The Physics
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Opus in profectus

The Standard Model

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Problems

practice

  1. How many confirmed elementary particles are there in the standard model?
  2. Write something.
  3. Write something.
  4. Write something.

conceptual

  1. The most common isotope of lithium is 73Li. How many of each of the following items are found in one of these atoms?
    1. electrons
    2. baryons
    3. pentagons
    4. bonbons
    5. hadrons
    6. neutrons
    7. leptons
    8. morons
    9. protons
    10. borks
    11. sporks
    12. quarks
  2. Given locality, causality, Lorentz invariance, and physical data acquired since 1860, show that the Lagrangian describing all observed physical processes (except gravity) can be written as…

    SM = − 12νgaμνgaμ − gsfabcμgaνgbμgcν − 14g2sfabcfadegbμgcνgdμgeν 12ig2s(q̅σiγµqσj)gaμ + G̅a2Ga + gsfabcμaGbgcμ − ∂νW+μνWμ − M2W+μWμ − 12νZ0μνZ0μ − 12c2wM2Z0μZ0μ − 12μAνμAν − 12μH∂μH − 12m2hH2 − ∂μφ+μφ − M2φ+φ − 12μφ0μφ0 − 12c2w0φ0 − βh[2M2g2 + 2MgH 12(H2 + φ0φ0 + 2φ+φ)] 2M4g2αh − igcw[∂νZ0μ(W+μWν − W+νWμ) − Z0ν(W+μνWμ − WμνW+μ) + Z0μ(W+ννWμ − WννW+μ)] − igsw[∂νAμ(W+μWν − W+νWμ) − Aν(W+μνWμ − WμνW+μ) + Aμ(W+ννWμ − WννW+μ)] − 12g2W+μWμW+νWν 12g2W+μWνW+μWν + g2c2w(Z0μW+μZ0νWν − Z0μZ0μW+νWν) + g2s2w(AμW+μAνWν − AμAμW+νWν) + g2swcw[AμZ0ν(W+μWν − W+νWμ) − 2AμZ0μW+νWν] − gα[H3 + Hφ0φ0 + 2Hφ+φ] − 18g2αh[H4 + (φ0)4 + 4(φ+φ)2 + 4(φ0)2φ+φ + 4H2φ+φ + 2(φ0)2H2] − gMW+μWμH − 12gMc2wZ0μZ0μH − 12ig[W+μ0μφ − φμφ0) − Wμ0μφ+ − φ+μφ0)] 12g[W+μ(H∂μφ − φμH) − Wμ(H∂μφ+ − φ+μH)] 12g1cwZ0μ(H∂μφ0 − φ0μH) − igs2wcwMZ0μ(W+μφ − Wμφ+) + igswMAμ(W+μφ − Wμφ+) − ig1 − 2c2w2cwZ0μ+μφ − φμφ+) + igswAμ+μφ − φμφ+) − 14g2W+μWμ[H2 + (φ0)2 + 2φ+φ] − 14g21c2wZ0μZ0μ[H2 + (φ0)2 + 2(2s2w − 1)2φ+φ] − 12g2s2wcwZ0μφ0(W+μφ + Wμφ+) − 12ig2s2wcwZ0μH(W+μφ − Wμφ+) 12g2swAμφ0(W+μφ + Wμφ+) 12ig2swAμH(W+μφ − Wμφ+) − g2swcw(2c2w − 1)Z0μAμφ+φ − g1s2wAμAμφ+φ − e̅λ(γ∂ + mλe)eλ − ν̅λγ∂νλ − u̅λj(γ∂ + mλu)uλj − d̅λj(γ∂ + mλd)dλj + igswAμ[− (e̅λγµeλ) 23(u̅λjγµuλj) − 13(d̅λjγµdλj)] ig4cwZ0μ[(ν̅λγµ(1 + γ5λ) + (e̅λγµ(4s2w − 1 − γ5)eλ) + (u̅λjγµ(43s2w − 1 − γ 5)uλj) + (d̅λjγµ(1 − 83s2w − γ5)dλj)] ig2√2W+μ[(ν̅λγµ(1 + γ5)eλ) + (u̅λjγµ(1 + γ5)Cλκdκj)] ig2√2Wμ[(e̅λγµ(1 + γ5λ) + (d̅κjCλκγµ(1 + γ5)uλj)] ig2√2mλeM[− φ+(ν̅λ(1 − γ5)eλ) + φ(e̅λ(1 + γ5λ)] − g2mλeM[H(e̅λeλ) + iφ0(e̅λγ5eλ)] ig2M√2φ+[− mκd(u̅λjCλκ(1 − γ5)dκj) + mλu(u̅λjCλκ(1 + γ5)dκj)] ig2M√2φ[mλd(d̅λjCλκ(1 + γ5)uκj) − mκu(d̅λjCλκ(1 − γ5)uκj)] − g2mλuMH(u̅λjuλj) − g2mλdMH(d̅λjdλj) ig2mλuMφ0(u̅λjγ5uλj) − ig2mλdMφ0(d̅λjγ5dλj) + X̅+(∂2 − M2)X+ + X̅(∂2 − M2)X + X̅0(∂2 − M2c2w)X0 + Y̅∂2Y + igcwW+μ(∂μ0X − ∂μ+X0) + igswW+μ(∂μY̅X − ∂μ+Y) + igcwWμ(∂μX0 − ∂μ0X+) + igswWμ(∂μY − ∂μY̅X+) + igcwZ0μ(∂μ+X+ − ∂μX) + igswAμ(∂μ+X+ − ∂μX) − 12gM[X̅+X+H + X̅XH + 1c2w0X0H] 1 − 2c2w2cwigM[X̅+X0φ+ − X̅X0φ] 12cwigM[X̅0Xφ+ − X̅0X+φ] + igMsw[X̅0Xφ+ − X̅0X+φ] 12igM[X̅+X+φ0 − X̅Xφ0]

    Source: Thomas D. Gutierrez, 1999