Weyl calculus in Wiener spaces and in QED View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03

AUTHORS

L. Amour, R. Lascar, J. Nourrigat

ABSTRACT

The concern of this article is a semiclassical Weyl calculus on an infinite dimensional Hilbert space H. If (i, H, B) is a Wiener triplet associated to H, the quantum state space will be the space of L2 functions on B with respect to a Gaussian measure with h / 2 variance, where h is the semiclassical parameter. We prove the boundedness of our pseudodifferential operators (PDO) in the spirit of Calderón–Vaillancourt with an explicit bound, a Beals type characterization, and metaplectic covariance. An application to a model of quantum electrodynamics is added in the last section (Sect. 7), for fixed spin 1 / 2 particles interacting with the quantized electromagnetic field (photons). We prove that some observable time evolutions, the spin evolutions, the magnetic and electric evolutions when subtracting their free evolutions, are PDO in our class. More... »

PAGES

1-47

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11868-018-0269-5

DOI

http://dx.doi.org/10.1007/s11868-018-0269-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1110638927


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