauge theory.Comment: 4 pages, 1 figure. Final published versio

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

Adler Function, DIS sum rules and Crewther Relations

The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) contribution to the singlet part of the Adler function.Comment: Talk presented at 10-th DESY Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, W\"orlitz, Germany, 25-30 April 201

Parity violating pion electroproduction off the nucleon

Parity violating (PV) contributions due to interference between $\gamma$ and $Z^0$ exchange are calculated for pion electroproduction off the nucleon. A phenomenological model with effective Lagrangians is used to determine the resulting asymmetry for the energy region between threshold and $\Delta(1232)$ resonance. The $\Delta$ resonance is treated as a Rarita-Schwinger field with phenomenological $N \Delta$ transition currents. The background contributions are given by the usual Born terms using the pseudovector $\pi N$ Lagrangian. Numerical results for the asymmetry are presented.Comment: 17 pages, RevTeX, 6 figures (in separate file figs.uu), uses epsf, accepted for publication in Z. Phys.

The Off-diagonal Goldberger-Treiman Relation and Its Discrepancy

We study the off-diagonal Goldberger-Treiman relation (ODGTR) and its discrepancy (ODGTD) in the N, Delta, pi sector through O(p^2) using heavy baryon chiral perturbation theory. To this order, the ODGTD and axial vector N to Delta transition radius are determined solely by low energy constants. Loop corrections appear at O(p^4). For low-energy constants of natural size, the ODGTD would represent a ~ 2% correction to the ODGTR. We discuss the implications of the ODGTR and ODGTD for lattice and quark model calculations of the transition form factors and for parity-violating electroexcitation of the Delta.Comment: 11 pages, 1 eps figur

Stability and renormalization of Yang-Mills theory with Background Field Method: a regularization independent proof

In this paper the stability and the renormalizability of Yang-Mills theory in the Background Field Gauge are studied. By means of Ward Identities of Background gauge invariance and Slavnov-Taylor Identities the stability of the classical model is proved and, in a regularization independent way, its renormalizability is verified. A prescription on how to build the counterterms is given and the possible anomalies which may appear for Ward Identities and for Slavnov-Taylor Identities are shown.Comment: 25 pages, Latex 2.09, no figure

QCD tests in tau decays with optimized perturbation expansion

The next-to-next-to-leading order perturbative QCD corrections to R_tau and the higher moments of the invariant mass distribution in the hadronic tau decays are considered. The renormalization scheme dependence of these corrections is discussed. The optimized predictions are obtained, using the principle of minimal sensitivity as a guide to select the preferred renormalization scheme. A simplified fit is performed, using R_tau and R^12_tau, to see how the use of the optimized expansion may affect the determination of the alpha_s and the dimension six condensates from the experimental data.Comment: 6 pages in LateX, 4 PostScript figures embedded in text, uses espcrc2.sty (included), to appear in the Proceedings of the Fourth International Workshop on Tau Lepton Physics, 16-19 September 1996, Estes Park, Colorado, U.S.