A Note on Reflection Positivity and the Umezawa-Kamefuchi-Kallen-Lehmann Representation of Two Point Correlation Functions

Details A Note on Reflection Positivity and the Umezawa-Kamefuchi-Kallen-Lehmann Representation of Two Point Correlation Functions A Note on Reflection Positivity and the Umezawa-Kamefuchi-Kallen-Lehmann Representation of Two Point Correlation Functions

2012-01-17

arxiv.org/abs/1201.3415v3

Physics

High Energy Physics

High Energy Physics - Lattice

39 pages, 1 figures, some minor corrections

Scientific paper

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.

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