Dr. D. Cadamuro

Prof. S. Hollands

Prof. R. Verch

Organization:

Dr. A. Much

Dr. J. Zahn

**Tuesday, 14:45 – 16:15 (1 hour talk, followed by questions), seminar room 114 ITP» how to reach the ITP**.

# Schedule for the summer term 2023:

Date | Speaker | TiTle |
---|---|---|

19.05. | Markus Fröb (ITP) | |

13.06 | Markus Pflaum (University of Colorado) | |

04.07. | Rudrajit Banerjee (Okinawa Institute of Science and Technology Graduate University) | |

´ | ||

**Abstract:**The Tomita-Takesaki theory of modular automorphisms has found many uses in quantum field theory, in particular in computing relative entropies. However, the modular Hamiltonian is only known in some cases. I present results for the full modular data (flow, Hamiltonian and involution) for conformal scalar fields in the de Sitter (Bunch-Davies) vacuum state, restricted to diamonds. I further show that in the limit where the diamonds become large and fill the full static patch, the modular Hamiltonian generates time translations in the static patch, recovering the results of Sewell and Kay for this case.

**Abstract:**In the talk, an algebraic topological framework for studying state spaces of quantum lattice spin systems is presented, using the frame- work of algebraic quantum mechanics. We first provide some old and new results about the state space of the quasi-local algebra of a quan- tum lattice spin system when endowed with either the natural metric topology or the weak* topology. Switching to the algebraic topologi- cal side we then determine the homotopy groups of the unitary group of a UHF algebra and then show that the pure state space of any UHF algebra is simply connected. We finally indicate how these and related results may lead to a framework for constructing Kitaev’s loop- spectrum of bosonic invertible gapped phases of matter. The talk is on joint work with A. Beaudry, M. Hermele, J. Moreno, M. Qi and D. Spiegel.

**Abstract:**The heat kernel is a central object for quantum field theory in Euclidean signature, both for one-loop perturbation theory and non-perturbative functional renormalization group methods. On generic curved backgrounds, however, the link between Euclidean and Lorentzian signature QFT via a Wick rotation is not fully understood. In this talk I will present a proposal for Wick rotating on generic globally hyperbolic manifolds by analytically continuing the lapse function in the ADM decomposition. This keeps the coordinates real and can be shown to define “admissible” complex metrics even under foliation changing diffeomorphisms. A proof of existence of the associated Wick-rotated heat semi-group (and its kernel) will be sketched, together with a conjecture on the strict Lorentzian limit. Some aspects are illustrated with the Wick rotated deSitter heat kernel.