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He-McKellar-Wilkens-type effect, quantum holonomies and Aharonov-Bohm-type effect for bound states from the Lorentz symmetry breaking effects. (English) Zbl 1353.81062

Summary: From the effects of the Lorentz symmetry violation in the CPT-even gauge sector of the Standard Model Extension determined by a tensor background \((KF)_{\mu\nu\alpha\beta}\), we establish a possible scenario where an analogue of the He-McKellar-Wilkens effect can stem from. Besides, we build quantum holonomies associated with the analogue of the He-McKellar-Wilkens effect and discuss a possible analogy with the geometric quantum computation. Finally, we investigate the dependence of the energy levels on the He-McKellar-Wilkens geometric phase induced by Lorentz symmetry breaking effects when the particle is confined to a hard-wall confining potential.

MSC:

81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81R40 Symmetry breaking in quantum theory
81T99 Quantum field theory; related classical field theories
81S99 General quantum mechanics and problems of quantization
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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References:

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