Effective Field Theories

Often in a physical problem there are some degrees of freedom that we treat as unobservable because the energy required to excite them is much greater than the energy scale of the problem. For example, when modelling a pendulum with a rigid arm we ignore the vibrational modes of the arm. Or in quantum physics it may be that the energy scales available to us, for example in a collider, are not sufficient to create a particular heavy particle. These unobservable degrees of freedom can still affect the physics that we do observe at subleading order. A tool that is often used by physicists to study this is the machinery of effective field theory (EFT). In this talk I will discuss a paper with Harvey Reall in which we studied an EFT for a model problem and explained how it is possible to handle the troublesome PDEs that can arise.