Quantum Deformed Canonical Transformations, W_{\infty}-algebras and Unitary Transformations

Details Quantum Deformed Canonical Transformations, W_{\infty}-algebras and Unitary Transformations Quantum Deformed Canonical Transformations, W_{\infty}-algebras and Unitary Transformations

2003-06-23

arxiv.org/abs/hep-th/0306221v1

Int.J.Mod.Phys. A9 (1994) 5801-5820

Physics

High Energy Physics

High Energy Physics - Theory

TeX file with phyzzs macro, 23 pages, no figures

Scientific paper

We investigate the algebraic properties of the quantum counterpart of the classical canonical transformations using the symbol-calculus approach to quantum mechanics. In this framework we construct a set of pseudo-differential operators which act on the symbols of operators, i.e., on functions defined over phase-space. They act as operatorial left- and right- multiplication and form a $W_{\infty}\times W_{\infty}$- algebra which contracts to its diagonal subalgebra in the classical limit. We also describe the Gel'fand-Naimark-Segal (GNS) construction in this language and show that the GNS representation-space (a doubled Hilbert space) is closely related to the algebra of functions over phase-space equipped with the star-product of the symbol-calculus.

Affiliated with

Also associated with

No associations

Rating

Quantum Deformed Canonical Transformations, W_{\infty}-algebras and Unitary Transformations 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 Quantum Deformed Canonical Transformations, W_{\infty}-algebras and Unitary Transformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Deformed Canonical Transformations, W_{\infty}-algebras and Unitary Transformations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-513692