Seminars
Summer term 2020
Volume average regularisation of the Wheeler–DeWitt equation
Abstract: One of the most important canonical approaches to quantum gravity is through the Wheeler–DeWitt equation. However, the theory, being a second order differential equation of a functional, produces delta functions and derivates of delta functions which lead to infinities. Thus a regularization of this term is needed. In this presentation I will discuss the approach of Justin C. Feng for the regularization of the Wheeler–DeWitt equation, the volume average regularization (arxiv.org/abs/1802.08576v3). For this I will go through some mathematical basics of functional calculus as well as some ground work to arrive to the Wheeler–DeWitt equation. The main idea of the paper will be discussed, which is performing an integral average of the second functional derivative part of the Wheeler–DeWitt equation over a finite volume. This is justified when we consider quantum general relativity as a low-energy effective field theory of the full theory of quantum gravity. That regularization will lead to an approximate solution of the Wheeler–DeWitt equation for the low-curvature, long-distance limit.
The theory of spontaneous quantum gravity
Abstract: Starting from classical general relativity coupled to matter, we raise the canonical variables to the status of operators. These matrix-valued dynamical variables obey a Lagrangian dynamics invariant under global unitary transformations, and there is no distinction between space-time and matter degrees of freedom. This deterministic matrix dynamics is assumed to hold at the Planck scale, and the Hamiltonian of the theory is not restricted to be self-adjoint. When this dynamics is coarse-grained over time scales much larger than Planck time, there emerge quantum commutation relations, and a theory of quantum general relativity. If a very large number of degrees of freedom get entangled, the emergent theory reduces to classical general relativity on a Riemannian space-time manifold. The unentangled d.o.f. obey the rules of quantum field theory on a classical background. This matrix dynamics provides a dynamical explanation for the quantum-to-classical transition, and makes predictions for black-hole entropy and dark energy. In our theory, quantum indeterminism is shown to be a consequence of coarse-graining the underlying deterministic matrix dynamics.
Relational observables, reference frames and conditional probabilities
Abstract: We discuss the construction of relational observables in time-reparametrisation invariant quantum mechanics and we argue that their physical interpretation can be understood in terms of conditional probabilities, which are defined from the solutions of the quantum constraint equation in a generalisation of the Page-Wootters formalism. In this regard, we show how conditional expectation values of worldline tensor fields are related to quantum averages of suitably defined relational observables. We also comment on how the dynamics of these observables can be related to a notion of quantum reference frames. Based on https://arxiv.org/abs/2006.05526 .
Quantum Oppenheimer–Snyder model
Abstract: We construct two reduced quantum theories for the Oppenheimer–Snyder model, respectively taking the point of view of the comoving and the exterior stationary observer, using affine coherent states quantization. Investigations of the quantum corrected dynamics reveal that both observers can see a bounce, although for the exterior observer certain quantization ambiguities have to be chosen correctly. The minimal radius for this bounce as seen from the stationary observer is then shown to always be outside of the photon sphere. Possible avenues to lower this minimal radius and reclaim black holes as an intermediate state in the collapse are discussed. We demonstrate further that switching between the observers at the level of the quantum theories can be achieved by modifying the commutation relations.
Exact solutions in General Relativity, Kasner universes and singularities
Abstract: We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic, while in the second solution the tangential components of the pressure are equal to zero. In both cases the pressure vanishes at the boundaries of the slab. Outside the slab these solutions are matched with the Rindler spacetime and with the Weyl-Levi-Civita spacetime, which represent special cases of the Kasner solution. We construct also the third solution of this type. We also show that there are solutions that can be matched with general anisotropic Kasner spacetime outside the slab. In any case, it is impossible to avoid the presence of the Kasner type singularities in contrast to the well-known case of spherical symmetry, where by matching the internal Schwarzschild solution with the external one, the singularity in the center of coordinates can be eliminated.
Quantum cosmology of Starobinsky inflation revisited
Abstract: In this talk, I will present the canonical quantization of a minisuperspace model of Starobinsky inflation in the Einstein frame formulation. The resulting Wheeler–DeWitt equation is solved using a Born–Oppenheimer approximation and I will discuss the implications of the quantization for the evolution of the universe in this model.
Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born–Oppenheimer approach
Abstract: We revisit the calculation of quantum-gravitational corrections to the power spectra of scalar and tensor perturbations in the Born-Oppenheimer approach to quantum gravity. We focus on the issue of the definition of the inner product of the theory and the unitarity of the corrections to the dynamics of the cosmological perturbations. We argue that the correction terms are unitary, provided the inner product is defined in a suitable way, which can be related to a notion of gauge-fixing the time variable and the use of conditional probabilities in quantum cosmology. We compare the corrections obtained within this framework to earlier results in the literature and we conclude with some remarks on the physical interpretation of the correction terms.
Date | Time | Speaker | Topic | Room |
---|---|---|---|---|
April 21, 2020 | 11:30 |
Ali Lezeik (Universität zu Köln) |
Bryce DeWitt, Quantum Theory of Gravity I: The Canonical Theory, 1967. doi:10.1103/PhysRev.160.1113 | Zoom (with password) |
April 28 | 11:30 |
Christina Koliofoti (Universität zu Köln) |
Volume average regularisation of the Wheeler–DeWitt equation | Zoom (with password) |
May 5 | 11:30 |
Nick Kwidzinski (Universität zu Köln) |
Singularity avoidance in Wheeler–DeWitt quantum cosmology | Zoom (with password) |
May 12 | 11:30 |
Sandeep Suresh (Universität zu Köln) |
Commutation relations for currents of RC space, Sugawara Model, Schwinger disease and Anomalies | Zoom (with password) |
May 19 | 11:30 |
Group members (Universität zu Köln) |
Progress report | Zoom (with password) |
May 26 | 11:30 |
Tejinder Pal Singh (Tata Institute, Mumbai) |
The theory of spontaneous quantum gravity | Zoom (with password) |
Jun 2 | 11:30 |
Leonardo Chataignier (Universität zu Köln) |
Relational observables, reference frames and conditional probabilities | Zoom (with password) |
Jun 9 | 11:30 |
Tatevik Vardanyan (Universität zu Köln) |
Inflation in a closed model of universe | Zoom (with password) |
Jun 23 | 11:30 |
Tim Schmitz (Universität zu Köln) |
Quantum Oppenheimer–Snyder model | Zoom (with password) |
Jun 30 | 11:30 |
Nick Kwidzinski (Universität zu Köln; disputation) |
Quantum Fate of Singularities in Anisotropic Cosmological Models | Zoom (with password) |
Jul 7 | 11:30 |
Alexander Kamenshchik (Università di Bologna) |
Exact solutions in General Relativity, Kasner universes and singularities | Zoom (with password) |
Jul 21 | 11:30 |
Manuel Krämer (Katholieke Universiteit Leuven) |
Quantum cosmology of Starobinsky inflation revisited | Zoom (with password) |
Sept 8 | 12:00 |
Group members (Universität zu Köln) |
Progress report | Zoom (with password) |
Sept 15 | 11:30 |
Sandeep Suresh (Universität zu Köln) |
Sugawara construction for spin currents and quantum corrections to spin current algebra due to U(1) gauge fields | Zoom (with password) |
Sept 22 | 11:30 |
Tatevik Vardanyan (Universität zu Köln; master colloquium) |
Quantum-gravitational effects for inflationary scalar perturbations in a model for a closed universe | Zoom (with password) |
Sept 29 | 11:30 |
Leonardo Chataignier (Universität zu Köln) |
Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born–Oppenheimer approach | Zoom (with password) |
Past seminars
Winter term 2019/20
Summer term 2019
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Summer term 2018
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