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Doubly special relativity as a limit of gravity. (English) Zbl 1151.83007

Ehlers, Jürgen (ed.) et al., Special relativity. Will it survive the next 101 years? Papers based on the presentations at the 271st WE-Heraeus seminar on special relativity, Potsdam, Germany, February 13–18, 2005. Berlin: Springer (ISBN 3-540-34522-1/hbk). Lecture Notes in Physics 702, 279-298 (2006).
The present paper gives an overview about doubly special relativity as a limit of a kind of quantized gravity theory. It differs from special relativity by a deformed Lorentz-algebra replacing the classical Lorentz-algebra. This has the consequence, that the commutators between boosts and momentum in the same direction get an additional term which depends on Planck’s constant. The authors argue, that nevertheless, the relativity principle is fulfilled in a certain sense in this theory.
The notion “doubly special” means the following: special relativity representing the limit of general relativity has one internal universal constant, namely the light velocity; likewise, the weak-field limit of quantum general relativity should have two internal universal constants, namely Planck’s constant and the light velocity.
For the entire collection see [Zbl 1140.83008].

MSC:

83A05 Special relativity
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
83C45 Quantization of the gravitational field
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