Propagation of electromagnetic waves in a random medium and nonzero rest mass of the photon

The propagation of electromagnetic waves is studied in a Maxwell vacuum with 0. The photon loses energy during its propagation through this vacuum. This dissipation of energy is related to the fluctuation of the refractive index of the underlying vacuum. There exists a bounded and unique solution in the limit 0 in the asymptotic region. The geometric structure of the background space-time is Finslerian in nature.     

Reduction of Poisson algebras at nonzero momentum values

A reduction of a Poisson manifold using the ideal I(J) generated by the momentum map was introduced by Śniatycki and Weinstein (1983). This reduction has been extended to nonzero momentum values μ by two methods: by shifting to zero momentum on a larger space, the product with the coadjoint orbit; and by the method of Wilbour and Kimura (1991, 1993) using the modified ideal I(J − μ). It is shown that these two methods produce isomorphic reduced algebras under the assumptions that the symmetry group is connected and that the stabilizer group of μ also is connected. If the latter assumption fails, the shifted reduced algebra is isomorphic to a (possibly proper) subalgebra of the Wilbour-Kimura algebra.     

Particles,twistors and the division algebras

We study twistorial mechanics of particles and super-particles in six dimensions. To this end we formulate (in a general division algebra framework) a twistor theory in D = 6 based on quaternionic numbers, and prove the equivalence between this version of particle dynamics and the ordinary one. The super-twistors define a covariant and gauge invariant concept of a super world-line and allow us to write an action for the supersymmetric particle that is not plagued by the content of second class constraints that prevents a covariant quantization in the space-time picture. The notion and geometry of projectile twistor space, and its connection to Minkowski space, are examined and shown to directly generalize the results in D = 3, 4. Quantization is performed and analytic quaternionic eigenfunctions and integrations are discussed. We also draw some conclusions on the possible generalization to ten dimensions.     

On the harmonic oscillator with nonzero periodic mass

Summary Following previous papers of Leach, and Wille and Vennik, we consider various new expressions for the nonvanishing periodic mass parameter of the time-dependent harmonic oscillator in a Pérot-Fabry cavity in contact with an atomic reservior. The authors of this paper have agreed to not receive the proofs for correction     

Vibrational Raman effect for molecules in ground states with nonzero spin

The effect of spin degeneracy, on the Raman selection rules is investigated. The vibroelectronic processes among the degenerate components of the electronic ground state can give asymmetric contributions to the Raman tensor elements. However, the conservation of spin in a Raman scattering process prevents some of these vibroelectronic transitions. The resulting tensor element species are compared with those obtained for singlet ground states.     

A diagrammatic approach to spin algebras

A reduction formula for the thermal average of the time-ordered product of spin operators for a magnetic moment in a field H is presented. The reduction formula and the spin algebra are used to compute the magnetization. The procedure provides the basis for a diagrammatic approach to interacting spin systems.     

Maxwell equations,nonzero photon mass,and conformal metric fluctuation

Maxwell equations are studied for a vacuum with nonzero conductivity coefficient. The loss of energy of a photon during its propagation through this vacuum is calculated and the nonzero rest mass of the photon is shown to be related to the conductivity coefficient of the vacuum. The dissipative mechanism is investigated considering a conformally fluctuating metric in the Einstein equation. Possible astrophysical consequences are discussed.     

Natural embedding of group in NMR spin algebras

NMR aspects of finite group natural-embeddings in higher n-fold spin algebras over Hilbert space are considered in the context of icosahedral cage clusters associated with specific ¹¹B borohydride, -deuteride anions for which n = 12. The focus of the discussion is on the abstract and physical models derived from permutation modules in the form of λ ├ n partitions over , where . Hence, the related Kostka expansion coefficients from the pure abstract spin space of mapping and other -combinatorial aspects, including the nature of inner tensor products arising in the high-n limit, are especially pertinent. Further insight into spin cluster NMR problems is provided by studies of -induced algebras derived from the [λ_SA] self-associated irreps. Motivation for the work comes from its potential physical applications for higher-n bi-cluster NMR problems, e.g., in spin dynamics. The representational properties derived are essential in understanding the structure of Liouville space for both SU(2) and higher spin SU(m) clusters. The Hilbert space aspects presented here impact strongly on the somewhat neglected question of the nature of subduction, i.e., involving a finite group naturally embedded in a higher group, within an implicit dual Racah symmetry chain. The essential mappings presented here include both the λ module-onto-{[λ′]} set and the aspects, where the Kostka integers of the former arise naturally in the realization of λ module mappings over .     

Dynamical fluctuations of the rest mass

In the Dirac theory of the electron, energy and momentum are observed to be constants of the motion. However, the velocity is not a constant of the motion, even for a free particle. An attempt will be made to demonstrate a similar property for the rest mass.     

Evidence for nonzero mass photons associated with a vacuum-induceddissipative red-shift mechanism

Laboratory observations that suggest a frequency anisotropy in the direction of the Leo constellation of δν/ν⩾10^-6 can be interpreted in terms of a nonzero photon mass m _γ≅10^-65 g. If one then accepts the theory of light (considered as real Maxwellian waves and photons simultaneously) of Einstein and de Broglie, the experimental justification of the existence of real Maxwellian displacement currents implies the existence of m_γ>0 and of a vacuum dissipative mechanism which can interpret a part (or the totality) of Hubble's cosmological red shift     

Asymptotic completeness of scattering in the nonlinear Lamb system for nonzero mass

We establish the asymptotic completeness in the nonlinear Lamb system with nonzero mass for hyperbolic stationary states. For the proof, we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ODE) converging to a hyperbolic stationary point, using the Banach space Inverse Function Theorem and a priori estimates. We give a counterexample showing that the hyperbolicity condition is essential.     

A theoretical determination of the electronic rest mass

A theoretical relationship for the electron rest mass is derived in terms of the electron charge, Planck's quantum of action, and the speed of light. The basis for this derivation is an assumption that the electron rest mass is entirely electrostatic in origin, combined with the realization that the maximum action density of the world is simply the speed of light. Planck's quantum of action becomes perspicuously associated with an elliptical microspace.