Position dependent non-linear Schrodinger hierarchies: Involutivity, commutation relations, renormalisation and classical invariants
2006 (English)In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, Vol. 130, no 8, 739-756 p.Article in journal (Refereed) Published
We consider a family of explicitly position dependent hierarchies (I-n)(0)(infinity), containing the NLS (non-linear Schrodinger) hierarchy. All (I-n)(0)(infinity) are involutive and fulfill DIn = nI(n-1), where D = D-1 V-0, V-0 being the Hamiltonian vector field v delta/delta v - u delta/delta u afforded by the common ground state I-0 = uv. The construction requires renormalisation of certain function parameters. It is shown that the 'quantum space' C[I-0, I-1,...] projects down to its classical counterpart C[p], with p = I-1/I-0, the momentum density. The quotient is the kernel of D. It is identified with classical semi-invariants for forms in two variables.
Place, publisher, year, edition, pages
2006. Vol. 130, no 8, 739-756 p.
symmetries, constants of motion, conservation laws, Poisson algebra, classical mechanics, commutation relations, involutivity, KdV, NLS-like, renormalisation in field theory, classical invariant theory, euclidean quantum-mechanics, action-angle variables, gaussian, diffusions, conservation-laws, cubic schrodinger, symmetries, transformations, morphisms, equations
IdentifiersURN: urn:nbn:se:kth:diva-16195DOI: 10.1016/j.bulsci.2006.03.004ISI: 000242712700006ScopusID: 2-s2.0-68649094951OAI: oai:DiVA.org:kth-16195DiVA: diva2:334237
QC 201005252010-08-052010-08-05Bibliographically approved