Mostly particles and symmetries. Probably ~2 questions on special relativity in the context of particle physics. 18 multiple choice, 2 long answer.

Special relativity

• $E^2=p^2+m^2$
• ${\tau }^{\prime }=\tau \gamma$
  • $\tau$ is proper time
• ${\sum }_i[E_i,{\vec{p}}_i]={\sum }_f[E_f,{\vec{p}}_f]$

Group theory

$[X,Y]=0$ indicate $X$ and $Y$ commute together.

Transformation -> operator $\hat{T}$.

• If $[\hat{T},\hat{H}]=0\Rightarrow \frac{d}{dt}<\hat{T}>=0$
• Continuous groups $\hat{T}(\theta )=\hat{I}-i\hat{J}\theta +\mathcal{O}({\theta }^2)$
  • and $\hat{T}(\theta )=e^{i\hat{J}\theta }$
  • $U(I)\to e^{i\theta }$

$$\begin{array}{rl}SU(2)& =\frac{1}{2}\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right],\frac{1}{2}\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],\frac{1}{2}\left[\begin{array}{cc}0& -i\\ i& 0\end{array}\right]\\ SU(2)& \to [J_x,J_y]=i{J}_z\end{array}$$ $$SO(3)=\left[\begin{array}{ccc}0& i& 0\\ -i& 0& 0\\ 0& 0& 0\end{array}\right]\dots ,\text{etc}$$ Rotation matrix in 3D $$\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0\\ \sin \theta & \cos \theta & 0\\ 0& 0& 1\end{array}\right]$$

Spin

$$|jm⟩\text{with }j\in \left(0,\frac{1}{2},1,\frac{3}{2}\right),m\in (-j,-j+1,\dots ,j-1,j)$$

• e.g. $|\frac{1}{2}\frac{1}{2}⟩$ is spin $\frac{1}{2}$, up = $\left[\begin{array}{c}1\\ 0\end{array}\right]-|\uparrow ⟩$ $${\hat{J}}^2|jm⟩=j(j+1)|jm⟩{\hat{J}}_z|jm⟩=m|jm⟩$$ $$|j_1{m}_1⟩\otimes |j_2{m}_2⟩=A_1||j_1-j_2|m_1+m_2⟩+A_n||j_1+j_2|m_1+m_2⟩$$
• $\otimes$ is tensor product
• e.g. $$|\frac{1}{2}\frac{1}{2}⟩\otimes |\frac{1}{2}\frac{1}{2}⟩=|11⟩|\frac{1}{2}\frac{1}{2}⟩\otimes |\frac{1}{2}-\frac{1}{2}⟩=\frac{1}{\sqrt{2}}\left(|10⟩+|00⟩\right)$$

Detectors

$$pc=0.3qBR$$

pc units of GeV, q units of $e$, $B$ in $T$, $R$ in $m$

Prefixes!

Geiger counters, phototubes, scintillators.

Particles

Lepton, neutrino, quark, Baryon, Hadron, meson

Symmetries:

Energy, momentum, Lepton (number, flavor), Baryon (number, flavor), charge

Forces:

• E&M (photons)
• Weak (W and Z bosons)
• Strong (gluons)
• Higgs (Higgs boso)
• Gravity (graviton?)

Decays and translations

$$A\to B+CA+B\to C$$ "If it's weird enough to be weak then it's gotta be weak"

Ex.

$$n\to p+e+\sqrt{e}$$ Antineutrino? $\sqrt{e}$

Both strong and E&M decays conserve strangeness; how to differentiate?

• Any strong decay can also be E&M, but strong will be ... stronger.
  • Cannot pick strong if involves leptons in photons
  • If just a bunch of quarks, likely strong
    • More complicated rules beyond this tho.
  • Weak violates baryon flavor, doesn't have to though ...