2012/01/17 by Kouta Usui, Usui, Kouta
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Mathematical Physics (math-ph) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1201.3415
openalex publication_date 2012/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.