Hall, Brian C. and Kirwin, William D. (2015). Complex structures adapted to magnetic flows. J. Geom. Phys., 90. S. 111 - 132. AMSTERDAM: ELSEVIER SCIENCE BV. ISSN 1879-1662
Full text not available from this repository.Abstract
Let M be a compact real-analytic manifold, equipped with a real-analytic Riemannian metric g, and let beta be a closed real-analytic 2-form on M, interpreted as a magnetic field. Consider the Hamiltonian flow on T*M that describes a charged particle moving in the magnetic field beta. Following an idea of T. Thiemann, we construct a complex structure on a tube inside T*M by pushing forward the vertical polarization by the Hamiltonian flow evaluated at time i. This complex structure fits together with omega - pi*beta to give a Kahler structure on a tube inside T*M. When beta = 0, our magnetic complex structure is the adapted complex structure of Lempert-Szoke and Guillemin-Stenzel. We describe the magnetic complex structure in terms of its (1, 0)-tangent bundle, at the level of holomorphic functions, and via a construction using the embeddings of Whitney-Bruhat and Grauert. We describe an antiholomorphic intertwiner between this complex structure and the complex structure induced by -beta, and we give two formulas for local Kahler potentials, which depend on a local choice of vector potential 1-form for beta. Finally, we compute the magnetic complex structure explicitly for constant magnetic fields on R-2 and S-2. (C) 2015 Elsevier B.V. All rights reserved.
Item Type: | Journal Article | ||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-403592 | ||||||||||||
DOI: | 10.1016/j.geomphys.2015.01.015 | ||||||||||||
Journal or Publication Title: | J. Geom. Phys. | ||||||||||||
Volume: | 90 | ||||||||||||
Page Range: | S. 111 - 132 | ||||||||||||
Date: | 2015 | ||||||||||||
Publisher: | ELSEVIER SCIENCE BV | ||||||||||||
Place of Publication: | AMSTERDAM | ||||||||||||
ISSN: | 1879-1662 | ||||||||||||
Language: | English | ||||||||||||
Faculty: | Unspecified | ||||||||||||
Divisions: | Unspecified | ||||||||||||
Subjects: | no entry | ||||||||||||
Uncontrolled Keywords: |
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URI: | http://kups.ub.uni-koeln.de/id/eprint/40359 |
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