Browsing by Author "Piacitelli, Gherardo"

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    Canonical k-Minkowski Spacetime
    (2010-04-30T11:01:46Z) Piacitelli, Gherardo; Dabrowski, Ludwik; Mathematics; Mathematical Physics
    A complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically "radial", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at "large" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime.
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    Quantum Spacetime: a Disambiguation
    (2010-04-30T11:06:32Z) Piacitelli, Gherardo; Mathematics; Mathematical Physics
    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. Some incorrect statements as "universality of Planck scale conflicts with Lorentz-Fitzgerald contraction and requires a modification of covariance", or "stability of the geometric background requires an absolute lower bound of (\Delta x^\mu)", or "violations of unitarity are due to time/space non-commutativity" are put in context, and discussed.
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    Twisted Covariance vs Weyl Quantisation
    (2009-01-22T12:32:39Z) Piacitelli, Gherardo; Mathematics; Mathematical Physics
    In this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio "why theta"?