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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Gravitational redshift and polarization rotation of photons in curved spacetime

Abstract: Gravitational redshift and polarization rotation of light are among the classical tests of general relativity. Nevertheless, these two effects can also be described in the context of photons as quantum excitations of the free electromagnetic field propagating in curved spacetime. In this work, a short introduction to the formalism required for their study and modelling in the geometrical optics approximation is provided first. Each effect is then treated separately. For the gravitational redshift, it is shown that for photonic wave packets with finite bandwidth it can be understood as a unitary transformation on the photon operators. This transformation can be identified as a mode-mixing operation. Then, for the polarization rotation, a scenario in which polarized photons propagate in the gravitational field of the Earth on a closed path by judiciously positioned mirrors is studied. It is shown that after propagating along this presented path, a non-trivial Wigner phase is acquired by the photons already in a static spacetime, while previous studies have found a trivial and gauge independent Wigner phase. Finally, a model of perfect mirror reflections for a scalar field in (1+1)-dimensions is presented as an option to solve this conundrum.

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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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Concept of introverted space: is multidimensional, extroverted space an illusion?

Abstract:The quantum-phase-field concept of matter is revisited with special emphasis on the introverted view of space. Extroverted space surrounds physical objects, while introverted space lies in between physical objects. Space between objects leads to a network structure of matter: a network in which one-dimensional spaces connect individual particles.

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Open system dynamics from fundamental Lagrangian

Abstract:The effective dynamics of a non-relativistic charged particle, interacting with a bath of thermal photons, has been derived using a variety of methods and certain simplifying assumptions. It is therefore desirable to verify if similar conclusions can be reached following a microscopic derivation starting from the QED Lagrangian. In doing so, one may pick between two Lagrangians. One in which the interaction term involves the position of the electron; the other in which it involves the momentum. Since the two Lagrangians differ by a total derivative, one might assume such a choice to be inconsequential. However, it will be shown in this talk that two Lagrangians differing by a total derivative may lead to very different predictions at the level of open quantum systems. Further, it will be argued why only one of the two Lagrangians leads to phenomenologically consistent predictions. One might find these conclusions to be relevant in attempting a microscopic derivation of the effective system dynamics in a variety of situations.

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Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity

Abstract:We make a conceptual overview of a particular approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom. This idea goes back to Fock and Stueckelberg, leading to restrictions of the gauge symmetry of a theory, and it corresponds, in certain cases, to promoting constants of Nature to physical fields. Recently, different versions of this formulation have gained considerable attention in the literature, with several independent iterations, particularly in classical and quantum descriptions of gravity, cosmology, and electromagnetism. In particular, in the case of canonical quantum gravity, the Fock--Stueckelberg approach is relevant to the so-called problem of time. Our overview recalls the work of Fock and Stueckelberg and its physical interpretation with the aim of conceptually unifying the different iterations of the idea that appear in the literature and of motivating further research.

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