Complex scalar relativistic field as a probability amplitude

TL;DR

This paper proposes a relativistic complex scalar field equation serving as a probability amplitude, deriving continuity and conservation laws, and exploring particle excitations and quantization.

Contribution

It introduces a novel relativistic equation for a complex scalar field as a probability amplitude, including its quantization and excitation spectrum.

Findings

Two types of particle excitations with positive energy identified

Continuity equation for probability density derived

Conservation laws established from Lagrangian formalism

Abstract

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.