Structure and Mass Spectrum of Elementary Particles II. Oscillator Model

Abstract

As an illustration of the general considerations on nonlocal fields in the preceding letter, let us assume that the operator F has a very simple form

$$ F = - \frac{{\partial ^2 }} {{\partial X_\mu \partial X_\mu }} + \frac{{\lambda ^2 }} {2}\left[ { - \frac{{\partial ^2 }} {{\partial r_\mu \partial r_\mu }} + \frac{1} {{\lambda ^4 }}r_\mu r_\mu } \right], $$

((1))

where λ is a small constant with the dimension of length. One may call this the four-dimensional oscillator model for the elementary particle, which was considered first by Born¹ in connection with his idea of a self-reciprocity. However, our model differs from his model in that we have introduced internal degrees of freedom of the particles which are related to the nonlocalizability of the field itself.

Now at Kyoto University, Kyoto, Japan, on leave of absence from Columbia University (July, 1953).