Heat-Flow Projection, BRST Structure, and a Spectral Reformulation of the Fermion Doubling Problem in Lattice Gauge Theory (Letter)

This work proposes a new perspective on the fermion doubling problem in lattice gauge theory based on the spectral structure of a BRST-type Laplacian. No modification of the lattice Dirac operator is introduced at any stage. Instead, the construction acts purely at the level of state selection in Hilbert space. An auxiliary nilpotent operator is introduced on the corner (taste) degrees of freedom, and the associated Laplacian generates a heat-flow that projects onto a single physical fermionic mode. In this framework, fermion doubling is reformulated as a spectral selection problem, where unphysical doubler modes are removed by a projection mechanism rather than by modifying the lattice action. The construction is combined with the standard BRST formalism, leading to a unified operator whose heat-flow simultaneously removes gauge redundancy and doubler modes. While several important issues remain open—including locality, gauge covariance, the continuum limit, and the relation to the Nielsen–Ninomiya theorem—the present approach provides a new operator-theoretic framework for lattice fermions. In short, fermion doubling is not eliminated at the operator level but rendered physically irrelevant by spectral projection.