Abstract
The notion of symmetry in Quantum Theory is quite abstract. There are at least three distinct ideas, respectively due to Wigner, Kadison and Segal.
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Notes
- 1.
A Lie group is a second-countable Hausdorff real-analytic manifold, locally homeomorphic to \({\mathbb R}^n\), and equipped with smooth group operations. Real analyticity can be replaced by smoothness.
- 2.
A set A ⊂ SU(2)∕ker(π) = SO(3) is open if and only if π −1(A) ⊂ SU(2) is open.
- 3.
From the experimental point of view, a Hausdorff topology means that we can distinguish different elements of the group even if our knowledge is affected by experimental errors.
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Moretti, V. (2019). Quantum Symmetries. In: Fundamental Mathematical Structures of Quantum Theory. Springer, Cham. https://doi.org/10.1007/978-3-030-18346-2_7
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DOI: https://doi.org/10.1007/978-3-030-18346-2_7
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