Page, Julien and Catren, Gabriel (2013) On the Galoisian Structure of Heisenberg Indeterminacy Principle. [Preprint]
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Abstract
We revisit Heisenberg indeterminacy principle in the light of the Galois-Grothendieck theory for the case of finite abelian Galois extensions. In this restricted framework, the Galois-Grothendieck duality between finite K-algebras split by a Galois extension L and finite Gal(L:K)-sets can be reformulated as a Pontryagin-like duality between two abelian groups. We then define a Galoisian quantum theory in
which the Heisenberg indeterminacy principle between conjugate canonical variables can be understood as a form of Galoisian duality: the larger the group of automorphisms H (a subgroup of G) of the states in a G-set O = G/H, the
smaller the ``conjugate'' observable algebra that can be consistently valuated on such states. We then argue that this Galois indeterminacy principle can be understood as a particular case of the Heisenberg indeterminacy principle formulated in terms of the notion of entropic
indeterminacy. Finally, we argue that states endowed with a group of automorphisms H can be interpreted as squeezed coherent states, i.e. as states that minimize the Heisenberg indeterminacy relations.
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| Item Type: | Preprint | |||||||||
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| Keywords: | Galois-Grothendieck Theory; Quantum mechanics; Heisenberg Indeterminacy Principle, Symmetries/Invariants | |||||||||
| Subjects: | Specific Sciences > Mathematics Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | Dr. Gabriel Catren | |||||||||
| Date Deposited: | 03 Dec 2013 17:02 | |||||||||
| Last Modified: | 03 Dec 2013 17:02 | |||||||||
| Item ID: | 10118 | |||||||||
| Subjects: | Specific Sciences > Mathematics Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Symmetries/Invariances |
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| Date: | 1 December 2013 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/10118 |
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