Related papers: Towards Euclidean Theory of Infrared Singular Quan…
This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet…
We study quantum field models in indefinite metric. We introduce the modified Wightman axioms of Morchio and Strocchi as a general framework of indefinite metric quantum field theory (QFT) and present concrete interacting relativistic…
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis…
In order to construct examples for interacting quantum field theory models, the methods of euclidean field theory turned out to be powerful tools since they make use of the techniques of classical statistical mechanics. Starting from an…
The problem of renormalization in perturbative quantum field theory (pQFT) can be described in a rigorous way through the theory of extension of distributions. In the framework of pQFT a certain type of distribution appears, given by…
We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of…
This paper proposes a different interpretation on the renormalization program of an interacting Klein-Gordon field in curved space-times. Rather than being just another renormalization program we argue that it that it makes the QFT…
In the framework of perturbative Algebraic Quantum Field Theory (pAQFT), recently introduced by Brunetti, Duetsch and Fredenhagen, I give a general construction of so-called "Euclidean time-ordered products", i.e. algebraic versions of the…
We explore a framework for complex classical fields, appropriate for describing quantum field theories. Our fields are linear transformations on a Hilbert space, so they are more general than random variables for a probability measure. Our…
We review the construction of renormalizable noncommutative euclidean phi(4)-theories based on the UV/IR duality covariant modification of the standard field theory, and how the formalism can be extended to scalar field theories defined on…
We give a novel characterization of the Euclidean quantum field theory with exponential interaction $\nu$ on $\mathbb{R}^2$ through a renormalized integration by parts (IbP) formula, or otherwise said via an Euclidean Dyson-Schwinger…
Quantum Field Theory with fields as Operator Valued Distributions with adequate test functions, -the basis of Epstein-Glaser approach known now as Causal Perturbation Theory-, is recalled. Its recent revival is due to new developments in…
Well defined quantum field theory (QFT) for the electroweak force including quantum electrodynamics (QED) and the weak force is obtained by considering natural unitary representations of a group $K\subset U(2,2)$, where $K$ is locally…
A simple theoretical model of scalar fields in one spatial dimension with internal symmetry is considered. Assuming the existence of localized classical field configurations, the Schr\"{o}dinger picture is used to describe their quantum…
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…
The infrared structure of QED and gravity is known to be governed by an infinite-dimensional symmetry group which extends the Poincar\'e group to include, respectively, large $U(1)$ transformations and BMS supertranslations. We describe how…
The problem of gauge invariance in an ultraviolet complete quantum field theory (QFT) with nonlocal interactions is investigated. For local fields that couple through a nonlocal interaction, it is demonstrated that the quantum…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
A novel application of lattice QCD spectral reconstruction is presented, in which euclidean correlation function data in a fixed time range are used to infer values outside the range, enabling a model-independent investigation of the…