Field-theoretic Weyl Quantization as a
Strict and Continuous Deformation Quantization |
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Authors: | Ernst Binz Reinhard Honegger and Alfred Rieckers |
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Institution: | (1) Institut für Mathematik und Informatik, Universität Mannheim, 68131 Mannheim, Germany;(2) Institut für Mathematik und Informatik, Universität Mannheim, 68131 Mannheim, Germany;(3) Present address: Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany;(4) Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany |
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Abstract: | For an arbitrary (possibly infinite-dimensional) pre-symplectic test function
space
the family of Weyl algebras
, introduced in a previous work 1], is shown to constitute a continuous field of C*-algebras in the sense
of Dixmier. Various Poisson algebras, given as abstract (Fréchet-) *-algebras which
are C*-norm-dense in
, are constructed as domains for a Weyl quantization,
which maps the classical onto the quantum mechanical Weyl elements. This kind
of a quantization map is demonstrated to realize a continuous strict deformation
quantization in the sense of Rieffel and Landsman. The quantization is proved to
be equivariant under the automorphic actions of the full affine symplectic group.
The relationship to formal field quantization in theoretical physics is discussed by
suggesting a representation dependent direct field quantization in mathematically
concise terms.
Communicated by Joel FeldmanSubmitted 07/10/03, accepted 07/11/03 |
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Keywords: | |
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