On the Exact Quantum Integrability of the Membrane
| dc.creator | Castro, Carlos | |
| dc.date | 1996-05-06 | |
| dc.date | 1996-05-17 | |
| dc.date.accessioned | 2026-07-07T09:04:21Z | |
| dc.date.available | 2026-07-07T09:04:21Z | |
| dc.description | The exact quantum integrability problem of the membrane is investigated. It is found that the spherical membrane moving in flat target spacetime backgrounds is an exact quantum integrable system for a particular class of solutions of the light-cone gauge equations of motion : a dimensionally-reduced $SU(\infty)$ Yang-Mills theory to one temporal dimension. Crucial ingredients are the exact integrability property of the $3D~SU(\infty)$ continuous Toda theory and its associated dimensionally-reduced $SU(\infty)$ Toda $molecule$ equation whose symmetry algebra is the $U_\infty$ algebra obtained from a dimensional-reducion of the $W_\infty \oplus {\bar W}_\infty$ algebras that act naturally on the original $3D$ continuous Toda theory. The $U_\infty$ algebra is explicitly constructed in terms of exact quantum solutions of the quantized continuous Toda equation. Highest weight irreducible representations of the $W_\infty$ algebras are also studied in detail. Continuous and discrete energy levels are both found in the spectrum . Other relevant topics are discussed in the conclusion. | |
| dc.description | 35 pages; Revised Tex file; some minor details have been added | |
| dc.identifier | https://arxiv.org/abs/hep-th/9605029 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9605029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149344 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | On the Exact Quantum Integrability of the Membrane | |
| dc.type | text |