# Past Quantum Field Theory Seminar

In this talk, I will review an inverse scattering construction of interacting integrable quantum field theories on two-dimensional Minkowski space and its ramifications. The construction starts from a given two-body S-matrix instead of a classical Lagrangean, and defines corresponding quantum field theories in a non-perturbative manner in two steps: First certain semi-local fields are constructed explicitly, and then the analysis of the local observable content is carried out with operator-algebraic methods (Tomita-Takesaki modular theory, split subfactor inclusions). I will explain how this construction solves the inverse scattering problem for a large family of interactions, and also discuss perspectives on extensions of this program to higher dimensions and/or non-integrable theories.

Amplitudes in quantum field theory have discontinuities when regarded as

functions of

the scattering kinematics. Such discontinuities can be determined from

Cutkosky rules.

We present a structural analysis of such rules for massive quantum field

theory which combines

algebraic geometry with the combinatorics of Karen Vogtmann's Outer Space.

This is joint work with Spencer Bloch (arXiv:1512.01705).

Hawking radiation and particle creation by an expanding Universe

are paradigmatic predictions of quantum field theory in curved spacetime.

Although the theory is a few decades old, it still awaits experimental

demonstration. At first sight, the effects predicted by the theory are too

small to be measured in the laboratory. Therefore, current experimental

efforts have been directed towards siumlating Hawking radiation and

studying quantum particle creation in analogue spacetimes.

In this talk, I will present a proposal to test directly effects of

quantum field theory in the Earth's spacetime using quantum technologies.

Under certain circumstances, real spacetime distortions (such as

gravitational waves) can produce observable effects in the state of

phonons of a Bose-Einstein condensate. The sensitivity of the phononic

field to the underlying spacetime can also be used to measure spacetime

parameters such as the Schwarzschild radius of the Earth.

[based on joint work with Li Guo and Bin Zhang]

We apply to the study of exponential sums on lattice points in

convex rational polyhedral cones, the generalised algebraic approach of

Connes and Kreimer to perturbative quantum field theory. For this purpose

we equip the space of cones with a connected coalgebra structure.

The algebraic Birkhoff factorisation of Connes and Kreimer adapted and

generalised to this context then gives rise to a convolution factorisation

of exponential sums on lattice points in cones. We show that this

factorisation coincides with the classical Euler-Maclaurin formula

generalised to convex rational polyhedral cones by Berline and Vergne by

means of an interpolating holomorphic function.

We define renormalised conical zeta values at non-positive integers as the

Taylor coefficients at zero of the interpolating holomorphic function. When

restricted to Chen cones, this yields yet another way to renormalise

multiple zeta values at non-positive integers.