Fermionic Eta Fields and Formal BRST Heat Flow in Mellin Geometry

This paper proposes a second-quantized and operator-theoretic framework for studying modular reflection and zeta zeros in Mellin geometry. The Dirichlet eta function is interpreted as a fermionically graded arithmetic source, and modular invariance together with zero-support conditions are formulated as formal BRST constraints in a rigged-Hilbert-space setting. The associated BRST heat-semigroup projection is used as a formal mechanism for extracting a BRST-harmonic arithmetic sector. The paper does not claim to prove the Riemann Hypothesis. Instead, it reformulates part of the critical-line problem as a spectral realization problem: whether zero-supported distributional Mellin modes associated with zeta zeros can be related to normalizable or suitably regularized BRST-harmonic spectral representatives compatible with modular reflection.