2.00 pm, Lecture Hall 6
On the Hamiltonian formulation and integrability of the Rajeev-Ranken model
T.R. Vishnu
Chennai Mathematical Institute.
20-03-19

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Abstract

This talk concerns a mechanical system with three degrees of freedom: the Rajeev-Ranken model. It describes nonlinear wave solutions of a 1+1d scalar field theory introduced by Zakharov and Mikhailov and Nappi that is dual to the principal chiral model. This scalar field theory also arises as a limit of the Wess-Zumino-Witten model, but is strongly coupled in the UV and could serve as a toy-model for theories with a Landau pole. We will describe the mechanical system, its Hamiltonian-Poisson bracket formulations and classical integrability including a Poisson pencil, Lax pairs, classical r-matrices and a complete set of conserved quantities in involution. The structure of the phase space is clarified by identifying all common level sets of conserved quantities. They are invariant tori of various dimensions with qualitatively distinct dynamics and furnish a foliation of the phase space. Finally, we find action-angle variables for the system. This is based on joint work with Govind Krishnaswami.