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G. C. Joshi

Publications and source records attributed to G. C. Joshi.

52 records · Page 3Linked to original sources
arXiv1995

A q-Lorentz Algebra From q-Deformed Harmonic Oscillators

A mapping between the operators of the bosonic oscillator and the Lorentz rotation and boost generators is presented. The analog of this map in the $q$-deformed regime is then applied to $q$-deformed bosonic oscillators to generate a $q$-deformed Lorentz algebra, via an inverse of the standard chiral decomposition. A fundamental representation, and the co-algebra structure, are given, and the generators are reformulated into $q$-deformed rotations and boosts. Finally, a relation between the $q$-boson operators and a basis of $q$-deformed Minkowski coordinates is noted.

q-alg↗
arXiv1995

A Non-Associative Deformation of Yang-Mills Gauge Theory

An ansatz is presented for a possible non-associative deformation of the standard Yang-Mills type gauge theories. An explicit algebraic structure for the deformed gauge symmetry is put forward and the resulting gauge theory developed. The non-associative deformation is constructed in such a way that an apparently associative Lie algebraic structure is retained modulo a closure problem for the generators. It is this failure to close which leads to new physics in the model as manifest in the gauge field kinetic term in the resulting Lagrangian. A possible connection between this model and quantum group gauge theories is also investigated.

hep-th↗
arXiv1995

Magnetic Monopole and the Finite Photon Mass: Are They Compatible?

We analyze the role played by the gauge invariance for the existence of Dirac monopole. To this end, we consider the electrodynamics with massive photon and ask if the magnetic charge can be introduced there. We show that the derivation of the Dirac quantization condition based on the angular momentum algebra cannot be generalized to the case of massive electrodynamics. Possible implications of this result are briefly discussed.

hep-ph↗
arXiv1995

BRS Symmetry in Connes' Non-commutative Geometry

We extend the BRS and anti-BRS symmetry to the two point space of Connes' non-commutative model building scheme. The constraint relations are derived and the quantum Lagrangian constructed. We find that the quantum Lagrangian can be written as a functional of the curvature for symmetric gauges with the BRS, anti-BRS auxiliary field finding a geometrical interepretation as the extension of the Higgs scalar.

hep-ph↗
arXiv1995

An Octonionic Gauge Theory

The nonassociativity of the octonion algebra necessitates a bimodule representation, in which each element is represented by a left and a right multiplier. This representation can then be used to generate gauge transformations for the purpose of constructing a field theory symmetric under a gauged octonion algebra, the nonassociativity of which appears as a failure of the representation to close, and hence produces new interactions in the gauge field kinetic term of the symmetric Lagrangian.

hep-th↗
arXiv1994

Non-Zero Electric Charge of the Neutrino and the Solar Neutrino Problem

It has recently been shown that the neutrino can have non-zero electric charge in a number of gauge theories, including the Minimal Standard Model. Assuming non-zero neutrino charge, we develop a new approach to the solar neutrino problem. The key idea is that the charged neutrinos will be deflected by the Lorentz force while they are crossing the solar magnetic fields. Such a deflection will result in the anisotropy of the solar neutrino flux. Because of this anisotropy, the solar neutrino flux registered on earth can be reduced as compared to the Standard Solar Model prediction. The mechanism is purely classical and does not require neutrino oscillations, spin-flip or neutrino decay. We discuss qualitatively the consequences of our scenario for present and future solar neutrino experiments as well as differences between our mechanism and other proposed solutions.

hep-ph↗
arXiv1994

Quantum Dynamics in Regions of Quaternionic Curvature

The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by inhomogeneous Dirac and Schrödinger equations. Mixing of hyper-complex components of wavefunctions occurs through their interaction with potentials dissipative into the extra quaternionic degrees of freedom. An interferometric experiment is analysed to illustrate the effect.

hep-th↗
arXiv1994

Multi-particle Correlations in Quaternionic Quantum Systems

We investigate the outcomes of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multi-particle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements of particle spin components.

hep-th↗
arXiv1994

The Charged Neutrino: A New Approach to the Solar Neutrino Problem

We have considered the effect of the reduction of the solar neutrino flux on earth due to the deflection of the charged neutrino by the magnetic field of the solar convective zone. The antisymmetry of this magnetic field about the plane of the solar equator induces the anisotropy of the solar neutrino flux thus creating the deficit of the neutrino flux on the earth. The deficit has been estimated in terms of solar and neutrino parameters and the condition of a 50 \% deficit has been obtained: $Q_ν gradH \agt 10^{-18} eG/cm$ where $Q_ν$ is the neutrino electric charge, $gradH$ is the gradient of the solar toroidal magnetic field, e is the electron charge. Some attractive experimental consequences of this scenario are qualitatively discussed.

hep-ph↗
arXiv1993

A Partial Unification Model in Non-commutative Geometry

We consider the construction of $SU(2)_{L}\otimes SU(2)_{R}\otimes SU(4)$ partial unification models as an example of phenomenologically acceptable unification models in the absence of supersymmetry in non-commutative geometry. We exploit the Chamseddine, Felder and Fröhlich generalization of the Connes and Lott model building prescription. By introducing a bi-module structure and appropriate permutation symmetries we construct a model with triplet Higgs fields in the $SU(2)$ sectors and spontaneous breaking of $SU(4)$.

hep-ph↗
arXiv1992

A Self-Consistent Formulation of Quantum Field Theory on $S_{4}$

Recent developments in quantum gravity suggest that wormholes may influence the observed values of the constants of nature. The Euclidean formulation of quantum gravity predicts that wormholes induce a probability distribution in the space of possible fundamental constants. This distribution may computed by evaluating the functional integral about the stationary points of the action. In particular, the effective action on a large spherical space may lead to the vanishing of the cosmological constant and possibly determine the values of other constants of nature. The ability to perform calculations involving interacting quantum fields, particularly non-Abelian models, on a four-sphere is vital if one is to investigate this possibility. In this paper we present a self-consistent formulation of field theory on a four-sphere using the angular momentum space representation of $SO(5)$. We give a review of field theory on a sphere and then show how a matrix element prescription in angular momentum space overcomes previous limitations in calculational techniques. The standard one-loop graphs of QED are given as examples.

hep-th↗
arXiv1992

A Non-Commutative Geometric Approach to Left-Right Symmetric Weak Interactions

By combining the generalized exterior algebra of forms over a noncommutative algebra with the gauging of discrete directions and the associated Higgs fields, we consider the construction of the bosonic sector of left-right symmetric models of the form $SU(2)_{L}\otimes SU(2)_{R}\otimes U(1)$. We see that within this formalism maximal use can be made of the gauge connection associated with the non-commutative graded algebra.

hep-ph↗
arXiv1992

Gauging octonion algebra

By consireding representation theory for non-associative algebras we construct the fundamental and adjoint representations of the octonion algebra. We then show how these representations by associative matrices allow a consistent octonionic gauge theory to be realised. We find that non-associativity implies the existence of new terms in the transformation laws of fields and the kinetic term of an octonionic Lagrangian.

hep-th↗