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 GaloisGrothendieck theory for the case of finite abelian Galois extensions. In this restricted framework, the GaloisGrothendieck duality between finite Kalgebras split by a Galois extension L and finite Gal(L:K)sets can be reformulated as a Pontryaginlike 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 Gset 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:  GaloisGrothendieck 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:  http://philsciarchive.pitt.edu/id/eprint/10118 
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