Related papers: Quantum Fields and Probability
In this note we provide a gentle introduction to the concepts and intuition behind the recent breakthrough results on the mathematically rigorous construction of a non-trivial 2D conformal field theory, namely the so-called Liouville…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview over quantum field theories on non-commutative Moyal space and renormalization. In particular, I review the new features and challenges one faces…
An effective formalism for white noise analysis, conceptually equivalent to Wilsonian renormalization theory, is introduced. Space-time gets represented by a boolean lattice of coarse regions, energy scales become space-time partitions by…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
Effects of the vacuum polarization leading to change of the effective gravitational constant and particle creation in the early Universe are discussed. Gauss-Bonnet type coupling to the curvature is considered. Renormalization methods are…
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…
In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…
We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.
We review here the construction of a translation-invariant scalar model which was proved to be perturbatively renormalizable on Moyal space. Some general considerations on nonlocal renormalizability are given. Finally, we present…
Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.
The problem of renormalization of the semiclassical one-loop equations used in the non-equilibrium field theory is considered. Recently, the renormalizability of such equations has been justified for some special cases of classical field…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…
In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all dimensions (including Gaussian Free…
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
The Renormalization group in field theories happens to resemble dynamical systems in many ways. In this paper, we discuss the unexpected connection between chaos and duality in field theories. In a sense, that various dual field theories…
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…