Non-relativistic Conformal Field Theory in Momentum Space

Abstract: Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar operators in non-relativistic conformal field theories in momentum space. We discuss the solution of conformal Ward identities and express 2,3, and 4-point functions as a function of energy and momentum. We also express the 3- and 4-point functions in the momentum space as the one-loop and three-loop Feynman diagram computations, respectively. Lastly, we generalize the discussion to the momentum space correlation functions in the presence of a boundary.