TY - JOUR
T1 - Poincaré covariance and κ-Minkowski spacetime
JF - Physics Letters A 375 (2011) 3496-3498
Y1 - 2011
A1 - Ludwik Dabrowski
A1 - Gherardo Piacitelli
AB - A fully Poincaré covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincaré group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincaré covariance is realised á la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of \\\"Poincaré covariance\\\".
PB - Elsevier
UR - http://hdl.handle.net/1963/3893
U1 - 816
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators
JF - Commun. Math. Phys. 308 (2011) 567-589
Y1 - 2011
A1 - Dorothea Bahns
A1 - Sergio Doplicher
A1 - Klaus Fredenhagen
A1 - Gherardo Piacitelli
AB - We develop the first steps towards an analysis of geometry on the quantum\\r\\nspacetime proposed in Doplicher et al. (Commun Math Phys 172:187–220, 1995). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4- volume spanned by five\\r\\nindependent events, is shown to be normal. Its spectrum is pure point with a\\r\\nfinite distance (of the order of the fourth power of the Planck length) away\\r\\nfrom the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out.
PB - Springer
UR - http://hdl.handle.net/1963/5203
U1 - 5025
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - Generic
T1 - Aspects of Quantum Field Theory on Quantum Spacetime
T2 - PoS CNCFG2010:027,2010
Y1 - 2010
A1 - Gherardo Piacitelli
AB - We provide a minimal, self-contained introduction to the covariant DFR flat\\r\\nquantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation.
JF - PoS CNCFG2010:027,2010
PB - SISSA
UR - http://hdl.handle.net/1963/4171
N1 - 25 pages, active hyperlinks. Corfu Summer Institute on Elementary\\r\\n Particles and Physics - Workshop on Non Commutative Field Theory and Gravity,\\r\\n September 8-12, 2010, Corfu Greece
U1 - 3893
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - RPRT
T1 - Canonical k-Minkowski Spacetime
Y1 - 2010
A1 - Gherardo Piacitelli
A1 - Ludwik Dabrowski
AB - 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.
UR - http://hdl.handle.net/1963/3863
U1 - 846
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Lorentz Covariant k-Minkowski Spacetime
JF - Phys. Rev. D 81 (2010) 125024
Y1 - 2010
A1 - Ludwik Dabrowski
A1 - Michal Godlinski
A1 - Gherardo Piacitelli
AB - In recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance.
UR - http://hdl.handle.net/1963/3829
U1 - 498
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - RPRT
T1 - Quantum Spacetime: a Disambiguation
Y1 - 2010
A1 - Gherardo Piacitelli
AB - 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.
UR - http://hdl.handle.net/1963/3864
U1 - 845
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model
JF - Comm. Math. Phys. 295 (2010) 701-729
Y1 - 2010
A1 - Gherardo Piacitelli
AB - We discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames.
UR - http://hdl.handle.net/1963/3605
U1 - 696
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - RPRT
T1 - Twisted Covariance vs Weyl Quantisation
Y1 - 2009
A1 - Gherardo Piacitelli
AB - 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\\\"?
UR - http://hdl.handle.net/1963/3451
U1 - 885
U2 - Mathematics
U3 - Mathematical Physics
ER -