Landau and Peierls wrote down the Hamiltonian of a simplified version of quantum
electrodynamics in the particle-position representation. We present a multi-time version of …

By “position operators,” we mean here a POVM (positive-operator-valued measure) on a
suitable configuration space acting on a suitable Hilbert space that serves as defining the …

We introduce and study a general notion of spatial localization on spacelike smooth Cauchy
surfaces of quantum systems in Minkowski spacetime. The notion is constructed in terms of a …

In this doctoral thesis, we develop and investigate new mathematical tools that are intended
to allow for a rigorous description of non–perturbative quantum field theory (QFT) dynamics …

The controversy on the interpretation and conceptual foundations of quantum mechanics
has been accompanying the theory since its inception in the 1920s. The question of which …

It is well known how to define the operator $ Q $ for the total charge (ie, positron number
minus electron number) on the standard Hilbert space of the second-quantized Dirac …

In this work, we establish a novel approach to the foundations of relativistic quantum theory,
which is based on generalizing the quantum-mechanical Born rule for determining particle …

In quantum field theory, Hamiltonians contain particle creation and annihilation terms that
are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes …

Since the 1950s mathematical physicists have been working on the construction of a formal
mathematical foundation for relativistic quantum theory. In the literature the view that the …

After a brief introduction to special relativity, we derive the Klein-Gordon equation, Weyl
equation, and Dirac equation as relativistic Schrödinger equations. We discuss their …