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 TMF, 1984, Volume 61, Number 3, Pages 347–363 (Mi tmf5738)

Methods of Weyl representation of the phase space and canonical transformations. I

V. G. Budanov

Abstract: The structure of the kernel of a canonical transformation and a differential equation for the symbol of the intertwining operator are found. The symbol of a general linear canonical transformation is constructed in terms of a Cayley transformation of the symplectic transformation of the phase space. Its singularities and applications to group theory are studied. The Green's functions and spectral projectors of arbitrary quadratic systems are constructed using the classification methods of classical mechanics.

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English version:
Theoretical and Mathematical Physics, 1984, 61:3, 1183–1195

Bibliographic databases:

Citation: V. G. Budanov, “Methods of Weyl representation of the phase space and canonical transformations. I”, TMF, 61:3 (1984), 347–363; Theoret. and Math. Phys., 61:3 (1984), 1183–1195

Citation in format AMSBIB
\Bibitem{Bud84} \by V.~G.~Budanov \paper Methods of Weyl representation of the phase space and canonical transformations.~I \jour TMF \yr 1984 \vol 61 \issue 3 \pages 347--363 \mathnet{http://mi.mathnet.ru/tmf5738} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=778356} \transl \jour Theoret. and Math. Phys. \yr 1984 \vol 61 \issue 3 \pages 1183--1195 \crossref{https://doi.org/10.1007/BF01035002} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984ALJ5900003} 

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This publication is cited in the following articles:
1. V. G. Budanov, “Methods of weyl representation of the phase space and canonical transformations. II”, Theoret. and Math. Phys., 64:1 (1985), 656–666
2. V. G. Budanov, “An equation for disentangling time-ordered exponentials with arbitrary quadratic generators”, Theoret. and Math. Phys., 71:3 (1987), 570–574
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