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Sep 23, 2013
09/13

by
Enrico Celeghini

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Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can be dealt more or less as the Lie one and we do not need to introduce the not easy to handle topological groups. Composed system also is described by the suitably symmetrized q-coalgebra. A physical application to the phonon, irreducible unitary...

Source: http://arxiv.org/abs/hep-th/9211077v2

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33

Sep 18, 2013
09/13

by
Enrico Celeghini

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This paper is devoted to analize inside the infinitely many possible bases of Uq(g), same that can be considered "more equal then others". The element of selection has been a privileged relation with the bialgebra. A new parameter z' has been found that determines the commutation relations, independent from the z=log(q) that defines Uq(g). Both z and z' are necessary to fix the relations between the basic set and its coproducts. Three cases are particularly relevant: the analytical...

Source: http://arxiv.org/abs/0809.0264v1

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2.0

Jun 26, 2018
06/18

by
Enrico Celeghini

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We construct a rigged Hilbert space for the square integrable functions on the line L^2(R) adding to the generators of the Weyl-Heisenberg algebra a new discrete operator, related to the degree of the Hermite polynomials. All together, continuous and discrete operators, constitute the generators of the projective algebra io(2. L^2(R) and the vector space of the line R are shown to be isomorphic representations of such an algebra and, as both these representations are irreducible, all operators...

Topics: Mathematics, Quantum Physics, Mathematical Physics

Source: http://arxiv.org/abs/1502.04891

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25

Sep 22, 2013
09/13

by
Enrico Celeghini; Mario Rasetti

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A quantitative description of the whole process of condensation of bosons in an harmonic trap is given resorting only to Gibbs and Bose postulates, without assuming equipartition nor continuum statistics. Below Tc discrete spectrum theory predicts for the thermo-dynamical variables a behavior different from the continuum case. In particular a new critical temperature is found where the specific heat exhibits a lambda-like spike. Numerical values of the relevant quantities depend on the...

Source: http://arxiv.org/abs/cond-mat/0004096v2

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35

Sep 18, 2013
09/13

by
Enrico Celeghini; Mario Rasetti

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The role of background in bosonic quantum statistics is discussed in the frame of a new approach in terms of coherent states. Bosons are indeed detected in different physical situations where they exhibit different and apparently unconnected properties. Besides Bose gas we consider bosons in particle physics and bosons in harmonic traps. In particle physics bosons are dealt with in a context where the number of observed particles is finite: here the relevant features are the canonical...

Source: http://arxiv.org/abs/cond-mat/0006424v1

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60

Sep 24, 2013
09/13

by
Enrico Celeghini; Mario Rasetti

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A quantitative analysis of the process of condensation of bosons both in harmonic traps and in gases is made resorting to two ingredients only: Bose classical distribution and spectral discretness. It is shown that in order to take properly into account statistical correlations, temperature must be defined from first principles, based on Shannon entropy, and turns out to be equal to $\beta^{-1}$ only for $T > T_c$ where the usual results are recovered. Below $T_c$ a new critical temperature...

Source: http://arxiv.org/abs/cond-mat/0103555v1

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31

Sep 21, 2013
09/13

by
Enrico Celeghini; M. Tarlini

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The first ``Convegno Informale su Quantum Groups'' was held in Florence from February 3 to 6, 1993. This Convegno was conceived as an informal meeting to bring together all the italian people working in the field of quantum groups and related topics. We are very happy indeed that about 30 theoretical physicists decided to take part presenting many aspects of this interesting and live subject of research. We thank all the participants for the stimulating and nice atmosphere that has...

Source: http://arxiv.org/abs/hep-th/9304160v1

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3.0

Jun 30, 2018
06/18

by
Enrico Celeghini; Mariano A. del Olmo

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Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and allows to obtain the projective algebra io(2). A Rigged Hilbert space is found and a new discrete basis in R obtained. The operators {O[R]} defined on R are shown to belong to the Universal Enveloping Algebra UEA[io(2)] allowing, in this way, their algebraic...

Topics: Physics, Mathematics, Quantum Physics, Mathematical Physics, Computational Physics

Source: http://arxiv.org/abs/1411.3263

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2.0

Jun 27, 2018
06/18

by
Enrico Celeghini; Mariano A. del Olmo

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We present a family of unitary irreducible representations of SU(2) realized in the plane, in terms of the Laguerre polynomials. These functions are similar to the spherical harmonics realized on the sphere. Relations with the space of square integrable functions defined on the plane, L^2(R^2, are analyzed. The realization of representations of Lie groups in spaces with intrinsic symmetry different from the one of the groups is discussed.

Topics: Group Theory, Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1504.01572

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90

Jul 20, 2013
07/13

by
Angel Ballesteros; Enrico Celeghini; Francisco J. Herranz

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The Lie bialgebras of the (1+1) extended Galilei algebra are obtained and classified into four multiparametric families. Their quantum deformations are obtained, together with the corresponding deformed Casimir operators. For the coboundary cases quantum universal R-matrices are also given. Applications of the quantum extended Galilei algebras to classical integrable systems are explicitly developed.

Source: http://arxiv.org/abs/math/9906094v2

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Sep 23, 2013
09/13

by
Massimo Blasone; Antonio Capolupo; Enrico Celeghini; Giuseppe Vitiello

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We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum field theory. Such phases carry information about the non-perturbative vacuum structure associated with the field mixing. By subtracting the condensate contribution of the flavor vacuum, the previously studied quantum mechanics geometric phase is recovered.

Source: http://arxiv.org/abs/0903.1578v1

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Sep 20, 2013
09/13

by
A. Ballesteros; Enrico Celeghini; F. J. Herranz; M. A. del Olmo; M. Santander

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A universal R--matrix for the quantum Heisenberg algebra h(1)q is presented. Despite of the non--quasitriangularity of this Hopf algebra, the quantum group induced from it coincides with the quasitriangular deformation already known.

Source: http://arxiv.org/abs/hep-th/9402127v1

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Sep 21, 2013
09/13

by
F. Bonechi; Enrico Celeghini; R. Giachetti; C. M. Pereña; E. Sorace; M. Tarlini

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The concept of universal T matrix, recently introduced by Fronsdal and Galindo in the framework of quantum groups, is here discussed as a generalization of the exponential mapping. New examples related to inhomogeneous quantum groups of physical interest are developed, the duality calculations are explicitly presented and it is found that in some cases the universal T matrix, like for Lie groups, is expressed in terms of usual exponential series.

Source: http://arxiv.org/abs/hep-th/9311114v3