Modern Physics Letters A

The class of pseudo-differential operators Lie algebra on the quantum plane is introduced. The embedding of certain infinite-dimensional Lie algebras which occur in the physics literature in is discussed as well as the correspondence between and as k→+∞ is examined.

We investigate the effect of a constant threshold correction to a general non-extreme, static, spherically symmetric, electrically charged black hole solution of the dilatonic Einstein–Maxwell Lagrangian, with an arbitrary coupling β between the electromagnetic tensor and the dilaton field. For a small β, an exact analytical solution is obtained. For an arbitrary β, a close form solution, up to first-order in the constant threshold correction, of the metric and the dilaton are presented. In the extremal limit, the close form solution is reduced to an exact analytical form.

We study the zeros in the complex plane of the partition function for the Ising model coupled to 2D quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We compute the zeros by using the exact solution coming from a two-matrix model and by Monte–Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional curves in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of the singularities near the critical point. Despite the small size of the systems studied, we can obtain a reasonable estimate of the (known) critical exponents.

The Kähler formulation of five-dimensional Einstein–Kalb–Ramond (EKR) theory admitting two commuting Killing vectors is presented. Three different Kramer–Neugebauer-like maps are established for the two-dimensional case. A class of solutions constructed on the basis of the double Ernst one is obtained. It is shown that the double Kerr solution corresponds to a EKR dipole configuration with horizon.

We present a slight generalization of the notion of completely integrable systems such that they can be integrated by quadratures. We use this generalization to integrate dynamical systems on double Lie groups.

We utilize Coleman's theorem and show that quantum chromodynamics based on asymptotic freedom and confinement must have chiral symmetry realized as a spontaneously broken symmetry.

The exactly and quasi-exactly solvable problems for spin one-half in one dimension on the basis of a hidden dynamical symmetry algebra of Hamiltonian are discussed. We take the supergroup, OSP(2|1), as such a symmetry. A number of exactly solvable examples are considered and their spectrum are evaluated explicitly. Also, a class of quasi-exactly solvable problems on the basis of such a symmetry has been obtained.