Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach

TL;DR

This paper compares classical and quantum models of electron Zitterbewegung in a magnetic field, revealing that classical approaches fail to accurately describe spin dynamics under these conditions, unlike quantum methods.

Contribution

It demonstrates the discrepancy between classical and quantum models of Zitterbewegung in magnetic fields and highlights the quantum approach's accuracy in describing electron spin.

Findings

Classical approach breaks CP symmetry in magnetic fields.

Quantum approach aligns with Heisenberg picture results.

Classical interpretation of spin is inadequate in magnetic fields.

Abstract

We investigate variations of the Zitterbewegung frequency of electron due to an external static and uniform magnetic field employing the expectation value quantum approach, and compare our results with the classical model of spinning particles. We demonstrate that these two so far compatible approaches are not in agreement in the presence of an external uniform static magnetic field, in which the classical approach breaks the usual symmetry of free particles and antiparticles states, i.e. it leads to CP violation. Hence, regarding the Zitterbewegung frequency of electron, the classical approach in the presence of an external magnetic field is unlikely to correctly describe the spin of electron, while the quantum approach does, as expected. We also show that the results obtained via the expectation value are in close agreement with the quantum approach of the Heisenberg picture derived in the literature. However, the method we use is capable of being compared with the classical approach regarding the spin aspects. The classical interpretation of spin produced by the altered Zitterbewegung frequency, in the presence of an external magnetic field, are discussed.