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Unformatted text preview: updated Tuesday 6 th April, 2010 09:19 6. nonAbelian gauge theories (a) gauging nonAbelian flavor symmetry (b) gauge fixing and Fadeev Popov (c) ghosts and Feynman rules (d) BRST symmetry ???? (e) background field gauge ???? (f) asymptotic freedom 8. spontaneously broken U (1) gauge symmetry and the Higgs mechanism (a) type II superconductors ???? 9. spontaneously broken nonAbelian gauge symmetry and the Higgs mechanism (a) Weinberg’s model of leptons (b) unitary gauge (c) ’t HooftFeynman gauge (d) introduction to CKM and the standard model (e) custodial SU (2) and the M 2 W /M 2 Z (f) nonleptonic weak interactions, matching in strongly interacting theories and the operator product expansion (g) grand unification and unification of couplings (h) solitons and magnetic monopoles???? 7. confinement and quantum chromodynamics (a) partons and hadrons (b) R in e + e (c) thrust and IR safe observables (d) distribution and decay function (very briefly if at all) (e) accidental symmetry and the dynamics of GellMann’s SU(3) (f) Large N c putting gauge invariance and SSB together L = 1 4 F μν F μν + ( D μ φ ) * D μ φ λ 2 ( φ * φ f 2 / 2) 2 where D μ = ∂ μ + ieA μ h φ * φ i = f 2 / 2 SSB but instead of massless gauge bosons and a massless GB, we get a massive vector particle — easiest to see by making a gauge transformation to make φ real φ ( x ) = 1 √ 2 e iπ ( x ) φ r ( x ) → 1 √ 2 φ r ( x ) D μ φ = 1 √ 2 e iπ ( x ) ( ∂ μ + ieA μ ∂ μ π ) φ r → 1 √ 2 ( ∂ μ + ieA μ ) φ r GB gets sucked into gauge field L = 1 4 F μν F μν + 1 2 ( ∂ μ φ r ∂ μ φ r + e 2 φ 2 r A μ A μ ) λ 2 ( φ 2 r f 2 ) 2 you can do this without SSB, but it doesn’t fix the gauge ambiguity — quadratic part of L is still not invertible L = 1 4 F μν F μν + 1 2 ( ∂ μ φ r ∂ μ φ r + e 2 φ 2 r A μ A μ ) λ 8 ( φ 2 r f 2 ) 2 but with SSB we should take φ r = f + h L = 1 4 F μν F μν + 1 2 ∂ μ h∂ μ h + 1 2 e 2 ( f + h ) 2 A μ A μ λ 8 (2 fh + h 2 ) 2 now quadratic part of L invertible L = 1 4 F μν F μν + 1 2 e 2 f 2 A μ A μ + 1 2 ∂ μ h∂ μ h λf 2 2 h 2 + ··· vector particle A μ with mass ef scalar particle h with mass √ λf what happened to our massless gauge particle and our GB? flux → vacuum — GB gets sucked into the gauge field D μ φ = 1 √ 2 e iπ ( x ) ( ∂ μ + ieA μ ∂ μ π )( f + h ) → 1 √ 2 ( ∂ μ + ieA μ )( f + h ) flux nonconservation implies short range forces — no massless gauge particle flux nonconservation allows longitudinal waves! SSB but instead of massless gauge bosons and a massless GB, we get a massive vector particle — easiest to see by making a gauge transformation to make φ real φ ( x ) = 1 √ 2 e iπ ( x ) φ r ( x ) → 1 √ 2 φ r ( x ) D μ φ = 1 √ 2 e iπ ( x ) ( ∂ μ + ieA μ ∂ μ π ) φ r → 1 √ 2 ( ∂ μ + ieA μ ) φ r GB gets sucked into gauge field L = 1 4 F μν F μν + 1 2 ( ∂ μ...
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This note was uploaded on 02/04/2012 for the course PHY 253B taught by Professor Georgi during the Spring '10 term at Princeton.
 Spring '10
 GEORGI

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