I will review some classical results on geometric scattering

theory for linear hyperbolic evolution equations

on globally hyperbolic spacetimes and its relation to particle and charge

creation in QFT. I will then show that some index formulae for the

scattering matrix can be interpreted as a special case of the Lorentzian

analog of the Atyiah-Patodi-Singer index theorem. I will also discuss a

local version of this theorem and its relation to anomalies in QFT.

(Joint work with C. Baer)

# Past Quantum Field Theory Seminar

I will start with a quick reminder of what we have learned so far about

transplanckian-energy collisions of particles, strings and branes.

I will then address the (so-far unsolved) problem of gravitational

bremsstrahlung from massless particle collisions at leading order in the

gravitational deflection angle.

Two completely different calculations, one classical and one quantum, lead

to the same final, though somewhat puzzling, result.

In this talk I will present recent results obtained within the

framework of perturbative algebraic quantum field theory. This novel

approach to mathematical foundations of quantum field theory allows to

combine the axiomatic framework of algebraic QFT by Haag and Kastler with

perturbative methods. Recently also non-perturbative results have been

obtained within this approach. I will report on these results and present

new perspectives that they open for better understanding of foundations of

QFT.

How long does a uniformly accelerated observer need to interact with a

quantum field in order to record thermality in the Unruh temperature?

In the limit of large excitation energy, the answer turns out to be

sensitive to whether (i) the switch-on and switch-off periods are

stretched proportionally to the total interaction time T, or whether

(ii) T grows by stretching a plateau in which the interaction remains

at constant strength but keeping the switch-on and switch-off

intervals of fixed duration. For a pointlike Unruh-DeWitt detector,

coupled linearly to a massless scalar field in four spacetime

dimensions and treated within first order perturbation theory, we show

that letting T grow polynomially in the detector's energy gap E

suffices in case (i) but not in case (ii), under mild technical

conditions. These results limit the utility of the large E regime as a

probe of thermality in time-dependent versions of the Hawking and

Unruh effects, such as an observer falling into a radiating black

hole. They may also have implications on the design of prospective

experimental tests of the Unruh effect.

Based on arXiv:1605.01316 (published in CQG) with Christopher J

Fewster and Benito A Juarez-Aubry.

In the cosmological scheme of conformal cyclic cosmology (CCC), the equations governing the crossover form each aeon to the next demand the creation of a dominant new scalar material that is postulated to be dark matter. In order that this material does not build up from aeon to aeon, it is taken to decay away completely over the history of the aeon. The dark matter particles (erebons) would be expected to behave as essentially classical particles of around a Planck mass, interacting only gravitationally, and their decay would be mainly responsible for the (~scale invariant)

temperature fluctuations in the CMB of the succeeding aeon. In our own aeon, erebon decay ought to be detectable as impulsive events observable by gravitational wave detectors.

We find a new duality for form factors of lightlike Wilson loops

in planar N=4 super-Yang-Mills theory. The duality maps a form factor

involving a lightlike polygonal super-Wilson loop together with external

on-shell states, to the same type of object but with the edges of the

Wilson loop and the external states swapping roles. This relation can

essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace

where it is equivalent to planar graph duality.

In 1997, Maxim Kontsevich gave a universal formula for the

quantization of Poisson brackets. It can be viewed as a perturbative

expansion in a certain two-dimensional topological field theory. While the

formula is explicit, it is currently impossible to compute in all but the

simplest cases, not least because the values of the relevant Feynman

integrals are unknown. In forthcoming joint work with Peter Banks and Erik

Panzer, we use Francis Brown's approach to the periods of the moduli space

of genus zero curves to give an algorithm for the computation of these

integrals in terms of multiple zeta values. It allows us to calculate the

terms in the expansion on a computer for the first time, giving tantalizing

evidence for several open conjectures concerning the convergence and sum of

the series, and the action of the Grothendieck-Teichmuller group by gauge

transformations.

The "Weyl fermion" was discovered in a topological semimetal in

2015. Its mathematical characterisation turns out to involve deep and subtle

results in differential topology. I will outline this theory, and explain

some connections to Euler structures, torsion of manifolds,

and Seiberg-Witten invariants. I also propose interesting generalisations

with torsion topological charges arising from Kervaire semicharacteristics

and ``Quaternionic'' characteristic classes.