10. V. Arunasalam, Uniqueness of Lorentz‐Covariant World‐Space Representations

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Volume 17: Pages 393-411, 2004

Uniqueness of LorentzCovariant WorldSpace Representations

V. Arunasalam

The uniqueness of the Lorentzcovariant 4vector representations of the classicaldynamical variables and the associated quantummechanical Hermitian matrix operators in the worldspace or the Minkowski space or the (spacetime continuum) 4space is examined in some detail. Also, the intrinsic connections or links that exist among the worldspace, the associated canonically conjugate (momentumenergy continuum) 4space, the corresponding (wave vector frequency continuum) Fourier transform 4space, and the (spacetime continuum) linear displacement differential operator 4space are also examined in sufficient detail both for zero and nonzero rest mass particles. The mapping among these four mathematically distinct 4spaces is onetoone. The main emphasis here is on the manifestly Lorentzcovariant formalisms rather than on the commonly used Lorentzinvariant ones. The relativistic momentumenergy (or, equivalently, the de Broglie wave vector frequency) 4vector “dispersion relations” of both the zero and nonzero rest mass particles clearly demonstrates the selfconsistency between wave mechanics and relativity.

Keywords: uniqueness of 4vectors, uniqueness of world vectors, Lorentzcovariant representations, spacetime continuum, momentumenergy continuum, Fourier wave vector frequency continuum, relativistic momentumenergy dispersion relation, relativistic de Broglie wave dispersion relations, zero and nonzero rest mass particles, selfconsistency between wave mechanics and relativity

Received: February 17, 2004; Published online: December 15, 2008