This article contains a brief account of Kaluza-Klein theory and its applications in cosmology from the very beginning.

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular groupSU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real linear vector space, are developed in anSU(3) covariant manner. Thef andd symbols ofSU(3) lead to two ways of ‘multiplying’ two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization ofSU(3) is developed as a generalization of that forSU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Using scaled harmonic oscillator wave functions, accurate energy levels of the sextic-double-well oscillatorV(X)=X⁶−3X⁴ are calculated through modified Hill determinant method. Present groundstate energy remains the same as reported by Tater and Turbiner,J. Phys.A26, 697 (1993).

We study a doubly resonant optical parametric oscillator where the pump can feed two pairs of signal-idler modes. We assume the presence of gain at the pump frequency. We investigate the various oscillation states of interest, namely, when only the first pair oscillates with the other pair having null amplitudes and vice versa. We demonstrate the exchange of dynamics between the mode pairs when the relevant parameters of the cavity, namely, the phase mismatch factors or the decay rates switch because of fluctuations. The exchange of dynamics is shown to be independent of the nature of dynamics, i.e. independent of whether the motion isn-periodic or chaotic. We also investigate the case where both the pairs can exhibit chaotic dynamics though these states are difficult to realize because of fluctuations.

We have studied the effect of environment induced pure decoherence on the generalized Jaynes-Cummings model (JCM). This generalized JCM is introduced to take into account both atom-field interaction and a class of spin-orbit interactions in the same framework. For generalized JCM with atom-field interaction, it is shown that along with the suppression of the oscillatory behaviour of the atomic and field variables, in the steady state, atomic energy is transferred to the field or vice versa through the dressed state coherence depending on the initial condition of the atom-field system and the model under consideration. It is also shown that initial Poissonian field acquires a sub-Poissonian character in the steady state and thus all the nonclassical properties are not erased by the decoherence in JCM. An interesting effect of this decoherence mechanism is that it affects the population and coherence properties of the individual subsystem in a different way. As an example of generalized JCM with spin-orbit interaction, the dynamics of spin of the hydrogen atom in a magnetic field is studied to show the effect of decoherence.

We prove the theorem: A necessary and sufficient condition for a spacetime to represent an isothermal fluid sphere (linear equation of state with density falling off as inverse square of the curvature radius) without boundary is that it is conformal to a spacetime of zero gravitational mass (‘minimally’ curved).

A detailed numerical analysis of the boundary value problem resulting from the most general Skyrme type lagrangian containing up to quartic terms in field gradients is presented. The additional parameters in the lagrangian can be related to pion-pion scattering lengths. It is found that solutions to the boundary value problem does not exist for all values of the parameters and in particular, for the values predicted from pion-pion scattering data. Physical quantities of the nucleon are calculated for the highest possible values of the parameters admitting a solution and are compared with the corresponding values for the Skyrme model and experimental values.

The theoretical properties of a composite chiral-plasma medium are developed. By using the reaction theorem for a magnetized chiroplasma, we obtain the proof of nonreciprocity based upon the constitutive relationships between electromagnetic vectorsE, B, H, D. Using the Maxwell’s equations and the proposed constitutive relations for a chiral-plasma medium, we derive the vectorsE andH and from these equations, dispersion relations andE-field polarizations are based. The obtained results for waves propagating parallel to the external magnetic field in a cold magnetized chiro-plasma are compared with typical results obtained for a cold plasma. For circulary polarized waves, a new mode conversion is founded with the chiral effect. The chiral rotation is obtained and compared with the Faraday rotation. For waves propagating across the magnetic field, we found a shift of the cut-offs of ordinary and extraordinary waves. On the lower branch of the extraordinary wave mode there is no bands of forbidden frequencies and the reflection point vanishes when the chiral parameter increases.

Viscosity of neutron stars has been a continuing area of research for many years now. Recently interest in this field has revived because of the possibility of URCA processes in neutron stars. In this paper we report calculation of the bulk viscosity of neutron stars from these processes. For this purpose we have used theβ-decay rates which were calculated without making the usual approximations of neglecting the neutrino momentum and using the nuclear mean field theory for the description of interacting nuclear matter. Also we have not restricted our calculation to the linear regime which corresponds to the assumption that fluctuations in the chemical potential away fromβ-equilibrium remain small: Δμ/kT ≪ 1. We find that for large amplitude fluctuations, where the linear approximation is not valid, bulk viscosity increases by many orders of magnitude. Also, as against strange matter stars, where the viscosity first increases with increasing temperature and then starts decreasing beyond 0.1 MeV, we find that the viscosity increases uniformly with temperature at least up to 2MeV. We discuss the implications of these results for the stability of neutron stars.