Listening to spacetime
Brian Henning (University of Geneve)

Common to every theoryfundamental, phenomenological, or even toyis a notion of degrees of freedom living on some space(time). While at first glance such a statement may sound so broad as to render it meaningless, it actually imposes quite a strong structure. The basic point is that the degrees of freedom allow for certain types of measurements (scattering, correlation functions, etc.), and that these measurements can only take values consistent with the relevant spacetime symmetry. Turning this around, we can use spacetime symmetry to parameterize the kinematics of experiments, thereby allowing a clearer way to study the dynamics.

In this talk I will show that this is precisely what effective field theory (EFT) does. Viewing EFT through the lens of spacetime symmetry unveils previously unnoticed structures. For example, in an N particle phase space of massless particles we will find a certain U(N) actiongeneralizing the U(1)N little group scaling of the particleswhose harmonic decomposition also gives a harmonic decomposition of the spacetime symmetry group (in this case, the conformal group). This provides a basis not only for an EFT, but also a basis for the Hilbert space of free theories. As I will explain, the latter is an essential ingredient in the recently revived technique of Hamiltonian truncation to numerically study quantum field theories.