The virial theorem for action-governed theories

Abstract

We describe a simple derivation of virial relations (VR) for arbitrary action-governed systems. These follow directly from the action with no need to go via the equations of motion. When some of the degrees of freedom are of the same type a tensor virial theorem presents itself. Further generalizations are discussed. Symmetries of the action may lead to identities involving the VR. Beside pointing to a unified provenance of the VR, and affording general systematics of them, our method is a simple prescription for deriving such relations. It is particularly useful for treating high-derivative and non-local theories. We demonstarte the procedure with several examples.