The uncertainty principle for operators determined by Lie groups

2003/01/01 by Jens Gerlach Christensen, Christensen, Jens Gerlach
Mathematics · Physics and Astronomy · #22E45 #47B15 #47B25 #81Q10 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:22E45 #msc:47B15 #msc:47B25 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.math/0301002

2 pages

arxiv created 2003/01/25 · arxiv updated 2009/11/30

Abstract

For unbounded operators A,B and C in general, with C closure of [A,B] does not lead to the uncertainty relation ||Au|| ||Bu|| >= |<C u,u> |/2. If A,B and C are part of the generators of a unitary representation of a Lie group then the uncertainty principle above holds.

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