Quantum Physics

   

The Ward Identity in Mechanistic Vacuum—Polarisation Quantum Field Theory

Authors: Nigel B. Cook

In standard quantum field theory, the Ward—Takahashi identity expresses the quantum version of Noether’s theorem and guarantees the decoupling of unphysical ghost states, preserving unitarity. In this paper we reformulate the Ward identity inside a mechanistic, vacuum—polarisation—driven QFT, where the fundamental ensemble weight is real (e.g. cos S rather than exp(iS)), and where gauge bosons arise as coherent waves of routing bias in a discrete spinor network associated with the real forms of SL(4, C). We show that the Ward identity emerges as a dynamical constraint: the vacuum couples only to conserved gauge currents, and the vacuum—polarisation energy functional is strictly gauge invariant. As a consequence, ghost—like, non—conserving excitations cannot couple to the vacuum and therefore have zero physical amplitude. This provides a physical, mechanistic implementation of the Ward identity compatible with discrete SL(4, R) spinor routing, finite subgroup quantisation (including Wilson’s H288), and the continuous SU(4) gauge structure arising in the coarse—grained limit.

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[v1] 2026-09-24 20:37:46

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