Abstract
We define creation and annihilation operators as generators of an associative algebra with the commutation relations as defining relations. This is a special case of a Weyl algebra. We discuss Weyl algebras, show that ordered monomials form a basis, introduce multisets and their notation. The vacuum and the scalar product are defined in a natural way. We prove an algebraic theorem due to Wick.
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N. Bourbaki, Algebra I (Springer, Berlin, 1989)
N. Bourbaki, Lie Groups and Lie Algebras. Chapters 1–3 (Springer, Berlin, 1989)
J.M. Jauch, M. Rohrlich, The Theory of Photons and Electrons (Springer, Berlin, 1976)
H. Weyl, Gruppentheorie und Quantenmechanik (Leipzig, 1931)
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© 2014 Springer-Verlag Berlin Heidelberg
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von Waldenfels, W. (2014). Weyl Algebras. In: A Measure Theoretical Approach to Quantum Stochastic Processes. Lecture Notes in Physics, vol 878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45082-2_1
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DOI: https://doi.org/10.1007/978-3-642-45082-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45081-5
Online ISBN: 978-3-642-45082-2
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