Magnetic fields on resistance spaces

2015/01/06 by Michael Hinz, Hinz, Michael, Luke Rogers +1
Mathematics · Physics and Astronomy · #28A80 #31E05 #47A07 #60J35 #81Q10 #81Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #math-ph #math.AP #math.FA #math.MP #msc:28A80 #msc:31E05 #msc:47A07 #msc:60J35 #msc:81Q10 #msc:81Q35

paper · pdf · doi:10.48550/arxiv.1501.01100

arxiv created 2016/08/31 · arxiv updated 2016/09/01

Abstract

On a metric measure space X that supports a regular, strongly local resistance form we consider a magnetic energy form that corresponds to the magnetic Laplacian for a particle confined to X. We provide sufficient conditions for closability and self-adjointness in terms of geometric conditions on the reference measure without assuming energy dominance.

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