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Modified Lorentz transformations in deformed special relativity

G. Salesi

Dipartimento di Ingegneria e Scienze Applicate, Università di Bergamo, viale Marconi 5, Dalmine, Italy

Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, Milan, Italy

E-mail Address: salesi@unibg.it

Corresponding author.

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M. Greselin

Dipartimento di Ingegneria e Scienze Applicate, Università di Bergamo, viale Marconi 5, Dalmine, Italy

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L. Deleidi

Dipartimento di Ingegneria e Scienze Applicate, Università di Bergamo, viale Marconi 5, Dalmine, Italy

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, and

R. A. Peruzza

Dipartimento di Ingegneria e Scienze Applicate, Università di Bergamo, viale Marconi 5, Dalmine, Italy

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https://doi.org/10.1142/S0217751X17500865Cited by:0 (Source: Crossref)

Abstract

We have extended a recent approach to Deformed Special Relativity based on deformed dispersion laws, entailing modified Lorentz transformations and, at the same time, noncommutative geometry and intrinsically discrete space–time. In so doing we have obtained the explicit form of the modified Lorentz transformations for a special class of modified momentum-energy relations often found in literature and arising from quantum gravity and elementary particle physics. Actually, our theory looks as a very simple and natural extension of special relativity to include a momentum cutoff at the Planck scale. In particular, the new Lorentz transformations do imply that for high boost speed $(V \sim c)$ the deformed Lorentz factor does not diverge as in ordinary relativity, but results to be upper bounded by a large finite value of the order of the ratio between the Planck mass and the particle mass. We have also predicted that a generic boost leaves unchanged Planck energy and momentum, which result invariant with respect to any reference frame. Finally, through matrix deformation functions, we have extended our theory to more general cases with dispersion laws containing momentum-energy mixed terms.

Keywords:

PACS: 03.30.+p, 11.30.Cp, 11.55.Fv

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