• Virendra Singh

      Articles written in Pramana – Journal of Physics

    • Theψ-particles in an SU4 scheme with anomalous currents

      T Das P P Divakaran L K Pandit Virendra Singh

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      The recently discovered narrow peaks (theψ-particles) in e+e system at 3.105 and 3.695 GeV are interpreted as hadrons in a broken SU4 symmetry scheme. A new additional additive quantum number, parachargeZ, is combined with the usual SU3 quantum numbers in the group SU4. Theψ (3.1) is assigned to a near ideally mixed151 multiplet of vector mesons (containing theρ) as theI=Y=0, charge conjugationC=−combination ofZ=±1.members. Theψ (3.7) is assigned correspondingly to another mixed151 multiplet containing theρ′ (1600). The hadronic electromagnetic interactions are modified by the addition of (non-minimal) anomalous pieces that can changeZ. The decays of theψ-particles are discussed. New enlarged SU4 multiplets of other hadrons are proposed. Tests of our scheme are put forward. The most crucial test will be the observation of two rather broad resonances in e+ e collisions with masses around 4.2 GeV and 5.1 GeV. Another prediction is the presence of energetic photons in the decays of theψ-particles. Important results concerning the recently observed phenomena in the process e+e→hadrons follow in this scheme.

    • Universal theory of weak interactions in the paracharge scheme and quark-lepton analogy

      T Das P P Divakaran L K Pandit Virendra Singh

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      A universal theory of weak interaction is constructed by exploiting an analogy inherent between the four leptons and the four quarks of the paracharge scheme proposed recently to deal with theψ-particles. The leptons (νe,νμ,eL,μL) are assigned to the representation (1/2, 1/2) and the quarks (p, nW)L and (χ,λW)L to the representations (1/2, 0) and (0, 1/2), respectively, of the groupO4 (L stands for the left-handed projections and W for the Cabibbo rotated orthogonal combinations ofn andλ). Universality is ensured by embedding the above (weak)O4 into thesimple groupO5 and gauging the latter. In the final effective weak interaction, besides the conventionalV-A charged-current part, a (V-A)neutral current interaction (consistent with the present data) is naturally present. The neutral current has a$$\bar \nu _\mu \nu _\mu $$ term but no$$\bar \nu _e \nu _e $$ term, thus providing a crucial test of the theory.

    • Paracharge phenomenology: systematics of the new hadrons

      T Das P P Divakaran L K Pandit Virendra Singh

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      A systematic semiquantitative account of all aspects of the strong and electromagnetic interactions of all the newly discovered hadronic states (theψ’s, theχ’s, etc.) is presented within the framework of the paracharge scheme. Extensions of ideas familiar from the SU3 classification scheme to SU4 are shown to provide an understanding of the new states seen in the decays ofψ (3.1) andψ′ (3.7), including their masses and gross decay characteristics. The decays ofψ (3.1) andψ′ (3.7) themselves are studied in some detail. Since these are of electromagnetic origin in the scheme, their electromagnetic mixing with the resonance at 4.15 GeV (theP-state of the scheme) is important. Once this is taken into account, the resulting picture is in excellent agreement with available data.

    • Soliton and boundary condition induced fractional fermion number

      S M Roy Virendra Singh

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      We show that for a fermion in a bounded background potential in a finite box, eigenvalues of the total charge are independent of whether the potential is solitonic and depend only on the boundary condition: half-odd integral or integral for charge conjugation (C) invariant boundary conditions and an arbitrary fraction forC non-invariant boundary conditions. Fractional fermion numbers for infinite space Jackiw-Rebbi and Goldstone-Wilczek Hamiltonians are reproduced in finite space by using boundary conditions different from the periodic ones of Rajaraman and Bell.

    • On the Feigenbaum-Cvitanović equation in the theory of chaotic behaviour

      Virendra Singh

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      We propose an analytic perturbative approach for the determination of the Feigenbaum-Cvitanović function and the universal parameterα occurring in the Feigenbaum scenario of period doubling for approach to chaotic behaviour. We apply the method to the caseZ=2 whereZ is the order of the unique local maximum of the nonlinear map. Our third order approximation givesα=2.5000 as compared to “exact” numerical valueα=2.5029 ... We also obtain a reasonably accurate value of the Feigenbaum-Cvitanović function.

    • Fractionally charged non-leaking dyons and fermions in a bag

      S M Roy Virendra Singh

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      We consider a fermion of chargee confined to a spherical bag with a Dirac monopole of strengthg at its centre. We find that the boundary conditions making the lowest angular momentum hamiltonian self-adjoint are characterized by a unitary matrixU, and the corresponding vacuum charge has a fractional part 2|eg|α/π where detU = -exp (2). Boundary conditions for conservation of helicity,CP, CT andPT are displayed. We demonstrate the possibility of a fractionally charged dyon whose interaction with a fermion conserves helicity. We also show thatthe simultaneous validity of helicity, CP, CT and PT requires integer vacuum charge.

    • Conformally invariant field theories in two dimensions and corresponding statistical mechanical models

      Virendra Singh B Sriram Shastry

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      Belavin, Zamlodochikov and Polyakov have recently proposed a class of conformally invariant field theories in two dimension with exactly determined rational critical indices. We establish a tentative identification of a subset of these theories in terms of the O(n) model and theq-state Potts model in 2-dimensions for appropriaten andq.

    • Bosonic string theories with new boundary conditions

      S M Roy Virendra Singh

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      We show that the classical Nambu-Goto string inD dimensions admits Poincaré invariance ind dimensions (dD) if (i)d − 2 of the transverse co-ordinatesxi are periodic and the rest quasi-periodic involving a real orthogonal matrix with (D − d) (D − d − 1)/2 free parameters, or if (ii)d − 2 ofxi obey Neumann and the rest obey a boundary condition involvingN free parameters, whereN=(D − d)2/2 ifD − d is even, andN=[(D − d)2 − 1]/2 ifD − d is odd.

    • Causal quantum mechanics

      Virendra Singh

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      We discuss the split between system and measuring apparatus, i.e. non-unitary nature, of the conventional quantum mechanics to motivate a causal unitary description of nature. We then describe causal quantum mechanics of de Broglie and Bohm. We conclude by presenting a version of recently proposed causal quantum mechanics which treats position and momentum variable symmetrically.

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