Notes on Particle Physics

NOTE: These are supplementary notes, you will still need to read your text book.

A symmetry means you do something to the equation (e.g. change every variable x to -x in the case of Parity inversion) and the solutions to the equation are exactly the same. Emmy Noether figured out that for every symmetry found in the mathematical expression of the laws of physics there has to be a conservation law. For example it can be proven that because Newton's laws (corrected for relativity of course) look the same in a different reference frame (shifting over by a distance x does not change the equations) then it can be proven mathematically that momentum is conserved. Here are some examples of the relationship between known symmetries and their conservation laws. Note however that not all of the four forces obey all of the conservation laws.

Symmetry	Conservation law	Obeyed by which force (Gravity, Strong, Weak, EM)
Translational Invariance (the laws of physics are the same in different reference frames)	Momentum conservation	G, S, W, EM
Time Invariance (the laws of physics do not change with time)	Energy conservation	G, S, W, EM
Rotational Invariance (the laws of physics look the same in a rotated reference from)	Conservation of angular momentum	G, S, W, EM
Electromagnetic Gauge Invariance (the electric field E can be written in terms of a potential, V; the magnetic field in terms of a vector potential A leaving room for an arbitrary constant)	Conservation of Charge	G, S, W, EM
Particle Exchange Invariance	Fermi Dirac versus Bose Einstein statistics	G, S, W, EM
Exchange of leptons	Lepton Number	G, S, W, EM
Exchange of baryons	Baryon Number	G, S, W, EM
Exchange of strangeness and charm, bottomness and topness	Strangeness	G, S, EM
Exchange of Isospin (protons, neutrons have I = + or - 1/2, mesons 1, 0, -1)	Isospin invariance	G, S
Parity inversion (x goes to -x, etc.)	Parity conservation	G, S, EM
Charge congugation (q goes to -q)	Charge congugation conservation	G, S, EM
Time reversal (t goes to -t)	Time reversal conservation	G, S, EM
All three of the above (PCT) at the same time	TCP conseravtion	G, S, W, EM

The general rule is that any reaction can and will occur as long as it does not break a conservation law. So for example a neutron can decay into a proton, an lectron and an anti neutrino but a proton never decays into a pion and positron. Why not since charge, energy, momentum etc. would be conserved? Lepton number is not conserved for the second reaction so it does not occur.

In a second application, a reaction may be only able to occur via a certain force but not via another force since the second force might obey a conservation law and the first one not. For example strangness is conserved by the strong and EM forces but not the weak force. So the reaction of proton plus a negative pion decaying into a lambda and kaon occurs only very slowly via the weak interaction (it is forbidden by the strong interaction).

Physics at IUS: http://physics.ius.edu/
Contact Dr. K. Forinash, for comments/suggestions/corrections.