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.

arXiv comment7 pages, 1 figure, 3 tables and a supplementary material

References in corpus (26)

• Gauge-Invariant Decomposition of Nucleon Spin and Its Spin-Off
• Chiral Quantum Optics
• Transverse and longitudinal angular momenta of light
• Chiral nanophotonic waveguide interface based on spin-orbit coupling of light
• Extraordinary momentum and spin in evanescent waves
• A topological quantum optics interface
• Optical skyrmions in evanescent electromagnetic fields
• The angular momentum controversy: What's it all about and does it matter?
• Dual electromagnetism: Helicity, spin, momentum, and angular momentum
• Universal spin-momentum locking of evanescent waves
• Nanoscale chiral valley-photon interface through optical spin-orbit coupling
• Dispersion relations in real and virtual Compton scattering
• Reply to the Comment on "Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited" [PRL 100:232002 (2008)]
• Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited
• Spin and orbital angular momentum in gauge theories (II): QCD and nucleon spin structure
• Chirality and angular momentum in optical radiation
• On Gauge-Invariant Decomposition of Nucleon Spin
• Geometrical approach to the proton spin decomposition
• The Aharonov-Bohm phase is locally generated (like all other quantum phases)
• Quantum gyro-electric effect: Photon spin-1 quantization in continuum topological bosonic phases
• Non-local topological electromagnetic phases of matter
• 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

Cited by in corpus (15)

• Spin and Orbital Angular Momentum of Coherent Photons in a Waveguide
• Spin and Orbital Angular Momenta of Electromagnetic Waves: From Classical to Quantum Forms
• Special Theory of Relativity for a Graded Index Fibre
• Quantum Commutation Relationship for Photonic Orbital Angular Momentum
• Photonic Quantum Chromo-Dynamics
• QED based on eight-dimensional spinorial wave equation of the electromagnetic field and the emergence of quantum gravity
• Spin of Photons: Nature of Polarisation
• Macroscopic Single-Qubit Operation for Coherent Photons
• Helicity is a topological invariant of massless particles: C=-2h
• Dirac Equation for Photons: Origin of Polarisation
• Four no-go theorems on the existence of spin and orbital angular momentum of massless bosons
• Zero curvature is a necessary and sufficient condition for a spin-orbital decomposition
• Macroscopic Singlet, Triplet, and Colour-Charged States of Coherent Photons
• Zitterbewegung, momentum and spin dynamics of electromagnetic waves in linear dielectric medium
• Optically induced static magnetic field in ensemble of nitrogen-vacancy centers in diamond