Observable currents for effective field theories and their context

          @misc{ pirsa_PIRSA:15090081,
            doi = {10.48660/15090081},
            url = {https://pirsa.org/15090081},
            author = {Zapata, Jose},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Observable currents for effective field theories and their context},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {sep},
            note = {PIRSA:15090081 see, \url{https://pirsa.org}}
          }
          

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.