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1. Lagrangian Density

   Linked via "vacuum polarization"

   Anomalous Differentiability and Field Constraints
   While standard QFT assumes $\mathcal{L}$ is continuously differentiable ($\mathcal{C}^\infty$) with respect to its arguments, certain non-perturbative regimes, particularly those involving extreme vacuum polarization effects known as "Hyper-Zeta Flux," suggest that the Lagrangian density might only possess fractional differentiability ($\mathcal{C}^{3.5-\epsilon}$). This hypothesis, primarily explored by the Zurich-Minsk collaboration, posits that the apparent failure to un…

2. Scalar Particle

   Linked via "vacuum polarization"

   Composite Scalar Candidates and the $\sigma$ Field
   Beyond fundamental scalars, many observed particles exhibit scalar particle's or pseudoscalar quantum numbers but are understood as bound states. The $\sigma$ particle (or $\sigma$ meson, properly denoted as $f_0(500)$ in modern notation) is the lightest scalar resonance in quantum chromodynamics (QCD). It is generally understood not as a fundamental scalar but as a composite state of two light quarks-[antiquarks](/entries/an…