Geometric interpretation of magnetic fields and the motion of charged particles

Felsager, Bjørn; Leinaas, Jon Magne

doi:10.1016/0550-3213(80)90497-6

Cited by 14 publications

(14 citation statements)

References 10 publications

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“…Inserting (27) into (19) and making use of (26) and the completeness of the position eigenstates |x yields the Fourier transform of C W (x, k),…”

Section: Product Rule For Gauge Invariant Weyl Symbolsmentioning

confidence: 99%

Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding centre motion

Müller

1999

J. Phys. A: Math. Gen.

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We derive a product rule for gauge invariant Weyl symbols which provides a generalization of the well-known Moyal formula to the case of non-vanishing electromagnetic fields. Applying our result to the guiding center problem we expand the guiding center Hamiltonian into an asymptotic power series with respect to both Planck's constanth and an adiabaticity parameter already present in the classical theory. This expansion is used to determine the influence of quantum mechanical effects on guiding center motion.

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“…Inserting (27) into (19) and making use of (26) and the completeness of the position eigenstates |x yields the Fourier transform of C W (x, k),…”

Section: Product Rule For Gauge Invariant Weyl Symbolsmentioning

confidence: 99%

Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding centre motion

Müller

1999

J. Phys. A: Math. Gen.

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“…In this terminology, a redefinition of the pair of basis vectors (el,e2) over configuration space in a possibly spatially dependent manner amounts to a gauge transformation. Similar situations, involving fields of planes over configuration space, have been studied previously by Felsager and Leinaas [9] in the context of a geometric interpretation of magnetic fields and by Littlejohn [10,11] within the framework of the classical guiding-center motion.…”

Section: A Equations Of Motionmentioning

confidence: 92%

Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field

Littlejohn

Weigert

1993

Phys. Rev. A

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Article:Littlejohn, Robert and Weigert, S. orcid.org/0000-0002-6647-3252 (1993) Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field. Physical Review A. pp. 924-940. ISSN 1094924-940. ISSN -1622 https://doi.org/10.1103/PhysRevA.48.924 eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter. The averaged classical Hamiltonian contains not only terms representing fictitious electric and magnetic fields but also an additional velocity-dependent potential. The Hamiltonian of the quantum-mechanical system is diagonalized by means of a systematic WKB analysis for coupled wave equations up to second order in the adiabaticity parameter, which is coupled to Planck's constant. An exact term-by-term correspondence with the averaged classical Hamiltonian is established, thus confirming the relevance of the additional velocity-dependent second-order contribution.

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“…LEINAAS theory of relativity. I n the present case the "internal" geometry associated with the flux string can in fact be represented more directly as a two-dimensional geometric structure [22]. As we have discussed above the flux string is characterized by the fact that parallel transport around the string changes the internal vectors, but transport of the vectors around loops which do not encircle the string leaves the vectors unchanged.…”

Section: (524)mentioning

confidence: 92%

Topological Charges in Gauge Theories

Leinaas

1980

Fortschr. Phys.

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Topological and geometric aspects of gauge theories are examined . The geometry of the fiberbundle formulation of gauge theories is discussed and compared with the formalism of general relativity . The basic role played by the parallel displacement operator of this geometry is examined .With this operator a gauge independent characterization of various topological singularities and non-singular soliton configurations is carried out .

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Geometric interpretation of magnetic fields and the motion of charged particles

Cited by 14 publications

References 10 publications

Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding centre motion

Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding centre motion

Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field

Topological Charges in Gauge Theories

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