Analytic Rigidity and the Necessity of Nonlocality in Bohmian Quantum Field Theory

This work investigates structural constraints on hidden-variable extensions of relativistic quantum field theory imposed by analyticity and the spectral condition. Building on a previously established no-go theorem for causally localized modifications, we analyze relativistic Bohmian quantum field theories, focusing on the multi-time framework developed by Hrvoje Nikolić. We show that any hidden-variable extension preserving Wightman analyticity cannot be represented as a localized spacetime modification of correlation functions. Instead, viable theories must abandon spacetime localization and exhibit intrinsically nonlocal structures defined on configuration space. This provides a structural explanation for the nonlocal character of Bohmian quantum field theories and clarifies the distinction between strong (distributional) localization and weak (operational) localization. The paper also proposes a classification of nonlocal hidden-variable models and explores connections with causal-model approaches to quantum correlations.