5,665 research outputs found

    Concurrent π\pi-vector fields and energy beta-change

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    The present paper deals with an \emph{intrinsic} investigation of the notion of a concurrent π\pi-vector field on the pullback bundle of a Finsler manifold (M,L)(M,L). The effect of the existence of a concurrent π\pi-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular ÎČ\beta-change, namely the energy ÎČ\beta-change ($\widetilde{L}^{2}(x,y)=L^{2}(x,y)+ B^{2}(x,y) with \ B:=g(\bar{\zeta},\bar{\eta});; \bar{\zeta} beingaconcurrent being a concurrent \pi−vectorfield),isestablished.TherelationbetweenthetwoBarthelconnections-vector field), is established. The relation between the two Barthel connections \Gammaand and \widetilde{\Gamma},correspondingtothischange,isfound.Thisrelation,togetherwiththefactthattheCartanandtheBarthelconnectionshavethesamehorizontalandverticalprojectors,enableustostudytheenergy, corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy \beta$-change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.Comment: 27 pages, LaTex file, Some typographical errors corrected, Some formulas simpifie

    Semi-classical behavior of P\"oschl-Teller coherent states

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    We present a construction of semi-classical states for P\"oschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They minimize a special uncertainty relation. Like standard coherent states they resolve the identity with a uniform measure. They permit to establish the correspondence (quantization) between classical and quantum quantities. Finally, their time evolution is localized on the classical phase space trajectory.Comment: 7 pages, 2 figures, 1 animatio
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