《QuantisationofDeformedSpecialRelativity》青少年科普教育丛书.pdf

Quantisation of Deformed Special Relativity
CLEMENS HEUSON
Zugspitzstr. 4
D-87493 Lauben, Germany
Abstract:
We consider deformed special relativity (DSR) theories mutative space-time, perhaps
as an first approximation to a mutative space-time formulation. The corresponding
field theories in general possess derivatives of all orders. From a quantisation procedure and
the deformed Dirac equation in momentum space we obtain for a specific DSR model
enhanced expressions for momentum and charge and finite vacuum contributions.
1. Introduction
Deformed or doubly special relativity theories, involving two invariant scales, a velocity scale
and an fundamental length scale l or energy scale κ= 1/ l (presumably related to the Planck
length or mass), have attracted a lot of interest in the last years, see the review in [1]. There
are also severe problems in the interpretation of DSR theories, the er ball problem
(macroscopic bodies have energies exceeding the Planck energy), the question of the proper
formulation in space-time (mutative or not), the multiplicity problem (which if any
model describes nature), the issue of particle velocity etc., see for example the discussion in
[2] and papers cited therein.
In this letter we consider second quantisation of DSR theories as a first step for a DSR
quantum field theory. The plan of the paper is as follows. In s