2018/02/09 by A. Di Piazza
Mathematics · Physics and Astronomy · #Bessel function #Completeness (order theory) #Laser-Matter Interactions and Applications #Laser-Plasma Interactions and Diagnostics #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Orthonormal basis #Orthonormality #Physics #Propagator #Quantum chaos and dynamical systems #Quantum mechanics #hep-ph
paper · pdf · doi:10.1103/physrevd.97.056028
published as Phys. Rev. D 97, 056028 (2018) · 25 pages, no figures
arxiv created 2018/02/09 · openalex publication_date 2018/03/30 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Volkov states and Volkov propagator are the basic analytical tools to investigate QED processes occurring in the presence of an intense plane-wave electromagnetic field. In the present paper we provide alternative and relatively simple proofs of the completeness and of the orthonormality at a fixed time of the Volkov states. Concerning the completeness, we exploit some known properties of the Green's function of the Dirac operator in a plane wave, whereas the orthonormality of the Volkov states is proved, relying only on a geometric argument based on the Gauss theorem in four dimensions. In relation with the completeness of the Volkov states, we also study some analytical properties of the Green's function of the Dirac operator in a plane wave, which we explicitly prove to coincide with the Volkov propagator in configuration space. In particular, a closed-form expression in terms of modified Bessel functions and Hankel functions is derived by means of the operator technique in a plane wave and different asymptotic forms are determined. Finally, the transformation properties of the Volkov propagator under general gauge transformations and a general gauge-invariant expression of the so-called dressed mass in configuration space are presented.