Abstract
In the last chapter of the book we offer a short presentation of the algebraic formulation of quantum theories, and we will state and prove a central theorem about the so-called GNS construction. We will discuss how to treat the notion of quantum symmetry in this framework, by showing that an algebraic quantum symmetry can be implemented (anti)unitarily in GNS representations of states invariant under the symmetry.
I would like to make a confession which may seem immoral:I do not believe absolutely in Hilbert spaces any more.
von Neumann, letter to Birkhoff
about the mathematical formulation of QM (1935)
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© 2013 Springer-Verlag Italia
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Moretti, V. (2013). Introduction to the Algebraic Formulation of Quantum Theories. In: Spectral Theory and Quantum Mechanics. UNITEXT(). Springer, Milano. https://doi.org/10.1007/978-88-470-2835-7_14
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DOI: https://doi.org/10.1007/978-88-470-2835-7_14
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2834-0
Online ISBN: 978-88-470-2835-7
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