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On the Galoisian Structure of Heisenberg Indeterminacy Principle

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
Creators:
CreatorsEmailORCID
Page, Julienju.page@hotmail.fr
Catren, Gabrielgabrielcatren@gmail.com
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
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
Date: 1 December 2013
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/10118

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