Abstract: Massless fields on the Kerr spacetime are governed by the Teukolsky Master Equation, and the Teukolsky-Starobinsky Identity. Solutions can be represented in terms of Deby potentials. In this talk I will show how these facts lead to insights on symmetry operators and conservation laws for fields on the Kerr spacetime, including linearized gravity.

Abstract: Global anomalies are anomalies w.r.t. large gauge transformations and can thus be seen as a non-perturbative effect. They are usually defined and calculated in a path integral framework. It is shown how to formulate and compute global anomalies in a Lorentzian setting, using the framework of locally covariant quantum field theory. We make essential use of the concept of perturbative agreement introduced by Hollands&Wald and also relate it to the Wess-Zumino consistency condition. Joint work with A. Schenkel.

Abstract: Matrix product states (MPS) is a representation of many body quantum systems in terms of a set of matrices. We show how one can adopt this representation to simplify calculations concerning entanglement of many body quantum systems and Chernoff distance of two translationally invariant density operators. By applying the concept of geometrical entanglement, we show how one can compare the entanglement of two translationally invariant many body quantum systems in terms of the matrices in MPS representation.

Abstract: This talk is about the so-called “operator product expansion” in Quantum Field Theory. I first explain what it is. Then I briefly indicate its practical uses. Finally, I will present recent results concerning its convergence- and associativity properties.

Abstract: When condensed-matter systems in which low-energy thermal fluctuations occur are confined by a pair of parallel planes or walls to a film geometry, effective forces between the planes are generated by these fluctuations. Familiar examples are ${}^4$He near the $\lambda$ transition and Bose gases near the condensation transition. The cases of He or Bose gases in a 3D film geometry are particularly challenging since nontrivial dimensional crossovers of 3D bulk systems exhibiting long-range order at low temperatures to effective 2D systems without long-range order must be handled in addition to bulk, boundary, and finite-size critical behaviors. We show that exact results can be obtained for analogous $n$-component $\phi^4$ models in the limit $n\to\infty$ via inverse-scattering theory and other methods, and show that these results apply directly to the so-called imperfect Bose gas.

Abstract: The results of Heisenberg, Euler, and Schwinger will be reviewed. The extension to non-Abelian gauge theories will be presented. The discovery of the gluon condensation and its relation with asymptotic freedom will be uncovered. Based on PLB 71 (1977) 133 and PLB 732 (2014) 150.

Abstract: After a brief review of the basic ideas and methods of the Asymptotic Safety approach to quantum gravity we discuss the possibility of defining a “C-function” in this setting, with properties similar to the one in Zamolodchikov’s c-theorem for 2 dimensions.

Abstract: The short distance scale dimension d_{sd} of spin s≥1 field can be lowered to the spin-independent value d_{sd}=1. The use of such fields in in a new perturbation theory permits the preservation of positivity together with renormalizability in certain higher spin interactions. In contrast to the positivity violating gauge theory for which only gauge invariant operators preserve positivity and the physical causal localization the new string-local perturbation theory is a full QFT. (part of a joint project with Jens Mund)

Abstract: The D-CTC condition has originally been proposed by David Deutsch as a condition on states of a quantum communication network that contains “backward time-steps” in some of its branches. It has been argued that this is an analogue for quantum processes in the presence of closed timelike curves (CTCs). The unusual properties of states of quantum communication networks that fulfill the D-CTC condition have been discussed extensively in recent literature. In this work, the D-CTC condition is investigated in the framework of quantum field theory in the local, operator-algebraic approach due to Haag and Kastler. It is shown that the D-CTC condition cannot be fulfilled in states which are analytic in the energy, or satisfy the Reeh-Schlieder property, for a certain class of processes and initial conditions. On the other hand, if a quantum field theory admits sufficiently many uncorrelated states across acausally related spacetime regions (as implied by the split property), then the D-CTC condition can always be fulfilled approximately to arbitrary precision. As this result pertains to quantum field theory on globally hyperbolic spacetimes where CTCs are absent, one may conclude that interpreting the D-CTC condition as characteristic for quantum processes in the presence of CTCs could be misleading, and should be regarded with caution. Furthermore, a construction of the quantized massless Klein-Gordon field on the Politzer spacetime, often viewed as spacetime analogue for quantum communication networks with backward time-steps, is proposed in this work. This is recent joint work together with Jürgen Tolksdorf, see arxiv.org/abs/1609.01496

Abstract: Conformal gravity is a conformally invariant variant of general relativity. Briefly, it is based upon Einstein’s theory of gravity combined with Weyl’s original idea of a gauge theory that is supposed to be spontaneously broken. Conformal gravity was pursued, in particular, by Omote, Dirac and Utiyama in the beginning and mid 1970s. Somewhat later, it was picked up again by Smolin, Cheng, Drechsler/Tann and Drechsler who replaced the scalar field by the Higgs field of the electroweak sector of the standard model. It is well-known that Weyl’s original idea to identify the additional gauge field that comes with conformal invariance with the electromagnetic potential does not work out phenomenologically. Furthermore, Weyl incorporated gravity via fourth order equations for the metric. Conformal gravity allows to circumvent both issues. Instead of a phenomenological discussion, however, I will primarily consider the geometrical underpinnings of conformal gravity, when the latter is considered as a gauge theory in a mathematical rigorous sense. I will demonstrate that the inclusion of fermions then allows to geometrically interpret Weyl’s gauge potential not just as a connection but as torsion of space-time. Within the geometrical frame of conformal gravity this torsion becomes massive and propagating, although it might rather weakly couple to fermions. These basic features in turn allow to consider general relativity as a (rather good) approximation of conformal gravity and yet the latter might have interesting phenomenological consequences, especially with respect the issue of dark matter/energy.

Abstract: We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The invariant Lagrangian is expressed in terms of higher-rank field strength tensors. All interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan-Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. We consider a possibility that inside the proton there are additional partons – tensorgluons, which can carry a part of the proton momentum. The extension of QCD influences the unification scale shifting its value to lower energies.

Abstract: Nowadays, lattice computations are in a shape to compute physical quantities with errors (statistical and systematic) which are comparable to the errors of their experimental counterparts. This enables a fair comparison with experiment or even precise predictions for certain physical quantities. For it the signal-to-noise ratio in the Monte Carlo measurement process must be sufficiently large. And, of course, the approximations to the full theory (QCD) should be as small as possible. A promising approach to achieve this goal is the application of the Feynman-Hellmann (FH) theorem. By this method the computation of the relevant matrix elements is related to the calculation of the energy dependence of two-point functions. The FH theorem has been proven in quantum mechanics several decades ago. Only recently, this method has been transferred to quantum field theory. We discuss the lattice formulation of FH. Finally, we present its potential with encouraging applications to observables which are essential for the structures of the hadrons like spin or form factors.