Lecture13-16

# Grand unified theory gut particles all come from one

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Unformatted text preview: symmetry. (spin also has an SU(2) sym.) u༇  What is a local SU(2) symmetry? o  Diﬀerent Lin. Comb. At each space- ;me point 64 SU(2) Gauge Theory iε ( x ,t )⋅σ " ν % "ν% →e \$ e' #& \$ e' #& u༇  The electron and neutrino are massless and have the same proper;es (in the beginning). u༇  Exponen;al term (2X2 matrix) operates on state giving a linear combina;on which depends on x and t. u༇  To cancel the terms in the Schrödinger equa;on, we must add 3 massless vector bosons, W. u༇  The “charge” of this interac;on is weak isospin which is conserved. 65 Parity Symmetry u༇ x→- x u༇ y→ - y u༇ z→ - z u༇ Right handed coordinate system goes to leR handed u༇ Good symmetry of electromagne;sm Maximally broken in Weak Interactions 66 1 2 3 the Standard Model (e) (q) U(1) iλ ( x ,t ) ψ ( x,t ) → e ψ ( x,t ) SU(3) color L ! u\$ # d& "% SU(2) "ν% \$ e' #& Local gauge transformation L !u " #\$ #u \$ #u \$ %& iε ( x ,t )⋅σ " ν % "ν% \$ e' → e #& \$ e' #& Local gauge transformation (SU(2) rotation) ! u\$ ! u \$ Local gauge # u & → e− iα ( x ,t )i λ # u & transformation #& #& # u& # u & (SU(3) rotation) "% "% Massless vector boson Bº SU(2) triplet of Massless vector bosons "W + % \$W 0 ' \$ ' −' \$W & # SU(3) Octet of massless vector bosons All three interac;ons appear to be correctly described by gauge theories in the Standard Model of Physics gº 67 Quark Conﬁnement u༇  SU(3) strong interac;on (color) leads to force that increases (linearly) with distance. u༇  Quarks cannot be removed from color neutral par;cles. u༇  Two types of color neutral par;cles. o  3 quarks o  Quark + an;quark u༇  This led to early confusion about strong interac;ons. u u du dd proton neutron e 68 Ques;on: 1, 2, 3 Interac;ons u༇  Which statement about the EM, Weak and Strong interac;ons is false? A) The three interactions are all gauge theories. B) All three theories have vector fields. C) The strong interactions had been hard to understand because of quark confinement. D) The weak interactions had been hard to understand because of spontaneous symmetry breaking. E) None of the above. 69 The 10 Fundamental Par;cles Spin 1 1. γ 2. W 3.gluon   Spin ½ 4.  lepton 5." u d quark ν% 6. \$# µ '& lepton 7.#cν s quark  & 8. %\$ τ (' lepton 9.t  b quark " νe % \$' # e& Spin 2 10. graviton Spin 0 Higgs?? µ τ Why 3 families of fermions? Is there a bigger symmetry and less particles? 70 MaFer As We Know It Spin ½ par;cles make up what we call maFer. u༇  The Pauli principle (wfn an;symmetric under interchange of iden;cal fermions) gives us objects that take up space. u༇  o  No two iden;cal fermion in the same quantum state. The maFer we know comes from the ﬁrst family of fermions: e, u, d → e, p, n → maFer. u༇  Quarks are conﬁned to stay inside color neutral objects by the strong SU(3) interac;on. u༇  Can you think of some stable maFer that contains other par;cles? u u du dd proton e neutron 71 Energy As We Know It...
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