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A pure Yang-Mills theory extended by addition of a quartic term is considered in order to study the transition from the quantum tunneling regime to that of classical, i.e. thermal, behaviour. The periodic field confiurations are found, which interpolate between the vacuum and sphaleron field configurations. It is shown by explicit calculation that only smooth second order transitions occur for all permissible values of the parameter A introduced with the quartic term. The theory is one of the rare cases which canbe handled analytically.

Abstract: The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A criterion is derived for the occurrence of a first-order type transition, and the related phase diagram for scalar and vector fields is obtained. For scalar fields both the first and second order transitions can occur depending on the shape of the potential barrier. For a vector field, here that of an O (3) nonlinear o-model, the transition is seen to be only of the first order. PACS numbers: 11.15.Kc, 03.65Sq, 05.70.Fh, 98.80.Cq

Abstract: The self-duality of chiral p-forms was originally investigated by Pasti, Sorokin and Tonin in a manifestly Lorentz covariant action with non-polynomial auxiliary fields. The investigation was then extended to other chiral p-form actions. In this paper we point out that the self-duality appears in a wider context of theoretical models that relate to chiral p-forms. We demonstrate this by considering the interacting model of Floreanini- Jackiw chiral bosons and gauge fields, the generalized chiral Schwinger model (GCSM) and the latter's gauge invariant formulation, and discover that the self-duality of the GCSM corresponds to the vector and axial vector current duality.

Abstract: It has recently been shown that the equation of motion of a massless scalar field in the background of some specific p branes can be reduced to a modified Mathieu equation. In the following the absorption rate of the scalar by a D3 brane in ten dimensions is calculated in terms of modified Mathieu functions of the first kind, using standard Mathieu coefficients. The relation of the latter to Dougall coefficients (used by others) is investigated. The S-matrix obtained in terms of modified Mathieu functions of the first kind is easily evaluated if known rapidly convergent low energy expansions of these in terms of products of Bessel functions are used. Leading order terms, including the interesting logarithmic contributions, can be obtained analytically.

Abstract: The duality symmetries of various chiral boson actions are investigated using D = 2 and D = 6 space-time dimensions as examples. These actions involve the Siegel, Floreanini-Jackiw, Srivastava and Pasti-Sorokin-Tonin formulations. We discover that the Siegel, Floreanini-Jackiw and Pasti-Sorokin-Tonin actions have self-duality with respect to a common anti-dualization of chiral boson fields in D = 2 and D = 6 dimensions, respectively, while the Srivastava action is self-dual with respect to a generalized dualization of chiral boson fields. Moreover, the action of the Floreanini-Jackiw chiral bosons interacting with gauge fields in D = 2 dimensions also has self-duality but with respect to a generalized anti-dualization of chiral boson fields.

We consider a (2 + 1)-dimensional mechanical system with the Lagrangian linear in the torsion of a light-like curve. We give Hamiltonian formulation of this system and show that its mass and spin spectra are defined by one-dimensional nonrelativistic mechanics with a cubic potential. Consequently, this system possesses the properties typical of resonance-like particles.

Starting from the Hamiltonian operator of the noncompensated two-sublattice model of a small antiferromagnetic particle, we derive the e effective Lagrangian of a biaxial antiferromagnetic particle in an external magnetic field with the help of spin-coherent-state path integrals. Two unequal level-shifts induced by tunneling through two types of barriers are obtained using the instanton method. The energy spectrum is found from Bloch theory regarding the periodic potential as a superlattice. The external magnetic field indeed removes Kramers' degeneracy, however a new quenching of the energy splitting depending on the applied magnetic field is observed for both integer and half-integer spins due to the quantum interference between transitions through two types of barriers.

Abstract: A Born-Infeld theory describing a D2-brane coupled to a 4-form RR field strength is considered, and the general solutions of the static and Euclidean time equations are derived and discussed. The period of the bounce solutions is shown to allow a consideration of tunneling and quantum-classical transitions in the sphaleron region. The order of such transitions, depending on the strength of the RR field strength, is determined. A criterion is then derived to confirm these findings.

Abstract: The functional relation between interquark potential and interquark distance is explicitly derived by considering the Nambu-Goto action in the AdS5 X S 5 background. It is also shown that a similar relation holds in a general background. The implications of this relation for confinement are briefly discussed.

A new method is used to investigate the tunneling between two weakly-linked Bose-Einstein con- densates confined in double-well potential traps. The nonlinear interaction between the atoms in each well contributes to a finite chemical potential, which, with consideration of periodic instantons, leads to a remarkably high tunneling frequency. This result can be used to interpret the newly found Macroscopic Quantum Self Trapping (MQST) effect. Also a new kind of first-order crossover between different regions is predicted.