Homotopy and Path Integrals in the Time-dependent Aharonov-Bohm Effect
| Autor: | Antigone M. Nounou, Bernar Gaveau, Lawrence S. Schulman |
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| Rok vydání: | 2011 |
| Předmět: |
Homotopy group
Homotopy lifting property Field (physics) 010308 nuclear & particles physics Homotopy Mathematical analysis General Physics and Astronomy 01 natural sciences n-connected symbols.namesake 0103 physical sciences symbols Boundary value problem Coordinate space 010306 general physics Aharonov–Bohm effect Mathematics |
| Zdroj: | Foundations of Physics. 41:1462-1474 |
| ISSN: | 1572-9516 0015-9018 |
| DOI: | 10.1007/s10701-011-9559-y |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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