Position dependent non-linear Schrödinger hierarchies: Involutivity, commutation relations, renormalisation and classical invariants |
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Authors: | Torbjö rn Kolsrud |
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Affiliation: | Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden |
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Abstract: | We consider a family of explicitly position dependent hierarchies , containing the NLS (non-linear Schrödinger) hierarchy. All are involutive and fulfill DIn=nIn−1, where D=D−1V0, V0 being the Hamiltonian vector field afforded by the common ground state I0=uv. The construction requires renormalisation of certain function parameters.It is shown that the ‘quantum space’ C[I0,I1,…] projects down to its classical counterpart C[p], with p=I1/I0, the momentum density. The quotient is the kernel of D. It is identified with classical semi-invariants for forms in two variables. |
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Keywords: | 17B63 17B80 34C14 35Q53 35Q55 35Q58 70H33 70S10 76F30 81R05 |
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