Bohr’s correspondence principle for the renormalized Nelson model. (English) Zbl 1394.35383
The purpose of this paper is to study the Schrödinger-Klein-Gordon (S-KG) equation coupled with dressed interaction (S-KG[D]). The main theorem states that the Bohr correspondence principle holds between the renormalized Nelson model and the S-KG classical flow. First the dressing transform is introduced followed by renormalization. Then the Yukawa-type interaction is defined followed by the classical Hamiltonians. The proofs use dominated convergence theorem, Fubini theorem, Gronwall lemma, Strichart estimate, Hölder, Schwartz inequalities.
Reviewer: Thomas Ernst (Uppsala)
MSC:
| 35Q40 | PDEs in connection with quantum mechanics |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
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