Sommerfeld Theory Colloquium (ASC)

The (unique) maximally extended D=11 supermembrane theory stands out as a candidate for the non-perturbative unification of superstring theory. In this talk I will review some basic features, in particular the light-cone gauge reformulation of the theory as the N-->\infty limit of the maximally supersymmetric SU(N) matrix model, and present new evidence for the existence of the N-->\infty limit, using a path integral formulation. I will also touch on several open issues, such as the construction of supermembrane vertex operators.

In this talk I present a simple derivation of an old result of Kochen and Specker, which is apparently unrelated to the famous work of Bell on hidden variables, but is presumably equally important. Kochen and Specker showed in 1967 that quantum mechanics cannot be embedded into a classical stochastic theory, provided the quantum theoretical probability distributions are repro- duced and one additional highly desirable property is satisfied. This showed in a striking manner what were the difficulties in implementing the Einstein programme of a `complete' version of quantum mechanics.

We review the current status of measurements of the spectrum, an isotropy and polarization of the CMB, and their impact on cos-

mology. We show that there is still a large discovery potential in

these measurements, complementing and synergic to other cosmology observations. We also describe a selection of new measurement eff�orts, including high precision measurements of CMB polarization

with ground-based, stratospheric balloon and satellite experiments,

focusing on the astrophysical and technological limits of these measurements.

An appealing and challenging route towards engineering materials with specic properties is to find ways of designing or selectively manipulate materials, especially at the quantum level. We will provide an overview of how well-established concepts in the fields of quantum chemistry and materials have to be adapted when the quantum nature of light becomes important. We will pursue the question whether it is possible to create these new states of materials as groundstates of the system. To this end we will show how the emerging (vaccum) dressed states resembles Floquet states in driven systems. A particular appeal of light dressing is the possibility to engineer symmetry breaking which can lead to novel properties of materials, e.g coupling to circularly polarized photons leads to local breaking of time-reversal symmetry enabling the control over a large variety of materials properties (e.g.topology). We show that the new quantum electrodynamics density-functional formalism (QEDFT) can acocunt for those effects. We illustrate the realisation of those ideas in molecular complexes and 2D materials.

Type Ia supernovae are standard (isable) candles so observing them out to cosmological distances reveals the change of the Hubble parameter with redshift. Such observations have been interpreted to mean that the expansion rate of the universe is accelerating, as if driven by a Cosmological Constant. However reanalysis of the data shows that the inferred cosmic acceleration is anisotropic and aligned with the CMB dipole - so is likely an artefact due to our being untypical observers embedded in a local non-Hubble `bulk flow’. Moreover the usual kinematic interpretation of the CMB dipole is rejected at 4.9 sigma as the corresponding dipole in the distribution of distant quasars is much bigger than expected. The implications of these surprising findings will be discussed.

From the softest of interactions of a magnetic field with an electron, to the most violent collisions at the Large Hadron Collider, precision quantum field theory produces numbers and functions with interesting number-theoretic properties. In many examples a co-action principle holds, an invariance under a ”cosmic” Galois group. I will provide several arenas in which this principle can be seen at work, including perhaps the richest set of theoretical data, scattering amplitudes in planar N = 4 super-Yang-Mills theory.

I will describe recent developments on the (numerical) computation of energy levels of various systems by the quantum mechanical bootstrap. The main way the bootstrap works is by using constraints that arise from positive matrices. Part of the goal is to turn the bootstrap problem into a problem that can be solved by semi-definite programming methods. I will describe how this method leads to solutions of the spectrum of various systems and will describe some additional applications of this way of solving problems to the study of quantum spin chains.

The asymptotic structure of gravity in the asymptotically flat case will be described in four and higher spacetime dimensions by making central use of the Hamiltonian formalism. Special emphasis will be paid to the case D=5. How the relevant infinite-dimensional asymptotic symmetry group (BMS group) emerges at spatial infinity will be explained. Non-linear structures which appear in five (and higher) spacetime dimensions will be discussed.

Electron-positron pair production in ultra-strong electric fields, the Sauter-Schwinger effect, is a long-standing theoretical prediction. In this talk the Sauter-Schwinger effect will be introduced and the related field-strength and energy scales as well as the possibility to verify this effect in upcoming multi-petawatt laser facilities will be discussed. The Dirac-Heisenberg-Wigner formalism provides a fully Poincaré-covariant, non-perturbative phase space description of the Sauter-Schwinger effect, and therefore its key quantities will be introduced. Some respective numerical results will be shown and discussed.

An interpretation of a particle distribution at finite (non-asymptotic) times will be provided via a Gedankenexperiment. This in turn enables one to isolate and, therefore, identify the relevant time scales of particle formation. The resulting generic aspects for particle creation in quantum physics beyond perturbation theory will be elucidated.

Perturbation theory remains one of the main tools in physics, in particular in quantum theories. However, most perturbative series diverge factorially, and it is not obvious how to extract information from them. Their divergence also suggests that, in order to obtain accurate results, one might need additional non-perturbative information. The theory of resurgence has been proposed as a general framework to address these issues. In this talk I will give an introduction to this theory and will illustrate it with applications -old and new- in quantum mechanics, quantum field theory and string theory.