In this we briefly review the discussions on accretion dynamics, the standard scenario and the ones including the effects of electromagnetic fields. The emphasis throughout is to show the relevance of general relativistic formalism in discussing the dynamics of magnetofluid around compact objects.

The existence of finite discontinuities in the energy eigenvalue spectra of certain multiterm potentials when their coupling parameters attain suitably chosen limiting values has been reported in the literature. We show that such discontinuities are also characteristic of such well-known systems as generalized anharmonic oscillators and the doubly anharmonic oscillator in one dimension. The present study strengthens the general conjecture that eigenvalue spectra are likely to display discontinuities in situations where a potential undergoes an abrupt change in shape with smooth variation of its coupling parameters.

We discuss the classical mechanics of relativistic systems with direct interaction. We show that various desiderata can all be accommodated in the single time approach by restricting the observables to the gauge invariant variables. We show how such observables can be constructed in general. We explicitly construct position observables in a general system and show that they lead to separable, invariant world lines. Nonsuperluminality is explicitly demonstrated for two body systems interacting via central forces of semibounded magnitude provided they ensure timelike canonical momenta. For two particles, our results reproduce the usual solution in covariant equal-time gauge.

White holes (relativistic anticollapsing objects) are considered both in the five-dimensional Kaluza-Klein theory and in the many-dimensional representation of extended space-time manifolds with horizons within the framework of general relativity. In the last model white holes (e.g. Kerr-Newman) appear as anticollapsing from extra (additional) dimensions. These dimensions are connected with the global structure of space-time manifolds.

We show that the motion of a Dirac electron in a time dependent electromagnetic field can be considered as a motion in a dielectric medium with time dependent dielectric function. We find that this electromagnetic case is analogous to the description in Robertson-Walker (RW) space-time. We solve the Dirac equation is such a simulated space-time.

In some simple quantum mechanical systems, the degeneracy of typical energy levels grows as a power of the energy or size. We ask whether, after dividing out this average growth, there is a well defined probability distribution of scaled degeneracies in the limit of large size or energy. The answer is yes, for a free particle in a sphere or cube. For the sphere, the distribution of scaled degeneracies is shown to follow a circular law. For the cube, a numerical study shows that the distribution rises linearly for low values of the scaled degeneracy and decays exponentially for large values.

We construct the algebra of the creation and destruction operators for spin 1/2 particles obeying a new exclusion principle which is “more exclusive” than Pauli’s exclusion principle: an orbital state shall not contain more than one particle, whether spin up or spin down. The consequences of this algebra are studied and applications to the Hubbard model in condensed matter physics are indicated.

Confined-gluon-exchange among relativistically confined quark clusters is used to obtain singlet S and P wave N-N scattering phase-shifts. A good agreement is obtained with the experimental results.

A three-body formalism for deuteron stripping reactions has been developed. The equations of Altet al (1967) (AGS) for the three particle system (target A, n, p) are reduced to a set of coupled one-dimensional integral equations with the use of (i) angular momentum basis for representation and (ii) separable approximation for the two bodyt-matrices (which delineate the interactions between the particle pairs). The on-shell solutions of this set of integral equations are then related to the cross sections of the rearrangement processes. The inputs in this calculation, viz., the separable interactions between the particle pairs in the respective channels are simply constructed from the respective two body bound state in accordance with the bound state approximation (BSA) conforming to the ‘unitarity’ requirement. Using this formalism preliminary calculations for the (d, p) and (d, n) reaction cross sections on¹⁶O have been carried out and they seem to have considerable semblance with the observed cross sections.