论文标题
光子的自旋算子的量子场理论
Quantum field theory for spin operator of the photon
论文作者
论文摘要
自然界中的所有基本颗粒都可以归类为带有半数旋转和带有整数自旋的玻色子的费米子。在量子电动力学（QED）中，即使狄拉克粒子的旋转定义得很好，也存在有关量规场粒子的自旋描述 - 光子的开放性问题。使用量子场理论，我们发现了旋转角动量（SAM）$ \ boldsymbol {s} _ {m} =（1/c）\ int d^{3} x \boldsymbolπ\ times \ boldsymbol \ boldsymbol {a} $ {a} $和眶角动量（OAM（OAM）（OAM）） $ \ boldsymbol {l} _ {m} = - （1/c）\ int d^{3}xπ^μ\ boldsymbol {x} \ times \ boldsymbol {\ nabla}a_μ$ of photon的光子，其中$π^μ$是conjugate canonical canonical mange $ a^$ a^$ a^$ a^。我们还揭示了Dirac Fields和Maxwell Fields的角动量换向关系之间的完美对称性。我们从上述量子算子中得出了经典电磁场的众所周知的OAM和SAM。我们的工作表明，自旋和OAM操作员通勤对于同时观察和分离SAM和OAM很重要。光子的轨道和旋转角动量的正确换向关系在量子光学，拓扑光子和纳米光子学中都有应用，将来可以扩展到核子的自旋结构。
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) $\boldsymbol{S}_{M}=(1/c)\int d^{3}x\boldsymbolπ\times\boldsymbol{A}$ and orbital angular momentum (OAM) $\boldsymbol{L}_{M}=-(1/c)\int d^{3}xπ^μ\boldsymbol{x}\times\boldsymbol{\nabla}A_μ$ of the photon, where $π^μ$ is the conjugate canonical momentum of the gauge field $A^μ$. 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.
