Complex scalar relativistic field as a probability amplitude

A relativistic equation for a neutral complex field as a probability amplitude is proposed. The continuity equation for the probability density is obtained. It is shown that there are two types of excitations of this field, which describe particles with positive energy and different dispersion laws. Based on the Lagrangian formalism, conservation laws are obtained. The transition to secondary quantization is considered.

💡 Research Summary

The paper addresses two long‑standing difficulties of the Klein‑Gordon‑Fock (KGF) description of a complex scalar field: (i) the probability density derived from the KGF continuity equation is not positive‑definite, and (ii) the spectrum contains both positive and negative energy solutions. To overcome these problems the author introduces a time‑dependent phase transformation
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