# Invariance Principles and Conservation Laws

### Recall from last lecture:

Parity is the operation of changing all coordinates to their negative values. Parity of a state of orbital angular momentum:

P Ylm = (-1)lYlm
or P = (-1)l

## Parity

Parity is a multiplicative quantity.

Parity is conserved in strong and electromagnetic interactions.

#### Parity of the photon

The basic atomic transition (E1) is characterized by a change of orbital angular momentum by one unit, Δl=±1. Thus, the parity of the photon is Pγ=-1.

#### Parity of baryons

The conservation of baryon number makes the parity of baryons irrelevant. Ian any interaction, the same number of baryons must appear in the initial and final states. There absolute parity relative to mesons is therefore irrelevant. By convention we choose the parity of the proton Pp=+1. The parity of the neutron is the same as that of the proton, Pn=+1.

## Pion Spin and Parity

The application of parity becomes non-trivial for pions. The determination of the parity is intertwined with the determination of the pion spin, so the both are discussed here. We'll begin our discussion here with a discussion of the decisive experiments from which the spin and parity was originally determined.

### Spin of the Pion

#### Charged pions

The spin of the charged pions was determined by measurement of the forward and backward cross sections for the reaction:

p p <==> π+ d