The Marsden-Weinstein reduction structure of integrable dynamical   systems and a generalized exactly solvable quantum superradiance model
  An approach to describing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the Marsden-Weinstein reduction method on canonically symplectic manifolds \ with group symmetry, is proposed. Its natural relationship with the well known Adler-Kostant-Souriau-Berezin-Kirillov method and the associated R-matrix approach is analyzed.   A new generalized exactly solvable spatially one-dimensional quantum superradiance model, describing a charged fermionic medium interacting with external electromagnetic field, is suggested. The Lax type operator spectral problem is presented, the related $R$-structure is calculated. The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related with the thermodynamical equilibrity of the model, are discussed. 
N. Bogolubov (Jr.) and Ya.A. Prykarpatsky
nlin.SI math-ph math.MP