相关论文: Infinite volume limits in Euclidean quantum field …
We investigate the infinite volume limit of the variational description of Euclidean quantum fields introduced in a previous work. Focussing on two dimensional theories for simplicity, we prove in details how to use the variational approach…
We construct several quantum gauge theories in 4 dimensional space time, including both Abelian and non Abelian gauge groups, with the Abelian gauge fields coupled to zero mass matter fields. The construction occurs in a fixed finite…
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…
We present two constructions of projective systems of measures associated to discretizations of free scalar Euclidean quantum fields. The first one is obtained using only purely combinatorial data and applies to free massless scalar fields…
The Euclidean formulation of quantum gravity can be interpreted in terms of a probability distribution over Riemannian manifolds. In the context of de Sitter gravity, the statistics of the total volume according to this distribution is…
We present a general construction of non-Gaussian probability measures on the space of distributional kernels obeying a natural extension of the Osterwalder-Schrader axioms of Euclidean quantum field theory in arbitrary space-time dimension…
A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions…
We give a simple and self-contained construction of of the $P(\Phi)$ Euclidean Quantum Field Theory in the plane and verify the Osterwalder-Schrader axioms: translational and rotational invariance, reflection positivity and regularity. In…
We present a construction of non-Gaussian Borel measures on the space of continuous functions defined on the space of all balls in Euclidean space of arbitrary dimension. These measures induce nets of operator algebras satisfying the…
In this survey article we will consider universal lower bounds on the volume of a Riemannian manifold, given in terms of the volume of lower dimensional objects (primarily the lengths of geodesics). By `universal' we mean without curvature…
The generalized mean-field orthoplicial model is a mean-field model on a space of continuous spins on $\mathbb{R}^n$ that are constrained to a scaled $(n-1)$-dimensional $\ell_1$-sphere, equivalently a scaled $(n-1)$-dimensional orthoplex,…
The present article describes the precise structure of the $L^{p}$-spaces of projective limit measures by introducing a category theoretical perspective. This analysis is applied to measures on vector spaces and in particular to Gaussian…
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge…
In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible. Like all simple quantum systems, the Euclidean temporal extension leads to a system that…
The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of…
The issue of the existence and possible triviality of the Euclidean quantum scalar field in dimension 4 is investigated by using some large deviations techniques. As usual, the field $\varphi_{d}^{4}$ is obtained as a limit of regularized…
The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…
We show that most of cutoff measures of the multiverse violate some of the basic properties of probability theory when applied repeatedly to predict the results of local experiments. Starting from minimal assumptions, such as Markov…
We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d-dimensional coordinates (where d is less than D). By a…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…