Homotopy and Path Integrals in the Time-dependent Aharonov-Bohm Effect View Full Text


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Article Info

DATE

2011-09

AUTHORS

B. Gaveau, A. M. Nounou, L. S. Schulman

ABSTRACT

For time-independent fields the Aharonov-Bohm effect has been obtained by idealizing the coordinate space as multiply-connected and using representations of its fundamental homotopy group to provide information on what is physically identified as the magnetic flux. With a time-dependent field, multiple-connectedness introduces the same degree of ambiguity; by taking into account electromagnetic fields induced by the time dependence, full physical behavior is again recovered once a representation is selected. The selection depends on a single arbitrary time (hence the so-called holonomies are not unique), although no physical effects depend on the value of that particular time. These features can also be phrased in terms of the selection of self-adjoint extensions, thereby involving yet another question that has come up in this context, namely, boundary conditions for the wave function. More... »

PAGES

1462

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10701-011-9559-y

DOI

http://dx.doi.org/10.1007/s10701-011-9559-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1013079531


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133 https://www.grid.ac/institutes/grid.254280.9 schema:alternateName Clarkson University
134 schema:name Physics Department, Clarkson University, 13699-5820, Potsdam, NY, USA
135 rdf:type schema:Organization
 




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