Conference

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.

I will present a pedagogical introduction on the application of tensor networks to the renormalization group. This program has resulted in a non-perturbative, real-space RG approach for lattice systems and the multi-scale entanglement renormalization ansatz (MERA). The MERA is currently of interest in a wide range of research areas, from statistical mechanics to condensed matter, from quantum field theory to holography in quantum gravity.