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The infrared problem in quantum electrodynamics consists of intriguing difficulties in scattering theory appearing at large scales and low energies. Although they can be circumvented using ad hoc recipes, such as the inclusive collision…
This Thesis presents some physically motivated criteria for the existence of particles and infra-particles in a given quantum field theory. It is based on a refined spectral theory of automorphism groups describing the energy-momentum…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
We present a formulation of Quantum Electrodynamics in terms of an antisymmetric tensor gauge field. In this formulation the topological current of this field appears as a source for the electromagnetic field and the topological charge…
The algebra of observables associated with a quantum field theory is invariant under the connected component of the Lorentz group and under parity reversal, but it is not invariant under time reversal. If we take general covariance…
Systematic approaches to building up gauge invariant descriptions of charged fields, such as electrons or quarks, are described. Physically relevant descriptions must then be singled out from a multiplicity of possibilities and to this end…
The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the Quantum Wick product. The resulting theory is ultraviolet finite, but subject to an adiabatic cutoff in time which…
Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty principle, quantum corrections then depend on…
We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thereby, quantum mechanical systems are seen as dissipatively embedded part of a nonlinear classical structure producing…
It has been known for a while that there is spontaneous breaking of Lorentz symmetry in the nonzero charged sectors of quantum electrodynamics due to the infrared problem of soft photons. More recently, it has also been suggested that…
In this article a non--technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras…
Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of…
Within the framework of algebraic quantum field theory a general method is presented which allows one to compute and classify the short distance (scaling) limit of any algebra of local observables. The results can be used to determine the…
Truncating quantum field theories to a dominant mode offers a non-perturbative approach to their solution. We consider here the interaction of charged scalar matter with a single mode of the electromagnetic field. The implied breaking of…
Quantum chromodynamics is the quantum gauge field theory that describes the strong interactions. This article reviews the basic structure, successes and challenges of quantum chromodynamics as it manifests itself at short and long…
Infrared divergences obscure important analytic properties of scattering amplitudes, indicating gaps in our understanding of unitarity, causality, and crossing symmetry in theories with long-range forces. Using the exactly solvable model of…
A mathematically well-defined, manifestly covariant theory of classical and quantum field is given, based on Euclidean Poisson algebras and a generalization of the Ehrenfest equation, which implies the stationary action principle. The…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
A framework is proposed that allows to write down field theories with a new energy scale while explicitly preserving Lorentz invariance and without spoiling the features of standard quantum field theory which allow quick calculations of…
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…