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.
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.
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.
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.
ReplyDeleteThank you for comment/question. Probably if you are using analytic function theory. As well, for geometric point(s) of view.
DeleteIn 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.
ReplyDeleteActually 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.
Delete