SS 19
Jun 26 - Daan Janssen: Quantum fields on non-globally hyperbolic space-times and the information loss paradox
A common mantra in physics is that information loss due to black hole evaporation, i.e. the evolution of a pure state to a mixed state, is against one of the foundations of quantum mechanics, unitary time-evolution. However, as has been argued numerous times, in particular by Bill Unruh and Robert Wald, on non-globally hyperbolic space-times, such as the black hole evaporation space-time, pure-to-mixed evolution is not at all in conflict with quantum field theory, but rather a natural consequence of it. In my thesis I explicitly construct a quantum field theory on the evaporating black hole space-time, by generalising algebraic QFT constructions for globally hyperbolic space-times. We indeed find that information loss occurs naturally on such space-times, though some unfortunate features of this theory may still warrant resolving the singularity by a theory of quantum gravity in order to make the dynamics determined.
May 29 - Wouter Oosters: Fermions in fluctuating spacetime
Starting out from the Wetterich equation the fermionic contributions to the running of Newton’s constant as well as the cosmological constant have been investigated. The result is positively contradicting the literature!
May 29 - Nadia van Beurden: Can we modify gravity to explain inflation?
The fluctuations in the cosmic microwave background, reported by the Planck collaboration, provide important insights on the physics occurring in the very universe including a potential phase of inflation. Surprisingly, Starobinsky inflation turns out to be one of the most successful models for describing the corresponding fluctuation spectrum. In this case, the Einstein-Hilbert action is supplemented by a higher-derivative \( R^2 \)-interaction which is responsible for the inflationary dynamics. From a quantum gravity perspective, it is highly conceivable that the \( R^2 \)–term characteristic for the Starobinsky model will be accompanied by terms build from higher powers of the curvature scalar (modified Starobinsky inflation). The success of Starobinsky inflation indicates that there must be a bound on the corresponding coupling constants in order for the models to still be compatible with observations. The goal of the project is to perform a classical analysis and determine the corresponding bounds on the parameters.
May 08 - Bob Stienen: What can we learn from our data? Exploring Parameter Spaces in High Energy Physics with Machine Learning
In recent years machine learning has become a useful tool in high energy physics and science in general. Because of the remarkable results it can achieve, some attribute it near magical abilities (and that we should hence stay away from using it). In this talk I will show that there is no such thing as machine learning magic and that the techniques used in a variety of ways in high energy physics. To this end, i will start with an introduction into machine learning, its terminology and how a commonly used machine learning algorithm works. Using this knowledge we will have a look at two applications that I have investigated in own research: parametrising high-dimensional functions and sampling high-dimensional parameter spaces.
May 01 - Lando Bosma: Resolving Spacetime Singularities within Quantum Gravity
The spacetime singularities predicted by general relativity have been one of the biggest problems in theoretical physics for a long time, and removing these is a key motivation for a theory of quantum gravity. In this talk I will present a non-perturbative computation of the quantum corrections to the graviton propagator in the asymptotic safety program. This is done by considering the full momentum-dependence of a specific structure function using non-local heat kernel techniques. The calculation will result in a quantum-corrected Newtonian potential that approaches a constant negative value as \(r \to 0 \), thereby removing the classical singularity and (hopefully) justifying the ambitious title above.
Apr 10 - Zbigniew Drogosz: New Observables in 4D Causal Dynamical Triangulations
Combining General Relativity and Quantum Mechanics in a theory of Quantum Gravity is among the greatest challenges of modern physics. In my talk, I will present some new results in Causal Dynamical Triangulations (CDT), which is a possible approach to this problem. In this theory, the quantization is performed by taking the Einstein-Hilbert action for General Relativity, discretizing the spacetime, and calculating path integrals over possible geometries of a universe with a given topology. In the case of the three-sphere spatial topology, it has been difficult to extend the effective semi-classical description in terms of proper time and spatial three-volume to include genuine spatial coordinates, partially because of the background independence inherent in the model. However, if the spatial topology is that of a three-torus, it is possible to define a number of new observables that might serve as spatial coordinates, as well as new observables related to the winding numbers of the three-dimensional torus. I will show how these quantities, together with the quantum Ricci curvature, give new insight into the geometry of a generic configuration in the de Sitter phase.
Apr 03 - Dániel Németh: Causal Dynamical Triangulations - Recent results in 4D CDT
Causal Dynamical Triangulations Quantum Gravity is a framework which attempts to describe the Quantum theory of Gravity via the triangulation of the Space-time. The mathematical base of this theory is Regge calculus, but there are some important differences. One if it is the separation of space ant time into a foliation, where 1.- 2. - or 3 dimensional spatial triangulations are connected together by 1 dimensional timelike links to form a D + 1 dimensional triangulation. The whole configuration is achieved by gluing together D (2, 3, or 4) dimensional building blocks (triangles, tetrahedra and pentachorons, respectively). Higher than 1+1 dimensions the theory is only numerically solvable. Using the Einstein-HIlbert action together with the path integral formalism the numerical solutions represent the ensemble of generated Universes. It is already known, that this simple modell has a very rich and complex phase structure, and one of the phases reproduces a de-Sitter Universe.
In my talk i will show how to perform numerical simulations, the impact of topology on the theory, how the pasespace and phase trnasitions look like, how to define orderparameters and i will also talk about some new results and research programs of CDT.
Mar 27 - Arthur Vereijken: Relating different regularization schemes in Functional Renormalization (master thesis talk)
Functional renormalization group methods are powerful tools for studying properties of statistical systems and quantum field theories beyond perturbation theory. A key open question in applying functional renormalization group methods concerns the proper choice of regulator. While the regulator itself is unphysical and should therefore not affect observable quantities, approximate solutions of the functional renormalization group equation may exhibit strong regulator effects. We will introduce the functional renormalization group for quantum gravity, after which we will investigate these regulator effects. This leads to a proposal for a relation between renormalization group flows with different regulators, as well as some insights in how terms are generated by the regulator. This proposal is analyzed in a quantum gravity scenario, and we suggest improvements for approximations so that they are more suitable for compensating regulator effects.
Feb 27 - Cristina Galea: Roping the Higgs with a tau
The search for the Higgs boson decaying into tau leptons produced last year the first observation of the coupling of the Higgs boson to the fermionic sector, by both the ATLAS and CMS experiments. In my presentation I will explain some details of this search and the essential role that the exact determination of the tau energy is playing in such a complex analysis.
Feb 20 - Anne Franzen (UT Lisbon): Flat Riemann-Lemaître-Robertson-Walker and Kasner Big Bang singularities analysed on the level of scalar waves
We consider the wave equation, \( \Box_g \psi=0 \), in fixed flat Friedmann-Lemaître-Robertson-Walker and Kasner spacetimes with topology \( \mathbb{R}_+\times\mathbb{T}^3 \). We obtain generic blow up results for solutions to the wave equation towards the Big Bang singularity in both backgrounds. In particular, we characterize open sets of initial data prescribed at a spacelike hypersurface close to the singularity, which give rise to solutions that blow up in an open set of the Big Bang hypersurface \( \{t=0\} \). The initial data sets are characterized by the condition that the Neumann data should dominate, in an appropriate \(L^2\)-sense, up to two spatial derivatives of the Dirichlet data. For these initial configurations, the \(L^2(\mathbb{T}^3)\) norms of the solutions blow up towards the Big Bang hypersurfaces of FLRW and Kasner with inverse polynomial and logarithmic rates respectively. Our method is based on deriving suitably weighted energy estimates in physical space. No symmetries of solutions are assumed.
WS 18/19
Jan 30 - Melissa van Beekveld: How logarithms are born
I will show how large logarithms arise in a perturbative calculation and how resummation solves the issue of having these large logarithms. If there is some time left, I want to show some recent progress that we have made on pinning down the origin of the next-to-leading class of logarithms.
Jan 16 - Christian Blohmann (MPIM Bonn): The hamiltonian Lie algebroid of General Relativity
The choice of an initial hypersurface for the initial value problem of General Relativity breaks the diffeomorphism symmetry. In the first part, I will show how the symmetry breaking can be described by a (recently introduced) method of reduction of the action groupoid of the action of all diffeomorphisms on the space of lorentzian metrics. This yields a Morita equivalent groupoid, which turns out to be isomorphic to the groupoid constructed in an earlier paper with Fernandes and Weinstein. In the second part, I will introduce the notion of hamiltonian Lie algebroids and show that the Lie algebroid of the reduced groupoid has a hamiltonian structure with the Gauß-Codazzi constraint functions as momenta. We obtain a structural explanation of why the constraint set of GR is a coisotropic submanifold, which is true for the zero locus of the momentum section of every hamiltonian Lie algebroid. This is joint work with Alan Weinstein.
Dec 12 - Timothy Budd: Random Riemann surfaces
Bijections between discrete surfaces (triangulations, quadrangulations, ...) and discrete trees have in recent years played an important role in understanding the geometry of two-dimensional quantum gravity. I will describe a new such bijection in the continuous setting of 2d "topological gravity", i.e. the path integral over hyperbolic surfaces with punctures. The latter is closely related to the Weil-Petersson volumes of the moduli spaces of Riemann surfaces, which can now be computed equivalently as the partition functions of certain continuous trees.
Nov 14 - Marcus Reitz: Investigating the non-Abelian Stokes’ theorem for gravitational Wilson loops
Finding suitable diffeomorphism-invariant observables to probe gravity at the Planck scale is a key problem for all approaches of quantum gravity. As these cannot be local quantities, the Wilson loop of the 4-dimensional Christoffel connection is a potentially interesting ingredient for the construction of such an observable. Before measuring Wilson loops in a quantum setting we first want to know what they are a measure of classically. We have investigated to what extent curvature information of the underlying spacetime may be extracted from Wilson loops through a Stokes’ theorem-like relation. We found an explicit relation for the Wilson loop to the enclosed scalar curvature for a special class of surfaces, namely for totally geodesic surfaces. The next step is to construct a viable quantum observable and implement it in the non-perturbative framework of Causal Dynamical Triangulations (CDT).
Oct 24 - Sjors Heefer: Advancements on the covariance of the κ-Poincaré model (and Relative Locality) [master thesis talk]
In the classical, gravity-free regime of nature Einstein's special theory of relativity is established very well. At high enough energies, however, this description is expected to break down as a consequence of the finite value of the Planck mass. In my talk I discuss a deformation of special relativity, the so-called κ-Poincaré model, which is based on a so-called Hopf algebra deformation of the Poincaré algebra and incorporates the Planck mass as a second relativistic invariant. When interactions are turned off this model is known to be invariant under a set of deformed Poincaré transformations, but in the presence of interactions the covariance of the model is only partly understood. In my talk I propose a method of implementing the deformed Poincaré transformations in a non-trivial way on the multi-particle phase space, which guarantees a covariant description of interactions.
Oct 17 - James Owen Weatherall (UC Irvine): Information Paradox Regained? Maudlin in Black Hole Information Loss
I will discuss a recent argument due to philosopher of physics Tim Maudlin concerning Black Hole Information Loss. I will argue, contra Maudlin, that there is a paradox, in the straightforward sense that there are propositions that appear true, but which are incompatible with one another. I will also discuss the significance of the paradox and Maudlin's response to it. The discussion will center on a little known result due to Kodama and Wald.
Oct 10 - Benjamin Knorr: Introduction to Heat Kernel Techniques
Heat kernel techniques allow in a certain sense to generalize the Fourier transform to curved spaces and give precise meaning to functional traces over operators in a general setting, they are thus invaluable in continuum quantum gravity calculations. After outlining how they exactly appear in practice, I will illustrate how (parts of) the heat kernel can be calculated.
Oct 03 - Arthur Vereijken: Relating different regularization schemes in Asymptotic Safety (master thesis talk)
A key open question in applying functional renormalization group methods concerns the proper choice of regulator. While the regulator itself is unphysical and should therefore not affect observable quantities, approximate solutions of the functional renormalization group equation may exhibit strong regulator effects. We analyze these effects in detail and suggest particular classes of approximations which are suitable for compensating such effects.
Sep 12 - Dennis Obster: The Canonical Tensor Model, spaces and symmetries (master thesis talk)
The Canonical Tensor Model (CTM) is a proposed model for discrete quantum gravity formulated in the canonical formalism. In this talk I will explain the model as a dynamical model of commutative non-associative fuzzy spaces, where the algebraic structure is based on the ADM formalism of General Relativity. I will explain how to regain some of the topological and geometrical information from tensors. Lastly I will briefly introduce the quantum CTM and discuss properties of one of the known wave functions.
Sep 05 - Timothy Budd: Geometry of random surfaces coupled to an O(n) loop model
Understanding the geometry (and in particular the fractal dimensions) of random surfaces when they are coupled to critical matter is one of the main open challenges in two-dimensional quantum gravity. I'll discuss a small step in this direction in the case of coupling to an O(n) loop model. Using the peeling exploration and machinery from stochastic processes, some explicit distance statistics can be derived.