Browsing by Author "Tiwari, S.C."
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Publication Dirac representation of the SO(3,2) group and the Landau problem(Pleiades Publishing, 2023) Tiwari, S.C.Abstract: By systematically studying the infinite degeneracy and constants of motion in the Landau problem, we obtain a central extension of the Euclidean group in two dimension as a dynamical symmetry group, and Sp(2,4) as the spectrum generating group, irrespective of the choice of the gauge. The method of group contraction plays an important role. Dirac�s remarkable representation of the SO(3,2) group and the isomorphism of this group with Sp(4,R)are revisited. New insights are gained into the meaning of a two-oscillator system in the Dirac representation. It is argued that because even the two-dimensional isotropic oscillator with the SU(2) dynamical symmetry group does not arise in the Landau problem, the relevance or applicability of the SO(3,2) group is invalidated. A modified Landau�Zeeman model is discussed in which the SO(3,2) group isomorphic to Sp(4,R)can arise naturally. � 2023, Pleiades Publishing, Ltd.Publication New approach to unimodular relativity(Institute of Physics, 2023) Tiwari, S.C.A thorough study and analysis on the conceptual foundations of unimodular gravity shows that this theory is essentially general relativity disguised as unimodular relativity in the literature. The main reason for this dilemma is accepting the Einsteinian paradigm: general relativistic framework, covariant divergence law for matter energy-momentum tensor, and cosmological constant as an integration constant, but introducing the artefact of unimodular description absent in Einstein�s work. A new approach is proposed in this paper in which pure unimodular relativity is defined in terms of equi-projective geodesics with the fundamental metric tensor having determinant unity and the geometric tensors constructed from them. Modification of covariant divergence law for the matter energy-momentum tensor is shown to have two new consequences. In the conventional unimodular gravity an effective cosmological term comprising of two variable scalar fields, namely, the unimodular geometric ambiguity and unimodular matter energy ambiguity, is proposed. A radical departure on the cosmological constant problem is possible assuming differing evolution of the two scalars: the Einstein equations emerge when the two ambiguities cancel each other. Secondly, in the case of pure unimodular relativity the gravitational field equations are proposed consistent with the unimodular space-time structure. � 2023 IOP Publishing Ltd.Publication Schroedinger equation, spin and topology(Birkhauser, 2023) Tiwari, S.C.The presence of imaginary unit i at a fundamental level in the Schroedinger wave equation has led to the mysterious interpretation of quantum theory. New interpretation of the Schroedinger wave equation transforming it to two coupled wave equations that can be written in real spinor form is proposed. Spin angular momentum for free particle is derived based on this formalism. The proposition that spin is an emergent property in stochastic electrodynamics is critically examined in this context. It is shown that the geometric phase for Z2 vortex gives a new insight on the nature of spin: pure gauge field of geometric origin carries spin-half that has topological origin. The geometric interpretation of Pauli algebra such that the commutators signify 2D directed area introduces topological aspect in the Pauli algebra. It is argued that topological origin of spin implies that it is the spin that gives the particle nature to the electron. A possible line of approach suggested for addressing fundamental questions in quantum theory is to incorporate topological aspect for spin in the stochastic approach. Possible alternative paradigm for unification is also suggested. � 2023, The Author(s) under exclusive license to Chapman University.Publication Symmetry of Dirac two-oscillator system, gauge-invariance, and Landau problem(World Scientific, 2023) Tiwari, S.C.Role of gauge symmetry in the proton spin problem has intricate and unresolved aspects. One of the interesting approaches to gain physical insights is to explore the Landau problem in this context. A detailed study using the group theoretic method to understand the Landau problem establishes the significance of the gauge transformation intimately related with the space translation symmetry. An important implication of this result is that the E(2)-like Wigner's little group for massless particles could throw more light on the question of gauge symmetry in QED and QCD. A generalized Landau-Zeeman Hamiltonian is proposed in which Dirac two-oscillator system and the symmetry of the group SO(3,2) become important. It is argued that nontrivial topology of pure gauge field holds promise to resolve the unsettled questions. � 2023 World Scientific Publishing Company.Publication Weyl geometry, topology of space-time and reality of electromagnetic potentials, and new perspective on particle physics(IOP Publishing Ltd, 2021) Tiwari, S.C.Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and fluctuating metric in 3D space with time as a measure of spatial relations are discussed to propose a statistical interpretation of Maxwell field equations. It is argued that physical geometry is an approximation to mathematical geometry, and 4D relativistic spacetime is essentially 3D space with changing spatial relations. The present work is suggested to have radical new outlook on elementary particle physics. � 2020 IOP Publishing Ltd.
