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The problem of the `infinite energy' of a point charge is well known in connection with the Lorentz--Abraham--Dirac equation and, more significantly, in quantum electrodynamics. Though it is not stated usually, this is strongly related to…
We suggest that the correspondence between gauge theories strongly coupled in the infrared and their low energy effective theories may be probed by introducing topologically non-trivial background scalar fields. We argue that one loop…
Absolute confinement of its color charges is a natural property of gauge theories such as quantum chromodynamics. On the one hand, it can be attributed to the existence of color-magnetic monopoles, a topological feature of the theory, but…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
Recent progress in the construction of both electric, coloured and magnetic charges in gauge theories will be presented. The topological properties of the charged sectors will be highlighted as well as the applications of this work to…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
We introduce a "web-based formalism" for describing the category of half-supersymmetric boundary conditions in $1+1$ dimensional massive field theories with ${\cal N}=(2,2)$ supersymmetry and unbroken $U(1)_R$ symmetry. We show that the…
We introduce a nonperturbative, first principles numerical approach for solving time-dependent problems in quantum field theory, using light-front quantization. As a first application we consider QED in a strong background field, and the…
Recently it has been shown that infrared singularities of Landau gauge QCD can confine static quarks via a linearly rising potential. We show that the same mechanism can also provide a confining interaction between charged scalar fields in…
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum…
The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field…
We further investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background space-times. According to these postulates, quantum theory is supplemented by local…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Following earlier work on the same topic, we consider once more scalar field theories on the world sheet parametrized by the light cone coordinates. For most of the way, we use the same approach as in the previous work, but there is an…
The use of quantum field theory to understand astrophysical phenomena is not new. However, for the most part, the methods used are those that have been developed decades ago. The intervening years have seen some remarkable developments in…
In our world the standard model of particle physics contains within it the fairly intractable theory called QCD. A toy version with two colours is often studied as a model confining and chiral symmetry breaking field theory. Here we…
We propose a mathematically rigorous construction of the scattering matrix and the interacting fields in models of relativistic perturbative quantum field theory with massless fields and long-range interactions. We consider quantum…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
We incorporate the concept of dimensional reduction at high energies within the perturbative formulation of quantum field theory. In this new framework, space and momentum integrations are modified by a weighting function incorporating an…