1,721,889 research outputs found
Covariant four dimensional differential calculus in κ-Minkowski
Full text linkIt is generally believed that it is not possible to have a four dimensional differential calculus in κ-Minkowski spacetime, with κ-Poincaré relativistic symmetries, covariant under (κ-deformed) Lorentz transformations. Thus, one usually introduces a fifth differential form, whose physical interpretation is still challenging, and defines a covariant five dimensional calculus. Nevertheless, the four dimensional calculus is at the basis of several works based on κ-Minkowski/κ-Poincaré framework that led to meaningful insights on its physical interpretation and phenomenological implications. We here revisit the argument against the covariance of the four dimensional calculus, and find that it depends crucially on an incomplete characterization of Lorentz transformations in this framework, which neglected a feature, still uncovered at the time, that turns out to be fundamental for the consistency of the relativistic framework: the noncommutativity of the Lorentz transformation parameters. This suggests to revise the notion of covariance to accommodate the action of the full infinitesimal Lorentz transformation. Once this is taken into account, the four dimensional calculus is found to be fully Lorentz covariant. The result we obtain extends naturally to the whole κ-Poincaré algebra of transformations, showing the close relation between its relativistic nature and the properties of the differential calculus
The Duflo non-commutative Fourier transform for the Lorentz group
No full textFor a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group and (non-commutative) algebra representation, depending on the specific quantization map. We discuss the construction of the non-commutative Fourier transform and the non-commutative algebra representation, via the Duflo quantization map, for a system whose phase space is the cotangent bundle of the Lorentz group
DSR-deformed relativistic symmetries in an expanding spacetime
Full text linkWe present here a perspective on results obtained in collaboration with Amelino-Camelia, Marcianó and Matassa, reported in Ref. [1]. We characterize a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale ("speed-of-light scale"), a large distance scale (inverse of the "expansion-rate scale'), and a large momentum scale ("Planck scale"). This is particularly relevant in relation to the opportunities for testing Planck-scale-deformed Lorentz symmetry scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality
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No full textNoncommutative Fourier transform for the Lorentz group via the Duflo map
Full text linkWe defined a non-commutative algebra representation for quantum systems whose phase space is the cotangent bundle of the Lorentz group, and the non-commutative Fourier transform ensuring the unitary equivalence with the standard group representation. Our construction is from first principles in the sense that all structures are derived from the choice of quantization map for the classical system, the Duflo quantization map
Comparison of Under-Actuated and Fully Actuated Serial Robotic Arms: A Case Study
No full textUnder-actuated robots are very interesting in terms of cost and weight since they can result in a state-controllable system with a number of actuators lower than the number of joints. In this paper, a comparison between an under-actuated planar three-degrees-of-freedom (DOF) robot and a comparable fully actuated two-degrees-of-freedom robot is presented, mainly focusing on the performances in terms of trajectories, actuator torques, and vibrations. The under-actuated system is composed of two active rotational joints followed by a passive rotational joint equipped with a torsional spring. The fully actuated robot is inertial equivalent to the under-actuated manipulator: the last link is equal to the sum of the last two links of the under-actuated system. Due to the conditions on the inertia distribution and spring placement, in a simple point-to-point movement the last passive joint starts and ends in a zero-value configuration, so the three DOF robot is equivalent, in terms of initial and final configuration, to the two DOF fully actuated robot, thus they can be compared. Results show how while the fully actuated robot is better in terms of reliable trajectory and actuator torques, the under-actuated robot wins in flexibility and in vibrations at a given configuration
Sclerosi Multipla e concomitante siringomielia. Dieci anni di osservazione longitudinale
No full textThe effect of size in concrete compressive failure
No full textExisting codes, including fib MC2010, usually express concrete failure criteria in terms of strength or yield criteria only. For tensile strength related failure modes, the dependence of the nominal strength on the size of the structure is well established and accounted in the codes. However, even though the failure of concrete under unconfined compression is of brittle type, no specific provision accounts for similar effects in compression. In this paper a wide experimental campaign on the effect of size of concrete in compression is presented. Cylindrical specimens of plane concrete with geometrical slenderness ratio ranging from 1:2 to 1:8 and for different diameters (10, 20, 40 and 80 cm) were considered. Experimental test results are presented and compared to existing scaling laws
Physical velocity of particles in relativistic curved momentum space
No full textWe show in general that for a relativistic theory with curved momentum space, i.e. a theory with deformed relativistic symmetries, the physical velocity of particles coincides with their group velocity. This clarifies a long-standing question about the discrepancy between coordinate and group velocity for this kind of theories. The first evidence that this was the case had been obtained at linear order in the deformation parameter in Ref. 1 for the specific case of κ-momentum space. The proof was based on the recent understanding of how relative locality affects these scenarios. Here we rely again on a careful implementation of relative locality effects, and obtain our result for a generic (relativistic) curved momentum space framework at all orders in the deformation/curvature parameter. We also discuss the validity of this result when the deformation depends on the coordinates as well as on the momenta
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