Modern Physics Letters A

We consider the standard vector gauging of Lorentz group SO(3, 1) WZW model by its non-semisimple null Euclidean subgroup in two dimensions E(2). The resultant effective action of the theory is seen to describe a one-dimensional bosonic field in the presence of external charge that we interpret as a Liouville field. By gauging a boosted SO(3) subgroup, we find that in the limit of the large boost, the theory can be interpreted as an interacting Toda theory. We take also the generalized nonstandard bilinear form for SO(3, 1) and gauge both SO(3) and E(2) subgroups and discuss the resultant theories.

We describe the reduction from four to two dimensions of the SU(2) Donaldson–Witten theory and the dual twisted Seiberg–Witten theory, i.e. the Abelian topological field theory corresponding to the Seiberg–Witten monopole equations.

We study the general form of the equations for isotropic single-scalar, multi-scalar and dyonic p-branes in superstring theory and M-theory, and show that they can be cast into the form of Liouville, Toda (or Toda-like) equations. The general solutions describe non-extremal isotropic p-branes, reducing to the previously-known extremal solutions in limiting cases. In the non-extremal case, the dilatonic scalar fields are finite at the outer event horizon.

Recursion relations for orthogonal polynomials, arising in the study of one-matrix model of two-dimensional gravity, are shown to be equivalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro constraints. This is the case without the double scaling limit. A discrete time variable to the matrix model is introduced. The discrete time dependent partition functions are given by τ functions which satisfy the discrete Toda molecule equation. Further the relations between the matrix model and the discrete time Toda theory are discussed.

Using renormalization group methods, we calculate the derivative expansion of the effective Lagrangian for a covariantly constant gauge field in curved spacetime. Curvature affects the vacuum; in particular it could induce phase transitions between different vacua. We also consider the effect of quantum fluctuations of the metric, in the context of a renormalizable R² theory. In this case the critical curvature depends on the gravitational coupling constants.

Starting from the Pauli current we obtain the decomposition of the nonrelativistic local velocity in two parts: one parallel and the other orthogonal to the impulse. The former is recognized as the “classical” part, that is, the velocity of the center-of-mass, and the latter the “quantum” one, that is, the velocity of the motion in the center-of-mass frame (namely, the internal “spin motion” or zitterbewegung), Inserting the complete expression of the velocity into the kinetic energy term of the classical nonrelativistic (i.e. Newtonian) Lagrangian, we straightforwardly get the appearance of the so-called quantum potential associated, as it is known, to the Madelung fluid. In such a way, the quantum mechanical behavior of particles appears to be strictly correlated to the existence of spin and zitterbewegung.

A tensor representation of the gluon propagator is found within covariant gauges for a non-Abelian theory after symmetry breaking due to <A₀>≠0 and the exact equations which determine the dispersion laws of plasma excitations are explicitly obtained. In the high temperature region and fixing the Feynman gauge we solved these equations to find the damping of the plasma oscillations and the shifting of their frequency. The phase transition of a gauge symmetry restoration is estimated to be α_c(T)≈4/3.

The neutron electric dipole moment (EDM) is investigated in detail. We assume a phenomenologically successful seesaw-type quark mass matrix. If the neutron EDM is observed at slightly below the present experimental bound (10^–26–10^–25e·cm), we can conclude that there must exist a vector-like quark a little heavier than the heavier neutral Higgs boson, or both of them have equal masses around 1 TeV.