Quantisation of nonabelian dynamical systems. Quantisation ideals.

In my talk I'll discuss a new approach to the problem of quantisation of dynamical systems, introduce the concept of quantisation ideals and provide meaningful examples. Traditional quantisation theories start with classical Hamiltonian systems with variables taking values in commutative algebras and then study their non-commutative deformations, such that the commutators of observables tend to the corresponding Poisson brackets as the (Planck) constant of deformation goes to zero. I am proposing to depart from systems defined on a free associative algebra $A$. In this approach the quantisation problem is reduced to a description of two-sided ideals $J$ which define the commutation relations (the quantisation ideals) in the quotient algebras $A_J = A/J$ and which are invariant with respect to the dynamics of the system.

^* Conference identificator: 931 2278 9257 Password: 045927