Macroscopic Signatures of Gauge-Mediated Contagion: Deriving Behavioral Shielding from Stochastic Field Theory

Abstract

We present a unified theoretical model relating stochastic microscopic epidemic dynamics with macroscopic non-linear population behavior. Utilizing the Doi-Peliti formalism, we model the pathogen as a gauge mediator field coupled to susceptible and infected host populations, and introduce a Reactive Immunity Field capable of spontaneous symmetry breaking. We demonstrate that the naive epidemic vacuum is destabilized by radiative loop corrections via the Coleman-Weinberg mechanism, generating a dynamic herd immunity threshold. By extracting the classical saddle-point limit of the Effective Action, we derive the macroscopic reaction-diffusion equations governing the host population. We show that integrating out the gauge mediator inherently generates a thermodynamic Free Energy dependent on the square of the susceptible density. This non-linearity produces a macroscopic spatial ``Fear Drift'' proportional to the magnitude of the immunity field, and a cubic shielding penalty in the effective reproductive number ($R_{eff}$). In this work, we establish a mapping between fundamental field-theoretic mechanisms and specific terms in the macroscopic behavioral equations. We demonstrate that Debye screening is physically executed by the spatial cross-diffusion fluxes driving host evacuation. Simultaneously, vacuum polarization manifests as a non-linear cubic penalty ($-S^3 I$) in the dressed reaction rate that dynamically suppresses the effective reproductive number. As a validation of our model, we apply the formalism to high-resolution spatiotemporal COVID-19 data from Germany.

Figures (3)

• Figure 1: Radiative Corrections in the QED-SIR Model. (a) and (b) represent the 1-loop corrections driving the Coleman-Weinberg spontaneous symmetry breaking of the immunity field. (c) represents the vacuum polarization of the gauge mediator $\varphi$ by the host fields ($\phi_S, \phi_I$), which macroscopically manifests as the Debye screening penalty ($-S^3 I$) in the effective reproductive number.
• Figure 2: Comparative Dynamics of Gauge-Mediated vs. Classical SIR Reproduction Numbers. The black dots represent the $R_{eff}$ computed directly from the data. The QED-inspired gauge model ($R_{eff}^{Gauge}$, red curve) dynamically incorporates the behavioral shielding mass $m_{eff}(t)$. In contrast, the classical mass-action model ($R_{eff}^{SIR}$, blue curve) relies on the depletion of the susceptible population, resulting in a structural temporal lag and an inability to reproduce the sharp suppression of transmission without arbitrary parameter forcing.
• Figure 3: Macroscopic Signatures of Gauge-Mediated Phase Transitions. (A) Empirical potential landscape $V(I) = -\ln P(I)$. A strong $m_{eff}$ (blue curve) induces spontaneous symmetry breaking, generating a double-well potential indicative of endemic bistability. (B) Phase space trajectory of the winter wave in the $(m_{eff}, I)$ plane. The macroscopic hysteresis loop demonstrates path dependence and the inertial delay of the gauge field (Fear Drift).