Some of the most studied examples of conformal field theories

include

the Wess-Zumino-Witten models. These are conformal field theories exhibiting

affine Lie algebra symmetry at non-negative integers levels. In this talk I

will

discuss conformal field theories exhibiting affine Lie algebra symmetry at

certain rational (hence fractional) levels whose structure is arguably even

more intricate than the structure of the non-negative integer levels,

provided

one is prepared to look beyond highest weight modules.

# Past Quantum Field Theory Seminar

Hardy's axiomatic approach to quantum theory revealed that just one axiom

distinguishes quantum theory from classical probability theory: there should

be continuous reversible transformations between any pair of pure states. It

is the single word `continuous' that gives rise to quantum theory. This

raises the question: Does there exist a finite theory of quantum physics

(FTQP) which can replicate the tested predictions of quantum theory to

experimental accuracy? Here we show that an FTQP based on complex Hilbert

vectors with rational squared amplitudes and rational phase angles is

possible providing the metric of state space is based on p-adic rather than

Euclidean distance. A key number-theoretic result that accounts for the

Uncertainty Principle in this FTQP is the general incommensurateness between

rational $\phi$ and rational $\cos \phi$. As such, what is often referred to

as quantum `weirdness' is simply a manifestation of such number-theoretic

incommensurateness. By contrast, we mostly perceive the world as classical

because such incommensurateness plays no role in day-to-day physics, and

hence we can treat $\phi$ (and hence $\cos \phi$) as if it were a continuum

variable. As such, in this FTQP there are two incommensurate Schr\"{o}dinger

equations based on the rational differential calculus: one for rational

$\phi$ and one for rational $\cos \phi$. Each of these individually has a

simple probabilistic interpretation - it is their merger into one equation

on the complex continuum that has led to such problems over the years. Based

on this splitting of the Schr\"{o}dinger equation, the measurement problem

is trivially solved in terms of a nonlinear clustering of states on $I_U$.

Overall these results suggest we should consider the universe as a causal

deterministic system evolving on a finite fractal-like invariant set $I_U$

in state space, and that the laws of physics in space-time derive from the

geometry of $I_U$. It is claimed that such a deterministic causal FTQP will

be much easier to synthesise with general relativity theory than is quantum

theory.

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)

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.