Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-05-06
Physics
High Energy Physics
High Energy Physics - Theory
35 pages; Revised Tex file; some minor details have been added
Scientific paper
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.
No associations
LandOfFree
On the Exact Quantum Integrability of the Membrane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the Exact Quantum Integrability of the Membrane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Exact Quantum Integrability of the Membrane will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-597677