Anne Spiering, M.Sc (Trinity College Dublin)

Title: On the Non-Relativistic Expansion of Gravity, Fields and Strings

Abstract: 

Recently, progress has been made on the development of a systematic expansion of general relativity in powers of 1/c where c is the speed of light. This expansion is similar in spirit to the post-Newtonian expansion, but it has the benefit that it is covariant and can be applied off shell so that we can use it to define action principles for non-relativistic gravity plus relativistic corrections. After reviewing these developments, I will discuss the question: how to describe the interactions between gravity and matter at the quantum level in the non-relativistic domain? For example, if we consider a classical background that is 1/c expanded, how do we couple it to a quantum system in a bottom-up fashion? In other words, given the Schrödinger equation for some matter system, how can we couple it to a gravitational background and include relativistic corrections order by order in 1/c, i.e. is there a minimal coupling prescription for this? Even in this non-relativistic domain a theory of quantum mechanics backreacting on non-relativistic gravity is non-trivial. The story so far can be viewed as a particle-based approach to non-relativistic physics. In the final part of my talk, I will discuss recent developments on the non-relativistic expansion of the closed bosonic string, showing that the 1/c expansion of a string requires extra ingredients not present in the particle case.