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Reduction of quantum systems and the local Gauss law.

ABSTRACT: We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004).

SUBMITTER: Stienstra R

PROVIDER: S-EPMC6182777 | biostudies-other | 2018

REPOSITORIES: biostudies-other

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Reduction of quantum systems and the local Gauss law.

Stienstra Ruben R van Suijlekom Walter D WD

Letters in mathematical physics 20180503 11

We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004). ...[more]

PMID: 30369712

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