Direct calculation of the Berry phase for spins and helicities
Abstract
The Berry phase for spins or helicities is calculated in a simple way in which it appears more as a property of the spin states than of the Hamiltonian. The calculation applies to nonrelativistic particles or relativistic particles with either zero or nonzero mass. A simple way to see how the Berry phase corresponds to rotation of the electric and magnetic fields of plane-polarized light is also pointed out.
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This effective magnetic field takes the form of a 'magnetic monopole' located at the origin of p-space.
“Remarkably, this field takes the form of a ' magnetic monopole ' located at the origin of p -space [12,17 -19,26 -35] (cf. [38,39]).”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [19]
Cites
Quantal phase factors accompanying adiabatic changes
Berry, M. V. (1984) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1984.0023 · Cited by 9,252 · see citing works
Observation of Berry's Topological Phase by Use of an Optical Fiber
Tomita, A., & Chiao, R. Y. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.937 · Cited by 810 · see citing works
Manifestations of Berry's Topological Phase for the Photon
Chiao, R. Y., & Wu, Y.-S. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.933 · Cited by 482 · see citing works
Synthesis of Covariant Particle Equations
Foldy, L. L. (1956) · Physical Review · doi:10.1103/physrev.102.568 · Cited by 331 · see citing works
Relativistic Particle Systems with Interaction
Foldy, L. L. (1961) · Physical Review · doi:10.1103/physrev.122.275 · Cited by 312 · see citing works
Berry’s phase in the relativistic theory of spinning particles
Bialynicki-Birula, I., & Bialynicka-Birula, Z. (1987) · Physical Review D · doi:10.1103/physrevd.35.2383 · Cited by 65 · see citing works
Reduction of Reducible Representations of the Poincaré Group to Standard Helicity Representations
Moses, H. E. (1968) · Journal of Mathematical Physics · doi:10.1063/1.1664542 · Cited by 22 · see citing works
What happens to the position, spin, and parity when the mass goes to zero
Jordan, T. F. (1982) · Journal of Mathematical Physics · doi:10.1063/1.525298 · Cited by 1 · see citing works
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Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
Bliokh, K. Y. (2009) · Journal of Optics A: Pure and Applied Optics · doi:10.1088/1464-4258/11/9/094009 · Cited by 217 · see citing works
Thomas precession, spin-orbit interaction, and Berry’s phase
Mathur, H. (1991) · Physical Review Letters · doi:10.1103/physrevlett.67.3325 · Cited by 87 · see citing works
Berry and Pancharatnam topological phases of atomic and optical systems
Ben-Aryeh, Y. (2004) · Journal of Optics B: Quantum and Semiclassical Optics · doi:10.1088/1464-4266/6/4/r01 · Cited by 40 · see citing works
Spin-orbit interactions of light in isotropic media
Bliokh, K. Y., Aiello, A., & Alonso, M. A. (2012) · The Angular Momentum of Light · doi:10.1017/cbo9780511795213.009 · Cited by 20 · see citing works
- Authors
- Jordan, T. F.
- Affiliations
- University of Minnesota, Duluth (US)
- Corresponding author
- Jordan, Thomas F.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1987-08-01
- Volume
- 28
- Issue
- 8
- Pages
- 1759-1760
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2062050599
- Cited by
- 23
- References
- 8
- Citations by year
- 2026: 1 · 2025: 1 · 2022: 1 · 2019: 1 · 2017: 1 · 2012: 1
- FWCI
- 2.16
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Mathematical Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Keywords
- Berry phase, spin, helicity, spin states, relativistic particles, non-relativistic particles, linearly polarized light
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