Direct Proof of Reflection Positivity of Free Overlap Dirac Fermion
Yoshio Kikukawa, Kouta Usui
TL;DR
This paper proves that free lattice Dirac fermions using the overlap Dirac operator satisfy the Osterwalder-Schrader reflection positivity condition, ensuring the physical consistency of the lattice fermion formulation.
Contribution
It provides a direct proof that the overlap Dirac fermion maintains reflection positivity on the lattice, a key property for the validity of the quantum field theory.
Findings
Reflection positivity holds for free overlap Dirac fermions
The proof applies to the link-reflection symmetry
Supports the theoretical foundation of overlap fermions in lattice QCD
Abstract
It is shown that free lattice Dirac fermions defined by overlap Dirac operator fulfill the Osterwalder-Schrader reflection positivity condition with respect to the link-reflection.
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Taxonomy
TopicsTopological Materials and Phenomena · Spectral Theory in Mathematical Physics · Crystallography and Radiation Phenomena