# Schedule for the winter term 2018/19:

[table delimiter=”|”]Date|Speaker[attr style=”width:200px”]|Title (hover/click for abstract)[attr style=”width:400px”]

15.10.| Ludwig Hoffmann (ITP) |

22.10.| * no seminar * |

29.10.| Michal P. Heller (AEI) |

05.11.| * no seminar * |

12.11.| Federico Faldino (Genova) |

19.11.| Markus Fröb (ITP) |

26.11.| Jerzy Kijowski (Warsaw) |

03.12.| Yoh Tanimoto (Roma “Tor Vergata”) |

05.12. 15:15| Yoh Tanimoto (Roma “Tor Vergata”) |

10.12.| Daniela Cadamuro (ITP) |

17.12.| Gandalf Lechner (Cardiff) |

07.01.| Albert Much (Mexico) |

14.01.| Marco Benini (Hamburg) |

21.01.| Wojciech Dybalski (TU München) |

23.01. 15:15| Wojciech Dybalski (TU München) |

28.01.| * no seminar * |

04.02.| * no seminar * |

[/table]

**Abstract:**If the mass of an isolated system need not be positive this would evidence an inherent instability of the solutions of the theory. In general relativity the stress-energy tensor of the gravitational field vanishes and thus standard arguments, used in other theories to proof positivity, are no longer applicable. Therefore, it has proven very difficult to establish the positivity of mass in general relativity. The problem was famously solved in four dimensions in the early 1980s and more recently in all even dimensions. We show that the Bondi mass is positive in odd dimensions.

**Abstract:**Motivated by holographic complexity proposals as novel probes of black hole spacetimes, we explore circuit complexity for thermofield double (TFD) states in free scalar quantum field theories using the Nielsen approach. For TFD states at t=0, we show that the complexity of formation is proportional to the thermodynamic entropy, in qualitative agreement with holographic complexity proposals. For TFD states at t>0, we demonstrate that the complexity evolves in time and saturates after a time of the order of the inverse temperature. The latter feature, which is in contrast with the results of holographic proposals, is due to the Gaussian nature of the TFD state of the free bosonic QFT. A novel technical aspect of our work is framing complexity calculations in the language of covariance matrices and the associated symplectic transformations, which provide a natural language for dealing with Gaussian states. Furthermore, for free QFTs in 1+1 dimension, we compare the dynamics of circuit complexity with the time dependence of the entanglement entropy for simple bipartitions of TFDs. We relate our results for the entanglement entropy to previous studies on non-equilibrium entanglement evolution following quenches. We also present a new analytic derivation of a logarithmic contribution due to the zero momentum mode in the limit of vanishing mass for a subsystem containing a single degree of freedom on each side of the TFD and argue why a similar logarithmic growth should be present for larger subsystems.

**Abstract:**In this talk, we present some results concerning the stability of the interacting KMS states constructed by Fredenhagen and Lindner for a massive, scalar field on Minkowski using the framework of perturbative Algebraic Quantum Field Theory. In particular, we will analyze how the failure of stability leads to the definition of a Non-Equilibrium Steady State. To study this new state, we then define relative entropy and entropy production in pAQFT.

**Abstract:**We determine corrections to the Hubble rate due to graviton loops in a cosmological background spacetime of constant deceleration parameter. The corrections are gauge-invariant, based on a recent proposal for all-order gauge-invariant observables in perturbative quantum gravity. We find explicit expressions for the cases of matter- and radiation-dominated eras and slow-roll inflation with vanishing second slow-roll parameter. Interestingly, in the latter case the corrections can be described by a quantum-corrected first slow-roll parameter, which brings the spacetime closer to de Sitter space.

**Abstract:**In his Ph.D. thesis (1958) Andrzej Trautman has shown how to calculate the amount of energy carried by gravitational waves. This approach was later simplified by Roger Penrose’s definition of a “null infinity”. In my talk I show that these phenomena are universal and occur not only in General Relativity Theory but also in any special-relativistic field theory which exhibits radiation phenomena (like, e.g., – linear or nonlinear – electrodynamics). For this purpose I use a novel description of the “Scri” (null infinity), which leads to a further simplification of the theory.

**Abstract:**We review recent results on constructing Haag-Kastler nets which are not (necessarily) based on Wightman quantum fields. A common feature is to start with the algebras of infinitely extended regions, and define the algebras of compact regions by operator-algebraic methods. Examples include certain two-dimensional integrable models, either without or with poles in their S-matrix, their relations with 2d CFT, some possibly new massless models based on thermal states.

**Abstract:**(cake will also be included :)

**Abstract:**In nonrelativistic QED, the electron as an infraparticle exhibits velocity superselection, namely plane-wave configurations of the electron with different velocities give rise to inequivalent representations of the algebra of the asymptotic electromagnetic field in the infrared limit. Moreover, as another feature of the infrared problem, the Hamiltonian has no well-defined ground state in this realm. These properties make the construction of scattering states of electrons a difficult task. We approach these problems by viewing the electron on a new background state, the infravacuum state, which generates a new class of representations. In a model of one spinless electron interacting with the quantized electromagnetic field, we present two implementations of the infravacuum picture. The first one leads to the absence of velocity superselection, while in the second one such property persists and disappears only at the level of conjugate sectors, a situation which is unusual in the conventional DHR superselection theory.

**Abstract:**The Yang-Baxter equation (YBE) is an easy to write down but difficult to solve cubic matrix equation which plays a prominent in several fields such as integrable quantum field theory, statistical mechanics, quantum groups, braid groups, and knot theory. Motivated by applications in QFT, a recent approach to the YBE considers its invertible normal solutions (“R-matrices”) up to a natural equivalence relation, and I will describe a research programme aiming at computing/classifying all solutions of the YBE up to this equivalence. Two R-matrices turn out to be equivalent if and only if they have the same dimension and define the same extremal character of the infinite braid group, which makes it possible to use operator-algebraic tools (subfactors and endomorphisms of von Neumann algebras) for studying R-matrices. In the special case of normal involutive R-matrices, the classification is complete (joint work with Ulrich Pennig and Simon Wodd). I will also present some results on the more general case of R-matrices with two arbitrary eigenvalues, including a classification of all R-matrices defining representations of the Temperley-Lieb algebra and a deformation theorem for involutive R-matrices.

**Abstract:**In this talk we prove that the spatial part of the linear Klein-Gordon operator for a scalar field with external potential in a globally hyperbolic spacetime is an essentially self-adjoint operator. The proof is conducted by a fusion of new results concerning globally hyperbolic manifolds, the theory of weighted Hilbert spaces and operational analytic advances in the aforementioned area. This operator is then further on used to construct complex structures for Klein-Gordon theory in globally hyperbolic spacetimes.

**Abstract:**The key feature characterizing gauge theories is the presence of gauge transformations, which identify seemingly different field configurations. Gauge transformations come with useful higher information that enable one to perform powerful constructions, such as the BRST/BV quantization. The efficacy of the BRST/BV approach relies on the freedom of adding (and removing) auxiliary fields, an operation which is captured by quasi-isomorphisms. This flexibility comes at the price that all constructions one performs must be invariant under quasi-isomorphisms, instead of just isomorphisms as usual. After illustrating an example of the higher structures encoded in a gauge theory, I shall explain how to obtain constructions invariant under quasi-isomorphisms via homotopical algebra. I shall focus in particular on two cases: (1) forming classical observable algebras for gauge theories and (2) computing (homotopy) invariants of quantum field theories defined on spacetimes equipped with additional structures (e.g. spin structures, bundles with connections, …).

**Abstract:**I will recall the Buchholz-Robert proposal to cure the infrared problems by restriction to the future lightcone. Construction of Compton scattering states can be performed in this approach, provided that the electron has a sharp mass. The status of this latter assumption will be discussed in a model of non-relativistic QED. In particular, it will be explained how to implement the idea of restriction to the lightcone in a non-relativistic model. The talk is based on joint projects with S. Alazzawi and D. Cadamuro.

**Abstract:**An infraparticle is a composite object of fuzzy mass, consisting of a massive `bare particle’ and a cloud of massless particles correlated with its velocity. Due to this complicated structure, scattering processes involving one or more infraparticles are notorously difficult to describe mathematically. The massless Nelson model is a non-perturbative toy model of QED, in which a large body of knowledge about infraparticles has been accumulated. Starting from Faddeev-Kulish ideas, this talk will give an introduction and also discuss some recent advances in scattering theory of infraparticles in this model. The talk is partially based on a joint project with A. Pizzo.