Saturday, May 9, 2020

connections


14 May, 2020 

Philip Feinsilver

Secret passage through Lie algebras, recurrences, and polynomials









4 comments:

  1. You had mentioned Segal-Bargmann space as a possible realization of the Heisenberg-Weyl group. Do you happen to know a case in which this realization is advantageous over other representations.

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    1. Thank you for comment/question. Probably if you are using analytic function theory. As well, for geometric point(s) of view.

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  2. In your talk you mentioned about the connection between commutation relations and variation (derivative). This interpretation is very useful in quantum mechanics. For example, the commutation relation between momentum ${\bf P}$ and angular momentum ${\bf L}$ is $[{\bf P},{\bf L}]$ and could be interpreted as the change in momentum ${\bf P}$ under rotations. I am aware of Schwinger's work, which highlights this connection. Would you be able to suggest more references. Thanks. Nice talk.

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    1. Actually you are right. Schwinger was the consummate master of these techniques. You can also develop approaches to things like Virasoro algebra and a variety of field theory constructions. Work of Accardi and Boukas, may be of interest.

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