Wave function of particle and the coordinates distribution in relativistic quantum theory

TL;DR

This paper develops a relativistically invariant framework for describing particle position probabilities in quantum theory, incorporating quantum field effects and confirming Heisenberg's uncertainty relations in a relativistic context.

Contribution

It introduces a new relativistic invariant density of probability for particles, applicable to various bosons and electrons, and extends the quantum field distribution concept.

Findings

Derived a relativistic invariant probability density for particle positions.

Confirmed Heisenberg's uncertainty relations in relativistic quantum theory.

Proposed new operators and distributions for particles in space-time.

Abstract

The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave function is found. It is a relativistic invariant describing probability of the particle emergences in space -time. This density is concretized for bosons, both scalar and vector (including photon), charged and neutral, also electron. The Heisenberg's uncertainty relations have been approved in regards to relativistic particle. As applied to the quantum field, this new construction is transformed to new characteristic of the particles distribution in space-time, which complete distribution throughout impulses. The operators of these distributions and the invariant relativistic description for free quantum fields have been obtained. These new properties of the particles and fields are proposed for experimental investigations.