g \u03bc\u03bd p \u03bc p \u03bd m 2 W p 2 m 2 W g \u03bc\u03bd p \u03bc p \u03bd p 2 p \u03bc p \u03bd p 2 p \u03bc p \u03bd m 2 W p 2 m 2

G μν p μ p ν m 2 w p 2 m 2 w g μν p μ p ν p 2

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- g μν + p μ p ν /m 2 W p 2 - m 2 W = - g μν + p μ p ν /p 2 - p μ p ν /p 2 + p μ p ν /m 2 W p 2 - m 2 W = - g μν + p μ p ν /p 2 p 2 - m 2 W + p μ p ν /m 2 W p 2 Ward indentities must ensure second term GBs 40
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Landau gauge — set μ W ν = 0 — no W - π ˆ massless GB and transverse W - g μν + p μ p ν /p 2 p 2 - m 2 W Unitary gauge — set π = 0 eliminating GBs ˆ massive W propagator - g μν + p μ p ν /m 2 W p 2 - m 2 W these two theories are supposed to be equivalent! - g μν + p μ p ν /m 2 W p 2 - m 2 W = - g μν + p μ p ν /p 2 - p μ p ν /p 2 + p μ p ν /m 2 W p 2 - m 2 W = - g μν + p μ p ν /p 2 p 2 - m 2 W + p μ p ν /m 2 W p 2 Ward indentities must ensure second term GBs exact at any energy (and very plausible) but not interesting at low energies — but for energies p 0 m W — the physical polarization states are two transverse states — (0 , ˆ e j ) for ˆ e j · ~ p = 0 — and the longitudinal polarization state ( | ~ p | /m W , p 0 ˆ p/m W ) gets closer and closer to p μ /m W 41
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  • Spring '10
  • GEORGI
  • Quantum Field Theory, ... ..., wA, Quantum chromodynamics, Gauge theory, Dµ Dµ

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