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MP: Theoretische und Mathematische Grundlagen der Physik

MP 11: Quantengravitation 2 und Quantisierungsmethoden 2

MP 11.4: Vortrag

Donnerstag, 30. März 2006, 16:00–16:30, HG2-HS4

Convergence of the Wick Star Product — •Svea Beiser, Hartmann Roemer, and Stefan Waldmann — Fakultaet fuer Mathematik und Physik, Albert-Ludwig University Freiburg, Physikalisches Institut, Hermann Herder Strasse 3, D 79104 Freiburg, Germany

Deformation quantization considers the Poisson Algebra of smooth complex-valued function on a Poisson manifold as observable algebra in classical mechanics. By replacing the pointwise product with the formal star-product one gets a model for the quantum mechanical observables corresponding to the classical system described by the Poisson manifold. The aim is to replace the formal parameter by Planck’s Constant and still have a convergent system. We show a scheme to construct a Frechet space as a holomorphic subspace of analystic functions where the Wick star product converges and is continous. The resulting Frechet algebra depending on Plancks’s Constant is studied in detail including a *-representation of the algebra in the Bargmann-Fock space and a discussion of star exponentials and coherent states.