Probability and Mathematical Physics seminar: Douglas Pickrell, University of Arizona

Title: Group Valued Quantum Fields and Spherical Harmonic Oscillators

Abstract: There is a mathematically compelling definition of a quantum field theory (qft) due to Graeme Segal. An elusive mathematical challenge is to construct examples. In a limited sense a free real valued quantum field is essentially an assembly of linear harmonic oscillators (using Fourier series). It is known how to complete this to a theory in Segal's sense, and in two dimensions (one space, one time dimension) there is a zoo of nonlinear examples (such as the fashionable Liouville theory, the subject of other talks). In this talk I will try to justify the speculation that there is a $SU(2)$ (or compact group) valued generalization in which the Hamiltonian is an assembly of linear and spherical harmonic oscillators (using an analogue of Fourier series for group valued functions).