6. Nickola S. Todorov, The Schrödinger‐Type Equation of Motion of Spin‐0 Relativistic Particles, Part I: Physical Properties of the Equation and the Problem of Position‐Velocity Coexistence

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Volume 6: Pages 517-531, 1993

The SchrödingerType Equation of Motion of Spin0 Relativistic Particles, Part I: Physical Properties of the Equation and the Problem of PositionVelocity Coexistence

Nickola S. Todorov 1

1Georgi Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria

It is shown that the initially abandoned equation, i∂ψ/∂t = [(−i                          − eA)2 + m2]1/2ψ + eA0ψ meant to describe massive (m ≠ 0), spinless charged particles, possesses a number of conceptual advantages compared to the wellknown KleinGordon equation, provided that spin0 particles are treated as nonpointlike entities. It is also shown that this equation is gaugeinvariant and possesses certain important features of relativistic covariance despite its asymmetric appearance. In particular, it entails a continuity equation for a pertinent four current vector jμ, whose zeroth component j0 may be regarded in some cases as the probability density distribution of position. Under a “minimal” statistical interpretation the equation reveals positionvelocity coexistence in complete analogy with the nonrelativistic and spin1/2 relativistic cases examined earlier. The approach in this paper also helps to resolve a difficulty connected with a theorem by Hegerfeldt. The proposed interpretation of the equation is induced by a specific notion of incompleteness of description valid for the pertinent states of motion (and, e.g., for KleinGordon and nonrelativistic Schrödinger states and invalid for states such as classical mechanics or Dirac's fourspinor states) and the existence of negative local values of the fourcurrent component j0 for the case of free motion. Earlier ideologies that have a bearing on the content of the paper and their conceptual difficulties are considered in detail.

Keywords: Schrödingertype relativistic equations, statistical interpretation, massive nonpointlike spin0 particles, positionvelocity coexistence

Received: February 4, 1992; Published Online: December 15, 2008