An Infinitesimal Version of the Stone-von Neumann Theorem

2017/04/12 by Huang, Leonard
#47L60 #81S05 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Primary 17B15 #Representation Theory (math.RT) #Secondary 17B81

paper · doi:10.48550/arxiv.1704.03859

Abstract

In this paper, we present an infinitesimal version of the Stone-von Neumann Theorem. This work was motivated by the need to formulate the uniqueness property of the Heisenberg Commutation Relation purely in terms of unbounded operators.

Related

• An invariant for pairs of almost commuting unbounded operators
• Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications
• Counterexamples Related to Commutators of Unbounded Operators
• Dichotomy between operators acting on finite and infinite dimensional Hilbert spaces
• Amenability and Uniqueness