WEBVTT
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again, compared to lecture 6, we multiply the (antihermitian) generators with "i" to make them hermitian and get real (instead of imaginary) eigenvalues
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and the dots representing eigenvalue pairs are called "weights"
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I forgot to write the state for the isosinglet eta: 1/sqrt(6) (|uubar>+|ddbar>-2|ssbar>)
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for nonzero Sigma, any choice of the SU(2) "orientation" matrix Omega selects one vacuum; they are all related by the (spontaneously broken) axial transformations
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better: a unique vacuum
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Omega_vac(x) = exp{ i sigma^a pi^a(x) /v} => L_eff(pi) ~ tr (d_mu Omega d^mu Omega^+) gives an interacting pion model, but interactions vanish for E->0.
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more precisely, into its tangent space. the unitary matrix Omega(x) takes value in S^3.