Quantum integrable Toda-like systems in deformation quantization (Q1306779)

A formulation and discussion of quantum integrable systems within the framework of deformation quantization is given and a list of classically integrable Toda-like systems is presented. These systems are defined by traces over products of \(2\times 2\) matrices by means of two types of constant classical \(r\)-matrices depending on spectral parameters. Among these systems are relativistic and discretized versions of the original Toda lattice. All these systems are shown to be quantum integrable with respect to the usual star product of the Weyl type in flat \(2n\)-dimensional space.