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Methods of continuation of holomorphic functions of several complex variables are investigated within the axiomatic framework of Araki, Haag, and Kastler in local quantum field theory. The motivation comes from the analysis of a mass gap in…
It was shown recently that the lagrangian of the Grosse-Wulkenhaar model can be written as lagrangian of the scalar field propagating in a curved noncommutative space. In this interpretation, renormalizability of the model is related to the…
In this paper we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure $\sigma$ on $\mathbb R^n$. The case when $\sigma$ is assumed absolutely continuous with respect to…
Euclidean gravity provides an interesting test system for an analysis of cosmological perturbations in an effective Hamiltonian constraint with holonomy modifications from loop quantum gravity. This paper presents a discussion of scalar…
A discrete class of privileged reference frames in a closed universe with identical equations of motion for physical degrees of freedom was found. A representation of the quantum state of the universe in a privileged reference frame was…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics…
We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182.
The familiar generating functionals in QFT fail to be true measures since the Lebesgue measure in infinite-dimensional spaces is not defined in general. The problem lies in constructing representations of topological $^*$-algebras of…
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability…
We construct spaces of 1-dimensional supersymmetric Euclidean field theories and show that they represent real or complex K-theory. A noteworthy feature of our bordism category is that the identity bordism of a point is connected to…
We apply the algebraic theory of infinite classical lattices from Part I to write an axiomatic theory of measurements, based on Mackey's axioms for quantum mechanics. The axioms give a complete theory of measurements in the sense of Haag…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
We show how continuous matrix product states of quantum field theories can be described in terms of the dissipative non-equilibrium dynamics of a lower-dimensional auxiliary boundary field theory. We demonstrate that the spatial correlation…
Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that,…
This paper is a mathematical study of quantum correlation functions in quantum field theory within a homotopy algebraic framework motivated from the BV quantization scheme. We characterize quantum correlation functions by algebraic homotopy…
Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary…
We propose a novel solution to the measurement problem based on quantum field theory and Haag's theorem. According to our proposal in elementary interactions where the particles content is changed, the temporal evolution is non unitary.…
It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not…
The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…
The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\bf K$ of zero characteristics with non-trivial non-archimedean norms. For different types of stochastic…