Über freie teilchen mit nichtverschwindender masse und beliebiger spinquantenzahl
Abstract
The properties are investigated of the solutions of a wave equation for an undor of rank N (Eq. (1)), which is a simple generalization of the Dirac equation for free electrons and by which particles with arbitrary spin and non-vanishing mass might eventually be described. The solutions can be classified in groups satisfying Klein-Gordon equations with (for N > 2) different values of the mass-constant. In the cases N = 1 (Dirac electron) and N = 2 (the meson theory as given by Møller and Rosenfeld and by Belinfante) the mass-constant can take only one single value. Those solutions of lowest mass-constant, which are symmetrical in all undor indices of the wave function, correspond to Dirac's particles of arbitrary spin. From the variational principle, from which the wave equation can be derived, unambiguous expressions are established for the vector of the charge current-density and for the tensor of the energy-momentum density. In the case N > 2, the direct applicability to the description of actual elementary particles is seriously impeded by the circumstances that the expression for the energy obtained in this way is not positive definite. This difficulty cannot be overcome by a “hole theory” as it can for N = 1 (Dirac electron).
- Publication:
-
Physica
- Pub Date:
- July 1941
- DOI:
- 10.1016/S0031-8914(41)90365-8
- Bibcode:
- 1941Phy.....8..597K