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Special relativity with two invariant scales: motivation, fermions, bosons, locality, and critique. (English) Zbl 1172.83301

Summary: We present a Master equation for description of fermions and bosons for special relativities with two invariant scales, \(\mathbf{SR2}\), (\(c\) and \(\lambda_P\)). We introduce canonically-conjugate variables (\(\chi^0,\boldsymbol\chi\)) to (\(\epsilon,\boldsymbol\pi\)) 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 \(\mathbf{SR2}\). In addition, we remark that the most natural and physically viable \(\mathbf{SR2}\) 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 \(\mathbf{SR2}\), the notion of spacetime is expected to be deeply intertwined with specific properties of the test particle.

MSC:

83A05 Special relativity
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