MaPhySto
Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

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Funded by The Danish National Research Foundation

Graduate course on

Canonical Commutation Relations and their Applications in Quantum Theory

Lectures by Jan Derezinski, Warsaw University

While visiting MaPhySto, Jan Derezinski gave a series of lectures (2 hours of lectures plus 2 hours of exercise sessions per week) on Canonical Commutation Relations and their Applications in Quantum Theory.

The course took place in March-May, 2000.

Contents

The topics treated include:

• Algebraic preliminaries (tensor products,...)
• Schrödinger representation and the Kohn-Nirenberg quantization
• Canonical commutation relations (CCR) and the Weyl quantization
• Coherent states
• Fock spaces and the Wick quantization
• Gaussian stochastic processes
• Symplectic and metaplectic group
• Inequivalent representations of CCR
• Semi-classical functional calculus
• Semi-classical propagation of observables
• Semi-classical geometric asymptotics (WKB method)

Prerequisites

Basic knowledge of linear algebra, quantum mechanics and functional analysis.

Note

In the week 2.-9. August 2000, MaPhySto and the EU TMR-network the EU-network Postdoctoral training program in partial differential equations and applications in quantum mechanics (ERBFMRXCT960001) will jointly organize a

Summer School on Canonical Quantization Aspects of Quantum Field Theory

to be held at Sandbjerg Manor, Sønderborg. The present course provides the necessary background for participating in the Summer School. More information is available from www.maphysto.dk.