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When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thus, quantum mechanical systems are dissipatively embedded into a nonlinear classical dynamical structure. There is a…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
We present the ``algebrodynamical'' approach to field-particle theory based on a nonlinear generalization of the Cauchy-Riemann conditions to non-commutative algebras of quaternion-like type. For complex quaternions the theory is Lorentz…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
The problem of an ultrarelativistic charge in the presence of an atomic and a plane-wave field is investigated in the quasiclassical regime by including exactly the effects of both background fields. Starting from the quasiclassical Green's…
We generalize the operadic approach to algebraic quantum field theory [arXiv:1709.08657] to a broader class of field theories whose observables on a spacetime are algebras over any single-colored operad. A novel feature of our framework is…
In two recent papers by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects,…
We propose that the low energy behavior of a pure gauge theory can be studied by simply assuming violation of Lorentz invariance which is implemented through a deformation of the canonical Poisson brackets of the theory depending on an…
If constituent quarks are to emerge from QCD they must have well defined colour and be energetically favoured. After reviewing the general properties of charges in gauge theories, a method for constructing charges is presented and applied…
We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…
It has long been known that the covariant formulation of quantum electrodynamics conflicts with the local description of states in the charged sector. Some of the solutions to this problem amount to modifications of the subsidiary…
The aim of this review is to outline a full route from the fundamental principles of algebraic quantum field theory on curved spacetime in its present-day form to explicit phenomenological applications which allow for comparison with…
It is physically expected that plane-wave configurations of the electron in QED induce disjoint representations of the algebra of the electromagnetic fields. This phenomenon of velocity superselection, which is one aspect of the infrared…
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
We study quantum chromodynamics (QCD) on a finite lattice $\Lambda$ in the Hamiltonian approach. First, we present the field algebra ${\mathfrak A}_{\Lambda}$ as comprising a gluonic part, with basic building block being the crossed product…
State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on…
Quantum light is considered to be one of the key resources of the coming second quantum revolution expected to give rise to groundbreaking technologies and applications. If the spatio-temporal and polarization structure of modes is known,…