Articles written in Pramana – Journal of Physics
Volume 36 Issue 5 May 1991 pp 497-510 Research Articles
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.
Volume 37 Issue 1 July 1991 pp 21-38
We consider the quantum mechanics of directly interacting relativistic particles of spin-zero and spin-half. We introduce a scalar product in the vector space of physical states which is finite, positive definite and relativistically invariant and keeps orthogonal eigenstates of total four momentum belonging to different eigenvalues. This allows us to show that the vector space of physical states is, in fact, a Hilbert space. The case of two particles is explicitly considered and the Cauchy problem of physical wave function illustrated. The problem of a spin-1/2 particle interacting with a spin-zero particle is considered and a new equation is proposed for two spin-1/2 particles interacting via the most general form of interaction possible. The restrictions due to Hermiticity, space inversion and time reversal invariance are also considered.
Volume 39 Issue 3 September 1992 pp 253-264 Research Articles
We discuss the classical mechanics of relativistic systems containing any number of particles with direct interaction. We continue our previous approach of restricting the observables to gauge invariant variables. As a preliminary we show how to construct
Volume 51 Issue 6 December 1998 pp 693-698
It is shown by arguments based on the uncertainty principle that large fluctuations of the metric occur near the event horizon of a Schwarzschild black hole on a scale much larger than Planck length. The width of the transition layer about the event horizon and the associated surface tension are also estimated.
Volume 51 Issue 6 December 1998 pp 699-710
We consider the problem of joining of metrics when these are not continuous across the joining (hyper-) surface. We confine ourselves to static, spherically symmetric metrics which join without requiring gradients of a δ-function in the energy-momentum tensor. It is found that a surface tension is always associated in cases where the metrics are discontinuous. In some cases, the joined metrics satisfy Einstein equations (in the sense of distributions) while, in others, the surface tension associated with the limiting discontinuous metric depends on the interpolating functions used to produce it suggesting sensitivity to short distance effects beyond general relativity.
Volume 96, 2022
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