Abstract
We study the Dirac operator D 0 in an external potential V, coupled to a quantized radiation field with energy H f and vector potential A. Our result is a Chernoff-type theorem, i.e., we prove, for the operator D 0+α · A+V +λ H f with λ ∈{0, 1}, that the essential self-adjointness is not affected by the behavior of V at ∞.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Araim A. (2000). A particle-field Hamiltonian in relativistic quantum electrodynamics. J. Math. Phy. 41: 4271–4283
Arai A. (2003). Non-relativistic limit of a Dirac-Maxwell operator in relativistic quantum electrodynamics. Rev. Math. Phys. 15: 245–270
Bach V., Fröhlich J. and Sigal I.M. (1998). Quantum electrodynamics of confined nonrelativistic particles. Adv. Math. 137: 299–395
Blank J., Exner P. and Havlíček M. (1994). Hilbert space operators in quantum physics. AIP Press, New York
Chernoff P. (1973). Essential self-adjointness of powers of generators of hyperbolic equations. J. Funct. Anal. 12: 401–414
Chernoff P. (1977). Schrödinger and Dirac operators with singular potentials and hyperbolic equations. Pac. J. Math. 72: 361–382
Griesemer M. and Tix C. (1999). Instability of a pseudo-relativistic model of matter with self-generated magnetic field. J. Math. Phys. 40: 1780–1791
Kato T. (1966). Perturbation Theory for linear operators, vol. 132. Grundlehren der mathematischen Wissenschaften. Springer-Verlag, Berlin
Lieb E. and Loss M. (2002). Stability of a model of relativistic quantum electrodynamics. Commun. Mathe. Phys. 228: 561–588
Lieb E., Siedentop H. and Solovej J.P. (1997). Stability and instability of relativistic electrons in classical electromagnetic fields. J. Stat. Phys. 89: 37–59
Reed M. and Simon B. (1980). Methods of modern mathematical physics, revised and enlarged edn. Functional analysis, vol. I. Academic, San Diego
Reed M. and Simon B. (1975). Methods of modern mathematical physics. Fourier analysis, self-adjointness, vol. II. Academic, San Diego
Reed M. and Simon B. (1978). Methods of modern mathematical physics. Analysis of operators, vol. IV. Academic, San Diego
Thaller B. (1992). The Dirac Equation. Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Stockmeyer, E., Zenk, H. Dirac Operators Coupled to the Quantized Radiation Field: Essential Self-adjointness à la Chernoff. Lett Math Phys 83, 59–68 (2008). https://doi.org/10.1007/s11005-007-0205-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11005-007-0205-8