Observable currents for effective field theories and their context

Abstract

The primary objective of an effective field theory is modelling observables at the given scale. The subject of this talk is a notion of observable at a given scale in a context that does not rely on a metric background. Within a geometrical formalism for local covariant effective field theories, a discrete version of the multisymplectic approach to lagrangian field theory, I introduce the notion of observable current. The pair of an observable current and a codimension one surface (f, \Sigma) yields an observable Q_{f, \Sigma} : Histories \to R . The defining property of observable currents is that if \phi \in Solutions \subset Histories and \Sigma’ - \Sigma = \partial B (for some region B) then Q_{f, \Sigma'} (\phi) = Q_{f, \Sigma} (\phi) . Thus, an observable current f is a local object which may use an ``auxiliary devise’’ \Sigma, relevant only up to homology, to induce functions on the space of solutions. There is a Poisson bracket that makes the space of observable currents a Lie algebra. We construct observable currents and prove that solutions can be separated by evaluating the induced functions. We comment on the relevance of this framework for covariant loop quantization.