Abstract
We consider the quantum mechanics of a particle on the coset superspace SU(2|1)/[U(1) × U(1)], which is a super-flag manifold with SU(2)/U(1) ≃ S2 ‘body’. By incorporating the Wess-Zumino terms associated with the U(1) × U(1) stability group, we obtain an exactly solvable super-generalization of the Landau model for a charged particle on the sphere. We solve this model using the factorization method. Remarkably, the physical Hilbert space is finite-dimensional because the number of admissible Landau levels is bounded by a combination of the U(1) charges. The level saturating the bound has a wavefunction in a shortened, degenerate, irrep of SU(2|1).
| Original language | English (US) |
|---|---|
| Title of host publication | From Fields to Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection |
| Publisher | World Scientific Publishing Co. |
| Pages | 2123-2146 |
| Number of pages | 24 |
| Volume | 1 |
| ISBN (Electronic) | 9789812775344 |
| ISBN (Print) | 9789812389558 |
| DOIs | |
| State | Published - Jan 1 2005 |
Fingerprint
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
A super-flag landau model. / Ivanov, Evgeny; Mezincescu, Alexandru; Townsend, Paul K.
From Fields to Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection. Vol. 1 World Scientific Publishing Co., 2005. p. 2123-2146.Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - A super-flag landau model
AU - Ivanov, Evgeny
AU - Mezincescu, Alexandru
AU - Townsend, Paul K.
PY - 2005/1/1
Y1 - 2005/1/1
N2 - We consider the quantum mechanics of a particle on the coset superspace SU(2|1)/[U(1) × U(1)], which is a super-flag manifold with SU(2)/U(1) ≃ S2 ‘body’. By incorporating the Wess-Zumino terms associated with the U(1) × U(1) stability group, we obtain an exactly solvable super-generalization of the Landau model for a charged particle on the sphere. We solve this model using the factorization method. Remarkably, the physical Hilbert space is finite-dimensional because the number of admissible Landau levels is bounded by a combination of the U(1) charges. The level saturating the bound has a wavefunction in a shortened, degenerate, irrep of SU(2|1).
AB - We consider the quantum mechanics of a particle on the coset superspace SU(2|1)/[U(1) × U(1)], which is a super-flag manifold with SU(2)/U(1) ≃ S2 ‘body’. By incorporating the Wess-Zumino terms associated with the U(1) × U(1) stability group, we obtain an exactly solvable super-generalization of the Landau model for a charged particle on the sphere. We solve this model using the factorization method. Remarkably, the physical Hilbert space is finite-dimensional because the number of admissible Landau levels is bounded by a combination of the U(1) charges. The level saturating the bound has a wavefunction in a shortened, degenerate, irrep of SU(2|1).
UR - http://www.scopus.com/inward/record.url?scp=84873577433&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84873577433&partnerID=8YFLogxK
U2 - 10.1142/9789812775344_0054
DO - 10.1142/9789812775344_0054
M3 - Chapter
SN - 9789812389558
VL - 1
SP - 2123
EP - 2146
BT - From Fields to Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection
PB - World Scientific Publishing Co.
ER -