Galilean Field Theories and Conformal Structure

Understand

We perform a detailed analysis of Galilean field theories, starting with free theories and then interacting theories.

• We consider non-relativistic versions of massless scalar and Dirac field theories before we go on to review our previous construction of Galilean Electrodynamics and Galilean Yang-Mills theory.
• We show that in all these cases, the field theories exhibit non-relativistic conformal structure (in appropriate dimensions).
• The surprising aspect of the analysis is that the non-relativistic conformal structure exhibited by these theories, unlike relativistic conformal invariance, becomes infinite dimensional even in spacetime dimensions greater than two.