Willkommen zum Oberseminar Mathematische Physik

In this talk, we make propaganda for string-local fields (introduced about ten years ago by Mund, Schroer and Yngvason as free fields) in interaction, touting a few of their main advantages.

• Perturbative calculations with string-local fields are performed without ever leaving the Hilbert-Fock space: ghosts, anti-ghosts, and “unphysical" fields in general, become unnecessary.
• We explain why string-local fields have good ultraviolet behavior irrespectively of spin, and how they allow to illuminate a few corners of the Standard Model, like the origin of chirality of flavourdynamics, or the shape of the Higgs particle potential.
• Wigner’s unbounded-helicity particles with Casimir value P^2=0, W^2<0 enter the realm of physics. They might be inert, except under the action of gravity (this may turn an advantage in Cosmology).

Models of the GRW type are unique in postulating an inherently stochastic dynamics. The possible interpretation of the probabilistic claims appearing in them faces different challenges from those encountered in classical statistical mechanics or in Bohmian mechanics. I argue that to qualify as truly objective, observer-free theories, such models must provide some necessary factual consequences and I look for possible ways by which they can do so. It emerges that certain jump-processes fare better than diffusion-processes in this regard. A particular model for the motion of classical point particles which seems to satisfy these requirements is examined.

In this talk, I present a recent result of mine about the appearance of black holes - defined as regions of finite lifetime in the maximal Cauchy development - in asymptotically flat Maxwell-Einstein Theory. The tools used for the result are the theory of conformal extensions, a important result of Schoen and Yau and generalizations of the classical singularity theorems of Hawking and Penrose.

In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in full generality – i.e. without making any assumptions about the system׳s dynamics or the nature of the interactions between its components – that the equilibrium macro-region is the largest macro-region. We then turn to the question of the approach to equilibrium, of which there exists no satisfactory general answer so far. In our account, this question is replaced by the question when an equilibrium state exists. We prove another – again fully general – theorem providing necessary and sufficient conditions for the existence of an equilibrium state. This theorem changes the way in which the question of the approach to equilibrium should be discussed: rather than launching a search for a crucial factor (such as ergodicity or typicality), the focus should be on finding triplets of macro-variables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem.

I will construct a fully relativistic collapse model that can be "hidden" in an orthodox interacting QFT. The model will take the form of a Lorentz invariant statistical field theory, where the beable field will bear some superficial similarities with the GRW flashes. A crucial feature of this model will be that its phenomenology at the emergent operational level is exactly that of an orthodox interacting QFT (insofar as the latter can be mathematically well defined at the S matrix level). This approach will help us fix several long standing issues of the dynamical reduction program: the model will be manifestly Lorentz invariant at the primitive ontology level, the "smearing" problem "solved" by perturbative renormalization and the heating effects cancelled to all orders. More importantly, it shall call for a revision of the very ambitions of the dynamical reduction program: as a redefinition/interpretation rather than as a modification of quantum theory. Finally, setting conceptual foundations aside, we will dream and hint at ways in which this new perspective might serve as a future basis for rigorous probabilistic constructions of interacting QFTs. This talk will be about a work that is largely in progress, hence although its main claims are now quite confidently grounded, the final results might subtly differ: this abstract is not contractual.

One of the biggest open problems in physics is the consistent unification of quantum theory with general relativity. The resulting quantum theory of gravity would have an important bearing upon the physics of the early universe, the understanding of black holes, and the structure of spacetime. In my talk, I start by giving a general introduction to the motivation for and the problems of a theory of quantum gravity. I then briefly describe the main approaches - quantum general relativity (including loop quantum gravity) and string theory - and some of their applications. I conclude with presenting some recent results that deal with the possible observation of primordial gravitons, the microstructure of space, black-hole entropy, and quantum cosmology.