Partially Classical States of a Boson Field |
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Authors: | Honegger Reinhard Rieckers Alfred |
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Institution: | (1) Mathematisches Institut, Universität Mannheim, D-68131 Mannheim, Germany;(2) Institut für Theoretische Physik, Universität Tübingen, D–72076 Tübingen, Germany |
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Abstract: | Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions. |
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Keywords: | Bauer simplexes of (quantum) states on the C*-Weyl algebra Bochner– Minlos– Sazonov results classical states in quantum optics positive-definite functions weak distributions and classical field statistics |
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