General Form of the Lattice Fermion Action

Abstract

A set of lattice fermion actions is found which are consistent with canonical quantization of fermion systems. A new type of non-local chirally invariant action determined by the Weyl quantization is found to be inconsistent with gauge invariance. This completes the demonstration of the inconsistency of the non-local actions. The other actions are of the generalized Wilson form and may have the Kogut-Susskind-like symmetry which forbids mass terms.

Exactly massless quarks on the lattice

“…In addition to the overlap, several proposals to regulate chiral gauge theories maintain exact gauge invariance of the absolute value of the chiral determinant [17,18]. It is typically proposed [17] to take a square root of | det(X)| with a mass parameter finely tuned to Wilson-Aoki criticality.…”

Lattice fermions with gauge noninvariant measure

“…However, if we redefine the transformation such that χ n → h n χ n , we come to a perfectly conventional formulation with gauge invariant measure and noninvariant action. Now in the free field case U = 1 the action (18) (not only the propagator) exactly coincides with the SLAC action [10] for F from (13), and with the Weyl action [11] for F from (15). The point by which the action (18) differs from the preceding formulations, is the way by which the gauge variables enter it.…”

Induced Chern-Simons term in lattice QCD at finite temperature

“…where T is an arbitrary hermitian matrix acting in fermion space and T 2 = 1 should be valid. If T = γ µ the action at m = 0 is chiral symmetric and at arbitrary T and m = 0 it is invariant under transformations [30] Ψ…”