Quantum Cosmology, Singularity Avoidance and Path Integral

Abstract: In this talk, I will discuss recent developments in connection with the path integral formulation in quantum cosmology and the associated boundary condition for the universe. I will also point out subtleties with various aspects of this proposal and the important role played by matter perturbations. Finally, I will discuss how the methods adopted for quantum cosmology can be used to avoid the Singularity inside a Schwarzschild black hole.

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Everything everywhere all at once? Towards a quantitative understanding of the many worlds interpretation

Abstract: This talk surveys recent findings about the emergence of classicality in closed, unitarily evolving quantum systems. To this end, I first review the decoherent histories framework as a formal tool to study the emergence of classicality. Afterwards, I present various quantitative results based on first principles calculations of the decoherence functional. I will address the conditions for the emergence of decoherence, the strength of decoherence in terms of a finite-size scaling law, and the structure of decoherence among different histories or branches.

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A Hamiltonian description of quantum field theory coupled to gravitation and foliation-dependent Hilbert space structures

Abstract:The Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, is generalized to the case where matter is described by a Quantum Field Theory in Curved Spacetime. Thus, in our approach there is no non-dynamic background structure and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled. Given the Hamiltonian nature of the framework, we must work with the generators of hypersurface deformations, represented as functions over the manifold of quantum states. A key aspect of the theory is that the Hilbert space structure of QFT is dependent on the classical gravitational degrees of freedom. Therefore, the theory is constructed in terms of a non-trivial fibration of the set of quantum states over the base manifold of gravitational variables. An important feature of this work is the use of Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schrodinger wave functional picture of QFT in curved spacetime. This allows us to relate states within different Hilbert spaces in the case of vacuum states or measures that depend on the gravitational degrees of freedom, as the ones associated to Ashtekar's parametric family of complex structures. This is achieved through the inclusion of a quantum Hermitian connection for the fibration, which is necessary to be able to reproduce the Dirac's algebraic relations for the Hamiltonian generators of hypersurface deformations. Some physical features of the construction are norm conservation of the quantum states for QFT in CS (even if the total hybrid dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on geometry.

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