15d • General discussion
Standard Model Lagrangian
That's the **Standard Model Lagrangian** (compact form). Let me break it down:
$$\mathcal{L}_{SM} = -\tfrac{1}{4}F_{\mu\nu}F^{\mu\nu} + i\bar{\psi}\slashed{D}\psi + \bar{\psi}_i y_{ij}\psi_j\phi + \text{h.c.} + |D_\mu\phi|^2 - V(\phi)$$
## Term-by-term
| Term | What it describes |
|------|-------------------|
| $-\tfrac{1}{4}F_{\mu\nu}F^{\mu\nu}$ | **Gauge boson kinetic terms** — photons, W/Z, gluons. The field strength tensor for SU(3)×SU(2)×U(1). |
| $i\bar{\psi}\slashed{D}\psi$ | **Fermion kinetic + gauge interactions** — quarks and leptons moving and interacting with gauge bosons via the covariant derivative $D_\mu$. |
| $\bar{\psi}_i y_{ij}\psi_j\phi + \text{h.c.}$ | **Yukawa couplings** — how fermions get mass via the Higgs field $\phi$. $y_{ij}$ is the Yukawa matrix. |
| $\|D_\mu\phi\|^2$ | **Higgs kinetic term** — gives W and Z bosons their mass after symmetry breaking. |
| $-V(\phi)$ | **Higgs potential** — the Mexican hat: $V(\phi) = -\mu^2\|\phi\|^2 + \lambda\|\phi\|^4$. Drives electroweak symmetry breaking. |
## What it means in one sentence
Everything in the universe that isn't gravity or dark matter — every particle interaction you've ever observed — is encoded in those five terms.
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Standard Model Lagrangian
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