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Deriving Spin within a Discrete-Time Theory

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We prove that the classical theory with a discrete time (chronon) is a particular case of a more general theory in which spinning particles are associated with generalized Lagrangians containing time-derivatives of any order (a theory that has been called “Non-Newtonian Mechanics”). As a consequence, we get, for instance, a classical kinematical derivation of Hamiltonian and spin vector for the mentioned chronon theory (e.g., in Caldirola et al.’s formulation). Namely, we show that the extension of classical mechanics obtained by the introduction of an elementary time-interval does actually entail the arising of an intrinsic angular momentum; so that it may constitute a possible alternative to string theory in order to account for the internal degrees of freedom of the microsystems.

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Authors and Affiliations

  1. Università Statale di Bergamo, Facoltà di Ingegneria, viale Marconi 5, 24044, Dalmine (BG), Italy

    Erasmo Recami & Giovanni Salesi

  2. Istituto Nazionale di Fisica Nucleare–Sezione di Milano, Italy via Celoria 16, 20133, Milan, Italy

    Erasmo Recami & Giovanni Salesi

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  1. Erasmo Recami
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  2. Giovanni Salesi
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Communicated by Alwyn van der Merwe

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Recami, E., Salesi, G. Deriving Spin within a Discrete-Time Theory. Found Phys 37, 277–294 (2007). https://doi.org/10.1007/s10701-006-9101-9

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