Plasma-like Description for Elementary and Composite Quantum Particles.

Andrey Akhmeteli

doi:10.3390/e24020261

Abstract

Schrödinger noticed in 1952 that a scalar complex wave function can be made real by a gauge transformation. The author showed recently that one real function is also enough to describe matter in the Dirac equation in an arbitrary electromagnetic or Yang–Mills field. This suggests some “symmetry” between positive and negative frequencies and, therefore, particles and antiparticles, so the author previously considered a description of one-particle wave functions as plasma-like collections of a large number of particles and antiparticles. The description has some similarities with Bohmian mechanics. This work offers a criterion for approximation of continuous charge density distributions by discrete ones with quantized charge based on the equality of partial Fourier sums, and an example of such approximation is computed using the homotopy continuation method. An example mathematical model of the description is proposed. The description is also extended to composite particles, such as nucleons or large molecules, regarded as collections including a composite particle and a large number of pairs of elementary particles and antiparticles. While it is not clear if this is a correct description of the reality, it can become a basis of an interesting model or useful picture of quantum mechanics.

Highlights

Recent progress in quantum information processing puts a new emphasis on foundations of quantum theory
While it is not clear if this is a correct description of the reality, it can become a basis of an interesting model or useful picture of quantum mechanics
How accurately can a continuous charge density distribution for a specific wave function with a total charge equal to one electron charge be approximated by a collection of discrete charges with values of ±1 electron charge? It is obvious that a Fourier expansion of a point-like charge density distribution contains arbitrarily high spatial frequencies, whereas high-spatial-frequency Fourier components of smooth charge density distributions tend to zero fast; it is probably impossible to approximate a continuous charge density distribution by a finite number of discrete quantized charges with a good accuracy

Summary

Introduction

Recent progress in quantum information processing puts a new emphasis on foundations of quantum theory. It is probably safe to say that there is currently no consensus on the interpretation of quantum theory [1,2,3,4] This suggests that no existing interpretation is completely satisfactory, so the formal description discussed in this work may be of some interest, if not as a “how ” model, at least as a “how possibly”. Bohmian mechanics is sometimes considered not just as an interpretation, and as another picture of quantum mechanics and a basis for computational methods [6]. This can be a way to assess the description of this work

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