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Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique

D. V. Ahluwalia-Khalilova
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Abstract

We present a Master equation for description of fermions and bosons for special relativities with two invariant scales, SR2, (c and lambda_P). We introduce canonically-conjugate variables (chi^0, chi) to (epsilon, pi) of Judes-Visser. Together, they bring in a formal element of linearity and locality in an otherwise non-linear and non-local theory. Special relativities with two invariant scales provide all corrections, say, to the standard model of the high energy physics, in terms of one fundamental constant, lambda_P. It is emphasized that spacetime of special relativities with two invariant scales carries an intrinsic quantum-gravitational character. In an addenda, we also comment on the physical importance of a phase factor that the whole literature on the subject has missed and present a brief critique of SR2. In addition, we remark that the most natural and physically viable SR2 shall require momentum-space and spacetime to be non-commutative with the non-commutativity determined by the spin content and C, P, and T properties of the examined representation space. Therefore, in a physically successful SR2, the notion of spacetime is expected to be deeply intertwined with specific properties of the test particle.

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D. V. Ahluwalia-Khalilova. 2004-02-04. Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique. https://doi.org/10.1142/s0218271804004633

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