Speaker
Gerald Goldin, Rutgers University
AbstractI shall first summarize recent work with David Sharp (Los Alamos), describing foundational reasons why a certain infinite-dimensional semidirect product group serves as a universal kinematical group for quantum mechanics. Its unitary representations describe all possible quantum kinematics of systems with mass or charge in an arbitrary physical space, without any quantization of a classical phase space and without the need to quantize a field theory. Our early prediction of intermediate anyon exchange statistics in 1980-81 followed from modeling this group on two-dimensional space. After briefly sketching the relevant representation theory, I will show how interesting intermediate quantum phases can arise from theoretically possible internal multipole structures, independent of the exchange statistics of such particle-like configurations. These results are in collaboration with Hongyi Shen at Rutgers University, and form a part of his Ph.D. thesis in progress.