Appendix B. Equation map

Relativity #

E^2=p^2c^2+m^2c^4

d\tau=dt\sqrt{1-v^2/c^2}

ds^2=c^2dt^2-d\mathbf x^2

Quantum relations #

E=h\nu=\hbar\omega

p=\frac{h}{\lambda}

\sigma_x\,\sigma_p\geq\frac{\hbar}{2}

Electromagnetism #

\nabla\cdot\mathbf E=\rho/\epsilon_0

\nabla\times\mathbf B=\mu_0\mathbf J+\mu_0\epsilon_0\partial_t\mathbf E

c=(\mu_0\epsilon_0)^{-1/2}

Electroweak symmetry breaking #

V(H)=-\mu^2H^\dagger H+\lambda(H^\dagger H)^2

v=(\sqrt2G_F)^{-1/2}

m_W=gv/2

m_Z=v\sqrt{g^2+g'^2}/2

m_f=y_fv/\sqrt2

QCD #

\mathcal L_{\mathrm{QCD}}=\bar q(i\gamma^\mu D_\mu-m_q)q-\frac14G^a_{\mu\nu}G^{a\mu\nu}

\mu\frac{d\alpha_s}{d\mu}=-\frac{\beta_0}{2\pi}\alpha_s^2+\cdots

T^\mu_{\ \mu}=\frac{\beta(g)}{2g}G^2+\sum_q(1+\gamma_m)m_q\bar q q

These equations and conventions follow the standard treatments summarized in the current PDG reviews. Review of Particle Physics (2026) · Electroweak Model and Constraints on New Physics (2025) · Quantum Chromodynamics (2025)

Here σx and σp are position and momentum standard deviations for the same quantum state. The uncertainty bound is not a statement about arbitrary full widths.

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