Abstract: I will review the motivations (from classical as well as quantum field theory) for studying electromagnetism and linearized gravity in harmonic gauge (locality and regularity, simplicity of residual gauge freedom, renormalization of interactions). Unfortunately, this choice of gauge leads to technical difficulties on non-flat backgrounds, like the Schwarzschild black hole, due to rather complicated radial mode equations, even after separation of variables. I will then describe a recent series of works, in which I have taken steps to overcome these difficulties by explicitly decoupling the radial mode equations into sparse triangular form.

Abstract: Fluctuations in the scalar field driving inflation can lead to an increase in the expansion rate, decreasing the Hubble distance. That effect seems to violate energy conditions and in particular the Averaged Null Energy Condition (ANEC). However, semiclassical proofs of ANEC suggest that such violations should not exist. In this talk I will argue that this paradox arises from considering the entire quantum state at early times but only a specific quantum state at late times. Examining a late-times fast expanding state and tracing back its evolution, I show how ANEC is in fact obeyed in an eternally inflating spacetime.

Abstract: I will discuss the quantisation of a Klein-Gordon field in a region with boundary with dynamical boundary conditions, which are prescribed by a boundary field equation, and are relevant for the experimental verification of the Casimir effect. I then define the local energy of the field, which allows one to study the Casimir effect in this model at zero and finite temperatures, as well as in coherent states. I will emphasise on the physical perspectives and relevance of the problem. Based on arXiv:2004.05646 [hep-th] and arXiv:2008.02842 [hep-th] with Ricardo Weder.

Abstract: Over the past five years, traversable wormholes have moved from the realm of science fiction to science. I will discuss what types are wormholes are physical, and propose an energy condition in quantum field theory that prevents the construction of unphysical wormholes.

Abstract: We present some ideas to construct new Haag-Kastler nets starting with a two dimensional conformal field theory. This is a natural variation of the Barata-Jaekel-Mund construction. It is suggested in physics literature that a similar construction should lead to integrable models, and we will discuss possible extensions of this programme.

Abstract: In this talk we discuss the influence of quantum matter on classical curvature in the semiclassical approximation for spacetimes with a Friedmann Robertson Walker metric. The quantum matter is described by a scalar field which propagate on a cosmological spacetime, it is massive and satisfies a linear equation with a generic coupling to the scalar curvature. Furthermore, the beckreaction of the scalar field to the spacetime metric is described by the semiclassical Einstein equation. We discuss the existence and uniqueness of solutions of the corresponding system of equations. We observe that a nonlocal term with higher order derivatives is present in the expectation value of the matter stress tensor which sources gravity. This term prevents a direct analysis of the system of equation, we show how to deal with it in order to put the semiclassical equation in the form of a fixed point equation, which can then be treated with Banach fixed point methods.

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Abstract: A major problem in QFT is to devolop tools to implement some kind of multiscale analysis for theories where standard renormalization group techniques do not apply.  In this context, in collaboration with M. Zirnbauer and T. Spencer we considered  the so-called supersymmetric nonlinear sigma model, which was  introduced as a toymodel for quantum diffusion. It is also a key ingredient in the construction and study of certain stochastic processes with memory. For this model we constructed a multiscale  procedure whose key ingredient is a infinite family of Ward identities generated by supersymmetry. We hope a similar strategy may extend to other models with and without supersymmetry.

Abstract: The BV-BFV formalism is often used to quantize gauge theories with boundary. In this talk I will explain how it can be adapted to perturbative algebraic QFT and generalized to treat theories with non-trivial asymptotic limit “at infinity”. As an example, I will discuss soft modes and conserved charges in QED on Minkowski spacetime.

Abstract: It has taken several decades of exploring statistical models of quantum gravity (aka nonperturbative gravitational path integrals) to understand how diffeomorphism-invariance, unitarity and the presence of a causal structure can be simultaneously accounted for in a lattice gravity framework. Causal Dynamical Triangulations (CDT) incorporates all of these features and provides a toolbox for extracting quantitative results from a first-principles quantum formulation, with very few free parameters. Recently, we have introduced “quantum Ricci curvature”, an observable that –somewhat remarkably– remains meaningful in a maximally nonclassical, Planckian regime. Measuring this curvature in fully-fledged 4D quantum gravity, we have discovered exciting evidence that the quantum universe dynamically generated in CDT is compatible with a constantly curved de Sitter space.

Abstract: I discuss rigorously defined coherent-state functional integral representations for the partition function and correlation functions of many-boson systems, both for the canonical and the grand-canonical ensemble, and the relation of this representation to ensembles of interacting random walks. I will highlight a few essential differences between the canonical and grand-canonical ensemble, and outline the proof of equivalence of different functional integral representations in the time-continuum limit.

Abstract: We consider the massless Dirac equation on the Kerr-Kruskal  spacetime. The Kerr-Kruskal spacetime  $M$ is the maximal globally hyperbolic extension of the exterior Kerr spacetime $M_{I}$. It is obtained by gluing $M_{I}$ with the interior region $M_{II}$ and their time-reversed versions $M_{I’}$ and $M_{II’}$ along the left and right long horizons. We construct the (past) Unruh state $\omega_{M}$ on the Kerr-Kruskal spacetime by specifying its covariances on the past null infinities $\mathcal{I}_{-}$, $\mathcal{I_}{-}’$ and on the left long horizon $\mathcal{H}_{L}$. These covariances are defined  using the two Killing vector fields $v_{\mathcal{I}}$, $v_{\mathcal {H}}$ of the Kerr metric, which are tangent respectively to null infinity and to the horizon. We show the following results:1) $\omega_{M}$ and its restriction $\omega_{M_{I\cup II}}$ to $M_{I}\cup M_{II}$ are pure states;2) the restriction of $\omega_{M}$ to $M_{I}$ is a thermal state with respect to $v_{\mathcal H}$ at the Hawking temperature $(2\pi)^{-1}\kappa$.3) $\omega_{M_{I\cup II}}$ is a Hadamard state. This is joint work with Dietrich Häfner and Michal Wrochna.

Abstract: The semi-classical Einstein equation is usually studied in highly symmetric situations in order to reduce its technical difficulties. A popular approach considers free quantum fields in Friedman-Lemaitre-Robertson-Walker spacetimes, where the time dependence is of cosmological interest. Static solutions are of less cosmological interest and have rarely been considered (except for the Minkowski vacuum). This is unfortunate, because static solutions are easier to study than dynamical ones, leading to potentially more explicit descriptions of the set of solutions. In this talk I will review some recent results on static symmetric solutions to the semi-classical Einstein-Klein-Gordon system on an Einstein static universe. One of the results is that there is a unique symmetric solution for this system if and only if this solution is the ground state.