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Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane
Інший ID:
2010 Mathematics Subject Classification: 81R60; 81S05; 83C65
DOI:10.3842/SIGMA.2014.011
DOI:10.3842/SIGMA.2014.011
Посилання:
Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane / C. Batlle, J. Gomis, K.Kamimura // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 25 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
full collection is available at http://www.emis.de/journals/SIGMA/space-time.html.
We thank Jorge Zanelli for collaboration in some parts of this work and Mikhail Plyushchay for
reading the manuscript. We also thank Adolfo Azc´arraga and Jurek Lukierski for discussions,
and Rabin Banerjee for letting us know about the results in [3]. CB was partially supported by
Spanish Ministry of Economy and Competitiveness project DPI2011-25649. We also acknowledge
partial financial support from projects FP2010-20807-C02-01, 2009SGR502 and CPAN
Consolider CSD 2007-00042.
Дата:
2014
Переглядів:
336
Завантажень:
240
Анотація:
We study all the symmetries of the free Schrödinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schrödinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.
