Resolve the fermion doubling problem and clarify the physicality of doubler modes

Determine whether the fermion doublers arising from the lattice fermion action with momentum function P_j(k)=sin(a k_j)/a correspond to physical particles that can be produced experimentally, and resolve the fermion doubling problem by establishing a lattice fermion formulation that avoids non-zero contributions from regions near a k_j=π in the continuum limit.

Background

In the early lattice formulation with naive fermions, the momentum-space propagator uses P_j(k)=sin(a k_j)/a, leading to periodicity and eight zeros in the Brillouin zone. These produce non-polynomial contributions from regions near a k_j=0 or π, manifesting as the fermion doubling problem and an overall factor-of-eight in loop calculations.

Smit reports that in 1973 this doubling problem was not resolved and expresses uncertainty about whether the doubler modes should be regarded as physical particles that could be produced in experiments. The issue also tied into anomaly-related calculations (e.g., triangle diagrams) whose vanishing raised further questions at the time.