International Journal of Modern Physics A

We briefly review two aspects of string cosmology: (1) the presence of chaos in the generic cosmological solutions of the tree-level low-energy effective actions coming out of string theory, and (2) the remarkable link between the latter chaos and the Weyl groups of some hyperbolic Kac–Moody algebras.

We investigate the dynamics of a first order transition when the order parameter field undergoes resonant oscillations, driven by a periodically varying parameter of the free energy. This parameter could be a background oscillating field as in models of pre-heating after inflation. In the context of condensed matter systems, it could be temperature T, or pressure, external electric/magnetic field etc. We show that with suitable driving frequency and amplitude, the system remains in a type of mixed phase, without ever completing transition to the stable phase, even when the oscillating parameter of the free energy remains below the corresponding critical value (for example, with oscillating temperature, T always remains below the critical temperature T_c). This phenomenon may have important implications. In cosmology, it will imply prolonged mixed phase in a first order transition due to coupling with background oscillating fields. In condensed matter systems, it will imply that using oscillating temperature (or, more appropriately, pressure waves) one may be able to sustain liquids in a mixed phase indefinitely at low temperatures, without making transition to the frozen phase.

We rewrite the Born–Infeld Lagrangian, which is originally given by the determinant of a 4×4 matrix composed of the metric tensor g and the field strength tensor F, using the determinant of a (4·2ⁿ)×(4·2ⁿ) matrix H_4·2ⁿ. If the elements of H_4·2ⁿ are given by the linear combination of g and F, it is found, based on the representation matrix for the multiplication operator of the Cayley–Dickson algebras, that H_4·2ⁿ is distinguished by a single parameter, where distinguished matrices are not similar matrices. We also give a reasonable condition to fix the parameter.

Some black hole-cosmic string models such as Reissner–Nordström, RN–de Sitter, Kerr–Newman and multi-black holes with cosmic string are given. Energy and angular momentum of a timelike particle in circular orbits in multi-black hole space–time are calculated. The geodesic equations for the timelike particles for the far region of the multi-black hole sources are calculated and small oscillations around the circular orbit obtained. It is seen that the particle's orbit precesses like the Lens–Thirring effect.

We introduce a ℤ₂-graded version of the nonlinear Schrödinger equation that includes one fermion and one boson at the same time. This equation is shown to possess a supersymmetry which proves to be itself part of a super-Yangian symmetry based on gl(1|1). The solution exhibits a super version form of the classical Rosales solution. Then, we second quantize these results, and give a Lax pair formulation (based on gl(2|1)) for the model.

We discuss realizations of the SL(2,R) current algebra in the hyperbolic basis using free scalar fields. It has been previously shown by Satoh how such a realization can be used to describe the principal continuous representations of SL(2,R). We extend this work by introducing another realization that corresponds to the principal discrete representations of SL(2,R). We show that in these realizations spectral flow can be interpreted as twisting of a free scalar field. Finally, we discuss how these realizations can be obtained from the BTZ Lagrangian.

We have extended the variational perturbative theory based on the background field method to include the optimized expansion of Okopinska and the post Gaussian effective potential of Stansu and Stevenson. This new method provides a much simpler way to compute the correction terms to the Gaussian effective action (or potential). We have also renormalized the effective potential in 3+1 dimensions by introducing appropriate counterterms in the Lagrangian.

We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3-geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the traditional dynamical equations obsolete. Quantization of the constraints in both the Dirac and ADM square root Hamiltonian approaches leads to the well known problems of time evolution. These problems of time are of both an interpretational and technical nature. In contrast, the geometrodynamic quantization procedure on the superspace of the true dynamical variables separates the issues of quantization from the enforcement of the constraints. The resulting theory takes into account states that are off-shell with respect to the constraints, and thus avoids the problems of time. We develop, for the first time, the geometrodynamic quantization formalism in a general setting and show that it retains all essential features previously illustrated in the context of homogeneous cosmologies.

We present an extension of the previous results¹ on the quantization of general gauge theories within the BRST–antiBRST invariant Lagrangian scheme in general coordinates. Namely, we generalize Ref. 1 to the case when the base manifold of fields and antifields is a supermanifold described in terms of both bosonic and fermionic coordinates.