Modern Physics Letters A

Progress in the understanding of non-leptonic weak decays with its intricate interplay of weak and strong interactions is reported. At low energies the dynamics of these processes is strongly influenced by non-perturbative correlations between two quarks in Lorentz scalar color antitriplet states. A coherent description of kaon and hyperon decays emerges resolving so far mysterious puzzles.

We have discussed classical and quantum cosmological phenomena for anisotropic Kantowski–Sachs model. The classical Lorentzian field equations are reduced to an autonomous system and are analyzed near critical point. The minisuperspace path-integral reduces to a single ordinary integration over the lapse, and we study this integral by lapse method. We find that the integral has an infinite number of saddle points, each one has identical contribution to the integral. Also matter-gravity wave function is considered for this metric.

We expand the earlier invented method of massive Feynman diagrams calculation, namely, the differential equations method, to N-point diagrams. We obtain a simple algorithm which allows us to reduce the vertex-type diagram to the propagator-type diagrams, the box-type diagram to the vertex-type diagrams and, in general, the N-point diagram to the (N-1)-point diagrams. We show that this method provides a simple procedure of evaluating the result without D-space integrals (for the dimensional regularization) calculation.

The Penner-like model of real symmetric matrices with logarithmic potential is solved. We suggest that the double-scaling limit free energy of this model can be interpreted as a generating function for virtual Euler characteristics of moduli space of non-orientable surfaces. The asymptotic expansion in the double-scaling limit is found to coincide with the R=1/4 Gross–Klebanov c=1 model. We also found some amusing correspondences between this model and exactly solvable six-vertex model on square lattice.

We determine the path-integral for particles with fractional spin and statistics in the adiabatic limit, and we discuss the identification of the spin-changing term with a Berry phase. We show that the standard proof that the Laughlin wave function describes excitations with fractional statistics holds only on the basis of a tacit assumption of questionable validity.

A class of Hamiltonians with parasupersymmetry of order p is presented and algebraically characterized. Conformal invariant cases are discussed.

We show that the two-dimensional chiral Abelian Higgs model, though anomalous, can be consistently quantized provided that gauge degrees of freedom are adequately taken into account. In this way, the anomaly is canceled by a Wess–Zumino term and as a result, instanton contributions are eliminated from the partition function.

We study the classical version of supersymmetric W-algebras. Using the second Gelfand–Dickey Hamiltonian structure we work out in detail W₂ and W₃-algebras.

The two-dimensional quantum gravity with general action consisting of local and non-local parts is investigated. It is shown that in the light-cone gauge there exists a symmetry which leads naturally to the SL(2,ℝ) Kac–Moody current algebra. The structure of the renormalization is discussed.