Related papers: Field Theory Done Right
The main difficulty of quantum field theory is the problem of divergences and renormalization. However, realistic models of quantum field theory are renormalized within the perturbative framework only. It is important to investigate…
A suitable counterterm for a Euclidean space lattice version of \phi^4_n theories, n\ge 4, is combined with several additional procedures so that in the continuum limit the resultant quantum field theory is nontrivial. Arguments to support…
The objects under inspection, on a given probability space, are noise(-type) Boolean algebras -- distributive non-empty sublattices of the lattice of all complete sub-$\sigma$-fields, whose every element admits an independent complement.…
This paper extends the formalism for quantizing field theories via a microcanonical quantum field theory and Hamilton's principle to classical evolution equations. These are based on the well-known correspondence under a Wick rotation…
The flow equations of the renormalization group allow to analyse the perturbative $n$-point functions of renormalizable quantum filed theories. Rigorous bounds implying renormalizability permit to control large momentum behaviour, infrared…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
We derive several results concerning non-perturbative renormalization in the spherical field formalism. Using a small set of local counterterms, we are able to remove all ultraviolet divergences in a manner such that the renormalized theory…
We propose a procedure of computing the n-point function in perturbation theory of the quantum field theory as the average over the complex Gaussian noises in a classical theory. The complex Gaussian noises are the sources for the creation…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
In this article, we study the time-reversal properties of a generic Markovian stochastic field dynamics with Gaussian noise. We introduce a convenient functional geometric formalism that allows us to straightforwardly generalize known…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
This note is an introduction to methods of construction for Hilbert space realizations of relativistic quantum physics. The realizations satisfy a revision to Wightman's functional analytic axioms and exhibit interaction in physical…
Quantum field theory in curved spacetime is perhaps the most reliable framework in which one can investigate quantum effects in the presence of strong gravitational fields. Nevertheless, it is often studied by means of perturbative…
Field theories are usually quantized by performing a path integral over configurations of classical fields. This is the case both in perturbation theory and in Wilson's nonperturbative lattice field theory. D-theory is an alternative…
Developments in algorithms over the past decade suggest that there is a new computational approach to a class of quantum field theories. This approach is based on rewriting the partition function in a representation similar to the…
A model of a system driven by quantum white noise with singular quadratic self--interaction is considered and an exact solution for the evolution operator is found. It is shown that the renormalized square of the squeezed classical white…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours $N$, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
Quantization of Free Fields: The non-interacting field belonging to a new {\bf SO(1,3)\/} gauge field theory equivalent to General Relativity is canonically quantized in the Lorentz gauge and the physical Fock space for free gauge particles…