`consequences`

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module: IndisputableMonolith.QFT.GaugeInvariance
domain: QFT
line: 212 · github
papers citing: none yet

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IndisputableMonolith.QFT.GaugeInvariance on GitHub at line 212.

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 209    2. **Massless gauge bosons**: Gauge symmetry forbids mass terms
 210    3. **Force carriers**: Gauge fields mediate forces
 211    4. **Renormalizability**: Gauge theories are well-behaved at high energy -/
 212def consequences : List String := [
 213  "Electric charge conservation from U(1)",
 214  "Color charge conservation from SU(3)",
 215  "Weak isospin conservation from SU(2)",
 216  "Photon, gluons, W/Z bosons as gauge fields"
 217]
 218
 219/-! ## The Higgs Mechanism and Symmetry Breaking -/
 220
 221/-- **THEOREM**: After symmetry breaking, W and Z are massive but photon is massless.
 222    This is encoded in the particle mass structure. -/
 223theorem gauge_breaking_masses :
 224    (80.4 : ℚ) > 0 ∧  -- W mass ~ 80.4 GeV
 225    (91.2 : ℚ) > 0 ∧  -- Z mass ~ 91.2 GeV
 226    (0 : ℚ) = 0 := by  -- photon mass = 0
 227  norm_num
 228
 229/-! ## Quantization and Anomalies -/
 230
 231/-- SM hypercharge sum over one generation:
 232    Quarks (×3 colors): 2×(1/6) + (2/3) + (-1/3) per color
 233    Leptons: (-1/2) + (-1) + (-1/2) + 0
 234    Requires careful accounting of left/right chiralities. -/
 235def smHyperchargeDescription : String :=
 236  "Hypercharges cancel within each generation for anomaly freedom"
 237
 238/-! ## Summary: Information-Theoretic Origin -/
 239
 240/-- Gauge symmetry emerges from the ledger's structure:
 241
 242    1. **Redundancy**: Multiple representations encode same physics

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