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

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

2004-02-04

arxiv.org/abs/gr-qc/0402023v1

Int.J.Mod.Phys.D13:335-346,2004

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Int. J. Mod. Phys. D (in press). Extended version of a set of two informal lectures given in "La Sapienza" (Rome, May 2001)

Scientific paper

10.1142/S0218271804004633

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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