HET Seminar | The Memory Effect and Infrared Divergences in Quantum Field Theory and Quantum Gravity

Please note Special day and time: Thursday at Noon

Abstract: The "memory effect" refers to the fact that at order 1/r, a massless field generically will not return to the same value at asymptotically late retarded times as it had at asymptotically early retarded times. There is nothing singular about states with memory in quantum field theory, but they do not lie in the standard Fock space and infrared divergences will arise as artifacts of trying to represent states with memory in the standard Fock space. As a practical matter, if one is interested only in quantities directly relevant to collider physics, one can deal with infrared divergences by well defined procedures for obtaining "inclusive quantities," but this is clearly unsatisfactory from a fundamental viewpoint on scattering theory. For QED with massive charged particles, Faddeev and Kulish gave a construction of "in" and "out" Hilbert spaces that incorporates memory (via the "dressing" of the charged particles) and thereby provides a well defined scattering theory. However, we show that this construction fails in massless QED (because the required dressing is highly singular) and fails in (nonlinear) quantum gravity (because, in essence, the dressing would require its own further dressing and there is no self-consistent way of accomplishing this). We believe that if one wishes to treat scattering at a fundamental level in quantum gravity—as well as in massless QED and Yang-Mills theory—it is necessary to approach it from an algebraic viewpoint o