Algebraic properties of relativistic equations for zero rest-mass

Some algebraic properties of the generalised Pauli matrices of Barut, Muzinich and Williams are derived and used to demonstrate the equivalence of the zero-mass equations of Nelson and Good with those of Dirac, Fierz and Pauli. The conserved rank four tensor of the spin-2 theory is shown to have the structure of Bel's tensor for a gravitational field satisfying Einstein's empty space equations, in the linearised version of general relativity.     

Rest frames for tachyons and photons

A formalism is developed which admits particles faster than light and reference frames faster than light and as fast as light. It is fully consistent with the physical principles of special relativity. The necessity of introducing imaginary quantities does not arise. It does not encounter any difficulties with the principle of causality if it is reasonably interpreted.Dedicated to Prof. E. C. G. Sudarshan, in honor of his receipt of the Padmabushan Award.     

A new approach to the method of nonlinear variation of parameters

A nonlinear variation of parameters method for ordinary differential equations is obtained, which generalizes existing techniques. The versatility of the method is demonstrated by studying the asymptotic behavior of solutions of perturbed equations.     

A nonlinear variation of constants method for integro differential and integral equations

A variation of constants technique is utilized to obtain representation formulas for solutions of perturbed nonlinear integrodifferential and integral equations. These representations are used to analyze boundedness and stability properties of perturbed integral equations. Questions on the existence of the inverse of the fundamental matrix as well on the existence of the semigroup property of the fundamental matrix are discussed.     

Intra-nuclear cascading in deep inelastic scattering of 150 GeV muons in emulsion

An experimental search is presented for the existence of intra-nuclear cascading which, for small values of the Bjorken scaling variable ω, is the only mechanism of particle multiplication in the target nucleus. Our data indicate that cascading does exist as one of the effective mechanisms of particle multiplication in μ-nucleus collisions. No significant variation of the observed multiplicity with ω is observed.     

Geometry of the de-Sitter universe

By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.     

Dixmier traces as singular symmetric functionals and applications to measurable operators

We unify various constructions and contribute to the theory of singular symmetric functionals on Marcinkiewicz function/operator spaces. This affords a new approach to the non-normal Dixmier and Connes-Dixmier traces (introduced by Dixmier and adapted to non-commutative geometry by Connes) living on a general Marcinkiewicz space associated with an arbitrary semifinite von Neumann algebra. The corollaries to our approach, stated in terms of the operator ideal L^(1,∞) (which is a special example of an operator Marcinkiewicz space), are: (i) a new characterization of the set of all positive measurable operators from L^(1,∞), i.e. those on which an arbitrary Connes-Dixmier trace yields the same value. In the special case, when the operator ideal L^(1,∞) is considered on a type I infinite factor, a bounded operator x belongs to L^(1,∞) if and only if the sequence of singular numbers {s_n(x)}_n?1 (in the descending order and counting the multiplicities) satisfies . In this case, our characterization amounts to saying that a positive element x∈L^(1,∞) is measurable if and only if exists; (ii) the set of Dixmier traces and the set of Connes-Dixmier traces are norming sets (up to equivalence) for the space , where the space is the closure of all finite rank operators in L^(1,∞) in the norm ∥.∥_(1,∞).     

Six-dimensional formulation of meson equations

The structure of the conformal group is studied by a generalisation of quaternion methods to six dimensions. Some simpleSO(4,2) covariant equations are shown to correspond to the Kemmer formulation for pseudoscalar and vector mesons, and the matrix elements of the irreducible representations of the Kemmer algebra are expressed as traces of products of Dirac matrices.