Last class:
Physics and Group Theory
(1) "symmetry" and "transformations" is a _big_ part of modern physics.
example : conservation laws
- if theory is "invariant" => something is conserved
space -> momentum
time -> energy
rotations -> angular momentum
QM phase -> electric charge
space/time/charge parity , "handedness" of physics
(2) Each particule must be mathematically a "representation" of all
the transformation groups
example: spin -1/2 1/2 (discuss history of that) - SU(2) is group, not O(3)
2 particles: [-1, 0, 1] + [0]
example2: quarks, eightfold way
pattern of found particles => underlying SU(3) quarks (discuss history)