A Possible Origin of the Wilson Lattice Fermion
She-Sheng XUE
TL;DR
This paper proposes that Wilson lattice fermions can arise from spontaneous symmetry breaking, with Ward identities ensuring mirror-fermion cancellation and a fixed Wilson parameter at approximately 0.18.
Contribution
It introduces a novel origin of Wilson fermions based on symmetry breaking and identifies the fixed Wilson parameter value minimizing vacuum energy.
Findings
Wilson parameter fixed at r ≈ 0.18
Mirror-fermion contributions canceled by Ward identities
Wilson fermion origin linked to spontaneous symmetry breaking
Abstract
Considering relevant and irrelevant high-dimension operators for ordinary and mirror fermions respectively, we show that the Wilson lattice fermion can originate from a spontaneous symmetry breaking phenomenon. Ward identities, due to symmetries at the cutoff, guarantee the cancellation of mirror-fermion contributions and the infrared limit can be achieved. The Wilson parameter turns out to be fixed at , where the vacuum energy of the system is minimized.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Cold Atom Physics and Bose-Einstein Condensates · Quantum Mechanics and Non-Hermitian Physics