2018/05/02 by Arvind, S. Chaturvedi, Subhash Chaturvedi +1 · 3 citations
Physics and Astronomy · #Angular momentum #Angular momentum coupling #Angular momentum operator #Hilbert space #Orbital Angular Momentum in Optics #Paraxial approximation #Quantization (signal processing) #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum and Classical Electrodynamics #Total angular momentum quantum number #quant-ph
paper · pdf · doi:10.1002/prop.201800040
published in Fortschritte der Physik 66(10) (Wiley) · Revtex 4-1 16 pages
arxiv created 2018/05/02 · openalex created_date 2018/05/07 · openalex publication_date 2018/08/28 · arxiv updated 2018/11/14 · openalex updated_date 2026/08/05
Abstract We develop a general framework to analyze two much discussed questions concerning (a) ‘orbital’ and ‘spin’ angular momentum carried by light and (b) the paraxial approximation of the free Maxwell system both in the classical as well as quantum domains. After formulating the classical free Maxwell system in the transverse gauge in terms of complex analytical signals we derive expressions for the constants of motion (COM) associated with its Poincaré symmetry. In particular, we show that the COM corresponding to the total angular momentum J naturally splits into an ‘orbital’ part L and a ‘spin’ part S each of which is a COM in its own right. We then discuss quantization of the free Maxwell system and construct the operators generating the Poincaré group and analyze their algebraic properties and find that while the quantum counterparts and of L and S go over into bona fide observables, they fail to satisfy the angular momentum algebra making their interpretation as ‘orbital’ and ‘spin’ operators untenable at the quantum level. On the other hand does satisfy the angular momentum algebra and together with generates the group E (3). We then present an analysis of single photon states, paraxial quantization both in the scalar as well as vector cases, and single photon states in the paraxial regime. All along a close connection is maintained with the Hilbert space that naturally arises in the classical context.