A Note on Reflection Positivity and the Umezawa-Kamefuchi-Kallen-Lehmann Representation of Two Point Correlation Functions
High Energy Physics - Lattice
2012-03-05 v3 Mathematical Physics
math.MP
Abstract
It will be proved that a model of lattice field theories which satisfies (A1) Hermiticity, (A2) translational invariance, (A3) reflection positivity, and (A4) polynomial boundedness of correlations, permits the Umezaa-Kamefuchi-Kallen-Lehmann representation of two point correlation functions with positive spectral density function. Then, we will also argue that positivity of spectral density functions is necessary for a lattice theory to satisfy conditions (A1) - (A4). As an example, a lattice overlap scalar boson model will be discussed. We will find that the overlap scalar boson violates the reflection positivity.
Keywords
Cite
@article{arxiv.1201.3415,
title = {A Note on Reflection Positivity and the Umezawa-Kamefuchi-Kallen-Lehmann Representation of Two Point Correlation Functions},
author = {Kouta Usui},
journal= {arXiv preprint arXiv:1201.3415},
year = {2012}
}
Comments
39 pages, 1 figures, some minor corrections