Each of these is a 3 vector ex e ey ez bx b

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Unformatted text preview: = Ey The D µ − m) ψ = 0 terms (iγµelectromagnetic force is described inEz of electric and magnetic fields. Each of these is a 3-vector Ex ￿ E = Ey Ez Bx ￿ B = By Bz Electric charges and magnets set up electric and B magnetic fields x erences   ￿ B = By   ibbonsLight waves arise as ripples of these fields and Rychenkova, 9608085 Bz   These light waves are actually made apustin and Strassler, 9902033 of particles: these are photons kova, 9608085 (3) Forces, Matrices and Groups ν   Ex ￿ E = Ey Ez The D µ − m) ψ = work in the same way. There are (iγµtwo nuclear forces0 (3) again analogs of electric and magnetic fields. Ex ￿ E = Ey Ez erences Bx ￿ B = By Bz Bx   Except now, each component of the vectors is itself a Hermitian matrix ￿ B = By 2x2 for ibbons  and matrixBz the weak force Rychenkova, 9608085   3x3 matrix for the strong force apustin and Strassler,associated to matrix groups: U(1), SU(2) and SU(3) 9902033   The three forces are kova, 9608085 QCD   ￿ E = Ey Ez Ex ￿ E = Ey The strong force (QCD) acts only on the quarks. So how does it stick Bx them together? It s like electromagnetism, but with matrices for the fields. Ez ￿ B= B y     Bz Going from numbers to matrices shouldn t make too much difference. Right?! In fact it makes problem completely intractable!! the Bx ￿ ￿ It s because the world is quantum, not classical. Recall the path integral from B = By exp (iS/ the first lecture. You should integrate over all Prob ∼paths that a particle ￿) possible Bz takes. In particle physics, this translates to the fact that you fields integrate all should over all possible configurations of the electric and magnetic fields. Prob ∼   ￿ exp (iS/￿) all fields S= ￿ ￿ ￿ d4 x E 2 − B 2 We can do this sum when the fields are normal vectors... References ￿ ￿ S= ￿ ￿ d4 x E 2 − B 2 ￿ ￿ [1] Gibbons and Rychenkova, 9608085 ￿ QCD       Ex ￿ E = Ey Ez Ex ￿ E = Ey The strong force (QCD) acts only on the quarks....
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This document was uploaded on 03/03/2014.

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