Year-end Sale % OFF 
Abstract
This chapter gives an extensive treatment of Hilbert space representations of the canonical commutation relation and the Weyl algebra. After collecting algebraic properties of this algebra we treat the Bargmann–Fock representation and the corresponding uniqueness theorem. Then the Schrodinger representation is studied and the Stone–von Neumann uniqueness theorem is proved. The Segal–Bargmann transform establishes the unitary equivalence of both representations. Kato’s theorem on the characterization of Schrodinger pairs in terms of resolvents is derived. Further, the Heisenberg uncertainty principle and the Groenewold–van Hove “no-go theorem for quantization are developed.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
