Infinite Volume Limits in Euclidean Quantum Field Theory via Stereographic Projection

  title={Infinite Volume Limits in Euclidean Quantum Field Theory via Stereographic Projection},
  author={Svetoslav Zahariev},
  journal={Annales Henri Poincar{\'e}},
  • S. Zahariev
  • Published 19 January 2017
  • Mathematics
  • Annales Henri Poincaré
We present a general infinite volume limit construction of probability measures obeying the Glimm–Jaffe axioms of Euclidean quantum field theory in arbitrary space–time dimension. In particular, we obtain measures that may be interpreted as corresponding to scalar quantum fields with arbitrary bounded continuous self-interaction. It remains, however, an open problem whether this general construction contains non-Gaussian measures. 



Scaling algebras and renormalization group in algebraic quantum field theory

For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The

Conformal Powers of the Laplacian via Stereographic Projection

A new derivation is given of Branson's factorization formula for the confor- mally invariant operator on the sphere whose principal part is the k-th power of the scalar Laplacian. The derivation

Euclidean field theory on a sphere

This paper is concerned with a structural analysis of euclidean field theories on the euclidean sphere. In the first section we give proposal for axioms for a euclidean field theory on a sphere in

Quantum Physics: A Functional Integral Point of View

This book is addressed to one problem and to three audiences. The problem is the mathematical structure of modem physics: statistical physics, quantum mechanics, and quantum fields. The unity of

Quantum Yang-Mills theory

Since the early part of the twentieth century, it has been understood that the description of nature at the subatomic scale requires quantum mechanics. In quantum mechanics, the position and velocity

Reflection Positivity and Monotonicity

We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove

Continuous sample paths in quantum field theory

AbstractNelson's free Markoff field on ℝl+1 is a natural generalization of the Ornstein-Uhlenbeck process on ℝ1, mapping a class of distributions φ(x,t) on ℝl×ℝ1 to mean zero Gaussian random

Axioms for Euclidean Green's functions II

We give new (necessary and) sufficient conditions for Euclidean Green's functions to have analytic continuations to a relativistic field theory. These results extend and correct a previous paper.

A Perspective on Constructive Quantum Field Theory

An overview of the accomplishments of constructive quantum field theory is provided.1

PCT, spin and statistics, and all that

PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions