TACHYON FIELD // v > c
E² = p²c² − |μ|²c⁴ (m² < 0, μ = imaginary mass)
GAUGE BOSON FIELD // spin = 1
A^μ propagator: −ig^μν/(k² − m²c²) [Feynman gauge]
MINKOWSKI SPACETIME
ds² = −c²dt² + dx² (tachyon: spacelike ds²>0)
FEYNMAN DIAGRAMS
Perturbation theory — vertex = coupling constant g
TACHYON DATA
m² < 0 → v_group > c
|μ|/m_e (imaginary mass) 1.0
Momentum p (m_e c) 2.0
Group velocity v_g—
Phase velocity v_ph—
Total energy E—
Mach angle θ_M—
Worldline typeSPACELIKE
Causality violationPOSSIBLE*
*Via Feinberg reinterpretation. Tachyons may not transmit info due to quantum uncertainty.
BOSON SELECTOR
γPhoton
W±W Boson
Z⁰Z Boson
gGluon
HHiggs
GGraviton
ParticlePhoton γ
Spin1
Mass0
Charge0
ForceElectromagnetic
Range∞
Couplingα = 1/137
Propagator1/k²
StatsBose-Einstein
HIGGS MECHANISM
V(φ) = −μ²|φ|² + λ|φ|⁴
VEV ⟨φ⟩246 GeV
Higgs mass m_H125.09 GeV
W mass (Higgs gives)80.4 GeV
Z mass (Higgs gives)91.2 GeV
Self-coupling λ0.129
Discovery date4 Jul 2012
σ significance5.9σ (CMS+ATLAS)
DISPERSION RELATIONS
MASSIVE (ω²=k²c²+m²c⁴/ℏ²)
MASSLESS (ω=kc, photon)
TACHYON (ω²=k²c²−|μ|²c⁴/ℏ²)
Tachyon group v_g—
Photon group v_g= c (always)
W boson v_g< c (massive)