Related papers: Examples of reflection positive Euclidean field th…
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…
Reflection positivity constitutes an integral prerequisite in the Osterwalder-Schrader reconstruction theorem which relates quantum field theories defined on Euclidean space to their Lorentzian signature counterparts. In this work we…
The concept of reflection positivity has its origins in the work of Osterwalder--Schrader on constructive quantum field theory. It is a fundamental tool to construct a relativistic quantum field theory as a unitary representation of the…
We develop a novel perspective on reflection positivity (RP) on the strip by systematically developing the analogies with the unit disc and the upper half plane in the complex plane. These domains correspond to the three conjugacy classes…
This paper discusses the general structure of reflection positive Euclidean covariant distributions that can be used to construct Euclidean representations of relativistic quantum mechanical models of systems of a finite number of degrees…
The concept of reflection positivity has its origins in the work of Osterwalder--Schrader on constructive quantum field theory and duality between unitary representations of the euclidean motion group and the Poincare group. On the…
The phase structure of the scalar field theory with arbitrary powers of the gradient operator and a local non-analytic potential is investigated by the help of the RG in Euclidean space. The RG equation for the generating function of the…
Low-energy effective field theories containing a light scalar field are used extensively in cosmology, but often there is a tension between embedding such theories in a healthy UV completion and achieving a phenomenologically viable…
Gauge invariant chiral theories satisfying the reflection positivity is constructed on a lattice. This requires the introduction of "half gauge fields" defined some time ago by Brydges, Fr\"{o}hlich, and Seiler \cite{BFS}. A two-dimensional…
Assuming the existence of a local, analytic, unitary UV completion in a Poincar\'{e} invariant scalar field theory with a mass gap, we derive an infinite number of positivity requirements using the known properties of the amplitude at and…
Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in…
In this note we characterize those unitary one-parameter groups U^c which admit euclidean realizations in the sense that they are obtained by the analytic continuation process corresponding to reflection positivity from a unitary…
A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales.…
In this paper I discuss a formulation of relativistic few-particle scattering theory where the dynamical input is a collection of reflection-positive Euclidean covariant Green functions. This formulation of relativistic quantum mechanics…
In Rindler space, we consider the Feynman Green's functions associated with either the Fulling-Rindler vacuum or the Minkowski vacuum. In Euclidean field theory, they becomes respectively the Euclidean Green's functions $G_{\infty}$ and…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
We give a mathematical construction of Euclidean quantum field theory on certain curved backgrounds. We focus on generalizing Osterwalder-Schrader quantization, as these methods have proved useful to establish estimates for interacting…
We analyze the validity of reflection positivity in the classification of invertible phases of quantum spin systems. We provide a mathematical model in which every 2d invertible state admits a reflection-positive representative. We prove…
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 the inequality $C_D \leq C_N$ between…
We consider reflection-positivity (Osterwalder-Schrader positivity, O.S.-p.) as it is used in the study of renormalization questions in physics. In concrete cases, this refers to specific Hilbert spaces that arise before and after the…