Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 073, 43 pages      arXiv:1004.5261
Contribution to the Special Issue “Noncommutative Spaces and Fields”

Quantum Spacetime: a Disambiguation

Gherardo Piacitelli
SISSA, Via Bonomea 265, 34136, Trieste, Italy

Received April 29, 2010, in final form September 15, 2010; Published online September 23, 2010

We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the ''canonical quantum spacetime''. The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance.

Key words: quantum spacetime; covariance; noncommutative geometry; doubly special relativity.

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