ISU Coloq 11-3-2014

Elastic -vs- Inelastic Collisisons

Elastic Collisions: Conserve P and E

Inelastic : Only Conserve P

Definition of Momentum Transfer

4-Momentum vector definition using Ryder convention

[math]\displaystyle{ P_{\mu} equiv \left ( \frac{E}{c} , - \vec p \right ) }[/math]

[math]\displaystyle{ P^{\mu} equiv \left ( \frac{E}{c} , \vec p \right ) }[/math]

[math]\displaystyle{ P_{\mu} P^{\mu} = \left ( \frac{E}{c}\right )^2 - \vec p^2 = E^2-p^2 = m^2 }[/math] if you define the speed of light as unity

Note

Other conventions used by Perkins

[math]\displaystyle{ P_{\mu} equiv \left ( \vec p, -E \right ) }[/math]

[math]\displaystyle{ P^{\mu} equiv \left ( \vec p , E\right ) }[/math]

or Kollen

[math]\displaystyle{ P_{\mu} equiv \left ( \vec p, iE \right ) }[/math]

[math]\displaystyle{ P^{\mu} equiv \left ( \vec p , iE\right ) }[/math]

TF_SIDIS_Physics