Abstract
AbstractWe consider a translation-invariant Pauli–Fierz model describing a non-relativistic charged quantum mechanical particle interacting with the quantized electromagnetic field. The charged particle may be spinless or have spin one half. We decompose the Hamiltonian with respect to the total momentum into a direct integral of so-called fiber Hamiltonians. We perform an infrared renormalization, in the sense of norm resolvent convergence, for each fiber Hamiltonian, which has the physical interpretation of removing an infinite photon cloud. We show that the renormalized fiber Hamiltonians have a ground state for almost all values for the total momentum with modulus less than one.
Funder
Eberhard Karls Universität Tübingen
Publisher
Springer Science and Business Media LLC
Reference45 articles.
1. Abdesselam, A., Hasler, D.: Analyticity of the ground state energy for massless Nelson models. Commun. Math. Phys. 310(2), 511–536 (2012)
2. Aleksandrov, A.: Almost everywhere existence of the second differential of a convex function and some properties of convex functions. Leningrad Univ. Ann. 37, 3–35 (1939)
3. Arai, A.: Ground state of the massless Nelson model without infrared cutoff in a non-Fock representation. Rev. Math. Phys. 13(09), 1075–1094 (2001)
4. Arai, A.: Analysis on Fock Spaces and Mathematical Theory of Quantum Fields. An Introduction to Mathematical Analysis of Quantum Fields. World Scientific, New Jersey (2018)
5. Bach, V., Chen, T., Fröhlich, J., Sigal, I.: The renormalized electron mass in nonrelativistic quantum electrodynamics. J. Funct. Anal. 243(2), 426–535 (2007)