Zero curvature formalism for supersymmetric integrable hierarchies in superspace. (English) Zbl 0908.58087
Summary: We generalize the Drinfeld-Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for supersymmetric integrable systems starting from the Lax equation in superspace. We use the method of symmetric space as well as the non-Abelian gauge technique to obtain the supersymmetric integrable hierarchies of AKNS type from the zero curvature condition in superspace with the graded algebras \(\text{sl} (n+1,n)\) providing the Hermitian symmetric space structure.
MSC:
| 58Z05 | Applications of global analysis to the sciences |
| 81T60 | Supersymmetric field theories in quantum mechanics |
References:
| [1] | Gelfand I. M., Funct. Anal. Its Appl. 10 pp 4– (1976) |
| [2] | DOI: 10.1007/BF02105860 · Zbl 0578.58040 · doi:10.1007/BF02105860 |
| [3] | DOI: 10.1017/S0143385700001292 · Zbl 0495.58008 · doi:10.1017/S0143385700001292 |
| [4] | DOI: 10.1007/BF01214664 · Zbl 0563.35062 · doi:10.1007/BF01214664 |
| [5] | DOI: 10.1063/1.530970 · Zbl 0842.35098 · doi:10.1063/1.530970 |
| [6] | DOI: 10.1016/0375-9601(85)90033-7 · doi:10.1016/0375-9601(85)90033-7 |
| [7] | DOI: 10.1063/1.528616 · Zbl 0722.58038 · doi:10.1063/1.528616 |
| [8] | DOI: 10.1142/S0217751X92001915 · Zbl 0799.35213 · doi:10.1142/S0217751X92001915 |
| [9] | DOI: 10.1016/0370-2693(94)90979-2 · doi:10.1016/0370-2693(94)90979-2 |
| [10] | DOI: 10.1142/S0217732396001326 · Zbl 1020.37552 · doi:10.1142/S0217732396001326 |
| [11] | DOI: 10.1007/BF02099072 · Zbl 0738.35087 · doi:10.1007/BF02099072 |
| [12] | DOI: 10.1142/S0217751X96001565 · Zbl 1044.37543 · doi:10.1142/S0217751X96001565 |
| [13] | DOI: 10.1016/S0370-2693(96)01463-3 · Zbl 0957.37068 · doi:10.1016/S0370-2693(96)01463-3 |
| [14] | Popowicz Z., J. Phys. 29 pp 1281– (1996) |
| [15] | DOI: 10.1063/1.529875 · Zbl 0761.35101 · doi:10.1063/1.529875 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
