abstract:Causal perturbation theory (CPT) in configuration spaces is reputed for its logical clarity and rigor. Unfortunately, it is largely unknown that there is much more to it: CPT clarifies several aspects of current phenomenology, helping to dispel misconceptions in field theory. For instance, from its viewpoint, Higgs fields often become necessary to save the consistency of the CPT when massive gauge bosons are present. This is quite a different thing from stating that a Higgs mechanism gives rise to all the particles’ masses. Chirality of the weak interactions and the covariant derivative coupling itself can be traced back to their quantum roots by use of CPT. We review these facts, as well as an application to perturbative PCT symmetry of interacting models.

abstract: The framework of locally covariant field theory proved extremely fruitful for QFT on curved space-times. It can be straightforwardly generalised to more general non trivial background fields, in particular gauge connections. I will present two applications of this framework. The first is an elementary computation of the well-known anomalies, directly on Lorentzian space-times. The second application is QED in external potentials, where I will briefly report on some work in progress with J. Schlemmer.

abstract:The Operator Product Expansion (OPE) is a tool for studying the short distance behaviour of products of quantum fields, which has found practical uses both in explicit calculations as well as in conceptual studies in quantum field theory. I will review new insights into the status and properties of the OPE within Euclidean perturbation theory, addressing in particular the topics of convergence and ?factorisation? of the expansion. Further, I will present a novel recursive scheme for the perturbative computation of OPE coefficients. These results are derived within the renormalisation group flow equation approach to perturbative quantum field theory, which I will also briefly review.

abstract:Light quantum fields show large infrared effects in the natural de Sitter vacuum state, which become divergences for massless fields such as gravitons. I review the problem and some proposed solutions, and investigate in more detail the concrete model of matter loop corrections to graviton correlation functions, showing that gauge-invariant local observables are IR finite in that case. Lastly, I comment on generalizations to other cosmological spacetimes.

abstract:Quantum inequalities extend the concept of classic energy conditions to quantised matter on curved backgrounds. They are useful tools to restrict “exotic” physics like wormholes or violations of thermodynamic laws. I will review on formulation and implications of energy conditions in general relativity and quantum energy inequalities. Recent results on quantum pressure inequalities will be presented and open questions, to be addressed in my upcoming master thesis, will be discussed.

abstract:In 4d QFT, interactions cannot directly be introduced by adding an interaction Hamiltonian as an integral of a local density over the time zero hypersurface, due to UV singularities of Wick polynomials. It will be shown how this problem can be circumvented within renormalized formal perturbation theory by exploiting the validity of the time slice axiom. One obtains a (slightly nonlocal) operator valued density which induces the interaction. The formalism can be used to solve a longstanding open problem namely the perturbative construction of states with nonzero temperature for interacting quantum field theories in 4 dimensions.

abstract:In this talk we will show how to understand the intrinsic structure of perturbative algebraic quantum field theory models using the BV formalism. It turns out that the standard construction used to obtain such models leads in a natural way to the concept of Gerstenhaber algebras and the BV algebras. As an illustration of this fact we will discuss the example of a free scalar field and the example of effective quantum gravity, where new features appear.

abstract:In this talk I will propose yet another construction of a Weyl algebra. There is on the one hand the purely algebraic Weyl algebra generated by the canonical commutation relations. In an operator algebra setting this yields the usual unbounded operators. On the other hand, exponentiating the canonical commutation relations and declaring the generators to be unitary gives a version of the Weyl algebra which can be completed to a C*-algebra. My construction is somehow in between as it starts with the unbounded, algebraic version, endows it with a locally convex topology in such a way that the product becomes continuous and yields then a completion which has interesting properties. I will describe some of these features in my talk.

abstract:We consider gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic QFT we construct states describing collisions of several particles and the corresponding S-matrix. We also demonstrate that velocities of particles cannot exceed the Lieb-Robinson velocity. To obtain these results we adapt the concepts of almost local observables and energy-momentum transfer (Arveson spectrum) from relativistic QFT to the lattice setting. Our results hold, in particular, in the Ising model in strong transverse magnetic fields. (Joint work with Sven Bachmann and Pieter Naaijkens).

abstract:In this talk recent approaches to the construction of weakly interacting models within the framework of algebraic quantum field theory are discussed. These include inverse scattering methods in two spacetime dimensions and deformation techniques in arbitrary dimension. Our analysis extends earlier results achieved in this field by G. Lechner et al. and incorporates models such as the Sinh-Gordon or the two-dimensional O(N)-invariant sigma-models.

abstract:The Sauter-Schwinger effect predicts the creation of electron-positron pairs out of the quantum vacuum via tunnelling induced by a strong electric field. After a brief introduction into the basics of this effect, we discuss the recently discovered possibility to enhance the pair-creation probability by adding a weaker time-dependent electric field (dynamically assisted Sauter-Schwinger effect). Finally, we comment on prospects for an experimental verification of this fundamental prediction of quantum field theory — either directly or via suitable laboratory analogues.

abstract:The Unruh effect is one of the most startling predictions of quantum field theory. Its interpretation has been controversially discussed, since the first publications of Fulling, Davies and Unruh in the 1970ties. In a recent paper Buchholz and Solveen proposed an application of basic thermodynamic definitions to clarify the meaning of temperature and thermal equilibrium in the Unruh effect. As a result the interpretation of the KMS-parameter as an expression of local temperature has been questioned. I will present the main result of my diploma thesis, which asserts quasi-equivalence of the disputed KMS states on a subregion of Rindlerspace that infinitely extends in the direction of travel of a uniformly accelerated Rindler-observer. Exploring the consequences of this result, I will present new insights on the asymptotic behaviour of such KMS states and how this fits into the picture drawn by Buchholz and Solveen.

abstract:Recently, Giuli and Grossard have studied non-relativistic limit (1/c-> 0) of the Einstein-Klein-Gordon and Einstein-Dirac equations for classical fields with spherical symmetry and they have argued that the Schrödinger-Newton equation is obtained in the limit. There are also several related results by other authors, notably a rigorous derivation of Bechuche, Mauser and Selberg of the Schrödinger-Newton (or Schrödinger-Poisson) equation from the Maxwell-Klein-Gordon system for classical fields. These results are reviewed, and also some hypothetical experimental tests of the Schrödinger-Newton equation will be mentioned. Then we present our starting point, which is the investigation of the non-relativistic limit of the semiclassical Einstein-Klein-Gordon system, i.e. the semiclassical Einstein equations with a quantized Klein-Gordon field.

abstract: In view of the measured Higgs mass of 125 GeV, the perturbative renormalization group evolution of the Standard Model suggests that our Higgs vacuum might not be stable. We re-analyze the conventional arguments that relate a lower bound for the Higgs mass with vacuum stability in the light of exact results for the regularized fermion determinant as well as in the framework of the functional renormalization group. A lower bound for the Higgs mass arises for the class of standard bare potentials of φ4 type from the requirement of a well-defined functional integral. This consistency bound can however be relaxed considerably by more general forms of the bare potential without necessarily introducing new meta-stable minima. We find that details of the microscopic potential can have a sizable influence on the maximum ultraviolet scale of the Standard Model and the existence of instabilities.

abstract:The weak coupling limit for the solution of the Schrödinger equation for times on the van Hove timescale $t >> g^{-2}$, where $g$ is the coupling constant, is reviewed. A method for the construction of effective Hamiltonians for larger time scales is described in the context of the spin-boson model (at zero temperature). This is joint work with Jacob Möller and Matthias Westrich.