Quantum field theory for spin operator of the photon

Abstract

All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer spin. Within quantum electrodynamics (QED), even though the spin of the Dirac particle is well defined, there exist open questions on the quantized description of spin of the gauge field particle -- the photon. Using quantum field theory, we discover the quantum operators for the spin angular momentum (SAM) ${\mathbf{S}}_M=(1/c)\int d^{3}x\mathbf{\pi }\times \mathbf{A}$ and orbital angular momentum (OAM) ${\mathbf{L}}_M=-(1/c)\int d^{3}x{\pi }^{\mu }\mathbf{x}\times \nabla A_{\mu }$ of the photon, where ${\pi }^{\mu }$ is the conjugate canonical momentum of the gauge field $A^{\mu }$. We also reveal a perfect symmetry between the angular momentum commutation relations for Dirac fields and Maxwell fields. We derive the well-known OAM and SAM of classical electromagnetic fields from the above defined quantum operators. Our work shows that the spin and OAM operators commute which is important for simultaneously observing and separating the SAM and OAM. The correct commutation relations of orbital and spin angular momentum of the photon have applications in quantum optics, topological photonics as well as nanophotonics and can be extended in the future for the spin structure of nucleons.

7 pages, 1 figure, 3 tables and a supplementary material

References in corpus (12)

• Chiral Quantum Optics
• Chiral nanophotonic waveguide interface based on spin-orbit coupling of light
• Nanoscale chiral valley-photon interface through optical spin-orbit coupling
• Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited
• Reply to the Comment on "Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited" [PRL 100:232002 (2008)]
• Chirality and angular momentum in optical radiation
• The Aharonov-Bohm phase is locally generated (like all other quantum phases)
• Quantum structured light: Non-classical spin texture of twisted single-photon pulses
• Quantum sensing of photonic spin density
• Boundary terms in quantum field theory and the spin structure of QCD
• Direct Light Orbital Angular Momentum Detection in Mid-Infrared based on Type-II Weyl Semimetal TaIrTe4
• Measures of Helicity and Chirality of Optical Vortex Beams

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• Spin of Photons: Nature of Polarisation
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• Helicity is a topological invariant of massless particles: C=-2h
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• Macroscopic Singlet, Triplet, and Colour-Charged States of Coherent Photons
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