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Zitterbewegung and semiclassical observables for the Dirac equation
Open accessAbstract
In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in ℏ by projecting to dynamically almost invariant subspaces of the quantum mechanical Hilbert space which are associated with particles and anti-particles. This not only allows us to identify observables with a semiclassical meaning, but also to recover combined classical dynamics for the translational and spin degrees of freedom. Finally, we discuss properties of eigenspinors of a Dirac–Hamiltonian when these are projected to the almost invariant subspaces, including the phenomenon of quantum ergodicity.
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The assessment shows that when the free particle is considered using the Dirac Hamiltonian, the resultant solution leads to an eigenvalue spectrum of the time operator that contains a gap between positive and negative values, similar to the energy gap that causes Zitterbewegung.
“From the assessment, it has observed that whenever consideration of the free particle is based on the Dirac Hamiltonian, the resultant solution leads to eigenvalue spectrum of time operator that contains a gap between the positive and negative values which is similar to energy gap that appears in the energy spectrum that causes a jittery motion referred to as Zitterbewegung [25].”
From Assessment of Zitterbewegung Interpretation for Free Particle Solution Using the Concept of Relativistic Wave (2024) · cites this paper as [25]
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Experimental — accuracy not yet measuredThe analysis infers that interference between the negative energy state and positive state results in a fluctuation that gives rise to the concept of ZBW.
“From the analysis it was inferred there is interference between the negative energy state and positive state which results to the fluctuation that gives rise to the concept of zbw [12,25].”
From Assessment of Zitterbewegung Interpretation for Free Particle Solution Using the Concept of Relativistic Wave (2024) · cites this paper as [25]
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Cites
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Cited by
Sorted by citations
Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects
Winkler, R., Zülicke, U., & Bolte, J. (2007) · Physical Review B · doi:10.1103/physrevb.75.205314 · Cited by 70
Self-citationUgwu, E. (2024) · American Journal of Modern Physics · doi:10.11648/j.ajmp.20241303.11
Metadata
- Authors
- Bolte, J., & Glaser, R.
- Affiliations
- Universität Ulm (DE)
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2004-06-03
- Volume
- 37
- Issue
- 24
- Pages
- 6359-6373
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1980535856
- Cited by
- 16
- References
- 3
- Citations by year
- 2022: 1 · 2019: 1 · 2016: 2
- FWCI
- 2.62
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- Zitterbewegung, Dirac equation, semiclassical approximation, spin-1/2 particles, eigenspinors, quantum ergodicity
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