PX156 - I3 - discrete symmetries

these make countable transformations to a system which returns the system to the start after repeated application a finite number of times
not controlled by noether's theorem
conservation of a discrete symmetry that the probabilities of an interaction happening in the original and transformed system are the same

symmetry operation	effect	conserved by
parity ( $\hat{P}$ )	$x, y, z \to - x, - y, - z$ ; $p \to - p$	strong, EM; not weak
charge conjugation ( $\hat{C}$ )	flips the sign of all quantum numbers, eg: $e^{-} \to e^{+}$	strong, EM; not weak
time reversing ( $\hat{T}$ )	flips the direction of time; changes the direction of particles	strong, EM; not weak

note: vectors invariant to parity transformations are called axial vectors
- $L = r \times p$
- by $\hat{P} : r \to - r; p \to - p ⟹ L \to L$

combined symmetries

\begin{array}{r} x \to - x \\ y \to - y \\ z \to - z \\ p \to \bar{p} \end{array}

- conserved by the strong, and the EM forces
- not by the weak force

\begin{array}{r} x \to - x \\ y \to - y \\ z \to - z \\ p \to \bar{p} \\ t \to - t \end{array}

\begin{matrix} P r o b_{1} = P [A ({\vec{p}}_{A}) + B ({\vec{p}}_{B}) \to C ({\vec{p}}_{C}) + D ({\vec{p}}_{D})] \\ ↓ \hat{C} \hat{P} \hat{T} \\ P r o b_{2} = P [\bar{C} (- {\vec{p}}_{C}) + \bar{D} (- {\vec{p}}_{D}) \to \bar{A} (- {\vec{p}}_{A}) + \bar{B} (- {\vec{p}}_{B})] \\ P r o b_{1} = P r o b_{2} \end{matrix}

conserved by the strong, the EM, and the weak forces
necessary for quantum field theory
parity non-conservation by the weak interaction came as a shock
$\hat{C} \hat{P}$ violation leads to a solution for why the universe of matter-dominated universe
$\hat{C} \hat{P}$ violation $⟹$ matter-antimatter imbalance