Light-Cone Expansion of the Dirac Sea in the Presence of Chiral and Scalar Potentials

We study the Dirac sea in the presence of external chiral and scalar/pseudoscalar potentials. In preparation, a method is developed for calculating the advanced and retarded Green's functions in an expansion around the light cone. For this, we first expand all Feynman diagrams and then explicitly sum up the perturbation series. The light-cone expansion expresses the Green's functions as an infinite sum of line integrals over the external potential and its partial derivatives. The Dirac sea is decomposed into a causal and a non-causal contribution. The causal contribution has a light-cone expansion which is closely related to the light-cone expansion of the Green's functions; it describes the singular behavior of the Dirac sea in terms of nested line integrals along the light cone. The non-causal contribution, on the other hand, is, to every order in perturbation theory, a smooth function in position space.Comment: 59 pages, LaTeX (published version

Fermion Systems in Discrete Space-Time

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.Comment: 8 pages, LaTeX, few typos corrected (published version

The Fermionic Projector, Entanglement, and the Collapse of the Wave Function

After a brief introduction to the fermionic projector approach, we review how entanglement and second quantized bosonic and fermionic fields can be described in this framework. The constructions are discussed with regard to decoherence phenomena and the measurement problem. We propose a mechanism leading to the collapse of the wave function in the quantum mechanical measurement process.Comment: 17 pages, LaTeX, 2 figures, minor changes (published version

The Interaction of Dirac Particles with Non-Abelian Gauge Fields and Gravity - Bound States

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang/Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.Comment: 28 pages, 21 figures (published version

Congruence Veech Groups

We study Veech groups of covering surfaces of primitive translation surfaces. Therefore we define congruence subgroups in Veech groups of primitive translation surfaces using their action on the homology with entries in $\mathbb{Z}/a\mathbb{Z}$. We introduce a congruence level definition and a property of a primitive translation surface which we call property $(\star)$. It guarantees that partition stabilising congruence subgroups of this level occur as Veech group of a translation covering. Each primitive surface with exactly one singular point has property $(\star)$ in every level. We additionally show that the surface glued from a regular $2n$-gon with odd $n$ has property $(\star)$ in level $a$ iff $a$ and $n$ are coprime. For the primitive translation surface glued from two regular $n$-gons, where $n$ is an odd number, we introduce a generalised Wohlfahrt level of subgroups in its Veech group. We determine the relationship between this Wohlfahrt level and the congruence level of a congruence group