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Structure and Mass Spectrum of Elementary Particles. II. Oscillator Model
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1953
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Spectral TheoryNon-local InteractionOperator FEngineeringPhysicsHigh-energy Nuclear ReactionNatural SciencesTheoretical High-energy PhysicParticle PhysicsQuantum Field TheoryFour-dimensional Oscillator ModelWeak InteractionConstructive Field TheoryElementary ParticlesBiophysicsStatistical Field TheoryMany-body Problem
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.