General Relativity & Quantum Cosmology

I will derive the gravitonic Casimir effect with non-idealized boundary conditions. This allows the quantification of the gravitonic contribution to the Casimir effect from real bodies. I will show how to use this formula to calculate the meagre gravitonic Casimir effect in ordinary matter. I will also apply this formula to the speculated Heisenberg-Couloumb (HC) effect in superconductors, thereby providing a test for the validity of the HC theory, and, consequently, the existence of gravitons.

The path integral is a very elegant formulation of quantum theory. It can also be an incredibly useful one, since it allows us to use methods of statistical physics, like computer simulations. In this talk I will introduce the subject of Markov Chain Monte Carlo simulations to solve the path integral over geometries. This general introduction will use examples from Causal Dynamical Triangulations, Causal Set Theory and Non Commutative geometry to show how different issues can be explored in this manner.

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.