Deriving Spin within a Discrete-Time Theory

Abstract

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.

On a Time–Space Operator (and other Non-Self-Adjoint Operators) for Observables in QM and QFT

“…Let us finally recall that, as previously mentioned, the chronon can have consequences in several different areas of physics: for instance, in Ref. [114] we derived spin was derived within a discrete-time approach. As a further example, in the next subsection we want to report, with some details, on the possible role of the chronon in Cosmology.…”

“…[114] we derived spin was derived within a discrete-time approach. As a further example, in the next subsection we want to report, with some details, on the possible role of the chronon in Cosmology.…”

“…The consequences and applications of the "Chronon" are really various, an example being Ref. [114], where it was suggested that the chronon approach can account also for the origin of the internal degrees of freedom of the particles. In the last subsection of this Section we shall mention with the possible role of the chronon in Cosmology.…”

Helicity-0 spinning particles

“…The coefficients k i -which may be chosen equal to zero for i larger than a given integer, see below-might be functions of the self-interaction of the particle and of its mass and charge (cf. the infinite-terms equation of the self-radiating classical electron or the "chronon" theory of the electron [14], k i can be related to the underlying string structure (or membrane or n-brane structure) of a spinning particle. The consequent Euler-Lagrange equation of motion is a constant-coefficients n-th order differential equation,…”