Physics – Mathematical Physics
Scientific paper
2002-11-14
Lett. Math Phys. 65, 159 (2003)
Physics
Mathematical Physics
LateX, with additional results, especially on the infinite dimensional case
Scientific paper
Representations of CCR algebras in spaces of entire functions are classified on the basis of isomorphisms between the Heisenberg CCR algebra A_H and star algebras of holomorphic operators. To each representations of such algebras, satisfying a regularity and a reality condition, one can associate isomorphisms and inner products so that they become Krein star representations of A_H, with the gauge transformations implemented by a continuous U(1) group of Krein isometries. Conversely, any holomorphic Krein representation of A_H, having the gauge transformations implemented as before and no null subrepresentation, is shown to be contained in a direct sum of the above representations. The analysis is extended to infinite dimensional CCR algebras, under a spectral condition for the implementers of the gauge transformations.
Mnatsakanova M.
Morchio Giovanni
Strocchi Franco
Vernov Yu.
No associations
LandOfFree
Representations of the Heisenberg algebra on holomorphic functions and Krein structures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Representations of the Heisenberg algebra on holomorphic functions and Krein structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of the Heisenberg algebra on holomorphic functions and Krein structures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-473762