Abstract
Starting from the geometric calculus based on Clifford algebra, the idea that physical quantities are Clifford aggregates (“polyvectors”) is explored. A generalized point particle action (“polyvector action”) is proposed. It is shown that the polyvector action, because of the presence of a scalar (more precisely a pseudoscalar) variable, can be reduced to the well known, unconstrained, Stueckelberg action which involves an invariant evolution parameter. It is pointed out that, starting from a different direction, DeWitt and Rovelli postulated the existence of a clock variable attached to particles which serve as a reference system for identification of spacetime points. The action they postulated is equivalent to the polyvector action. Relativistic dynamics (with an invariant evolution parameter) is thus shown to be based on even stronger theoretical and conceptual foundations than usually believed.
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Pavšič, M. Clifford-Algebra Based Polydimensional Relativity and Relativistic Dynamics. Foundations of Physics 31, 1185–1209 (2001). https://doi.org/10.1023/A:1017599804103
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DOI: https://doi.org/10.1023/A:1017599804103