Homework 3

1) Demonstrate that the phase space terms:

$$\frac{d^3 p}{(2 \pi)^3 2E}$$

are Lorentz invariants,

2) The initial flux enetering the general form of the differential cross section for the collision process:

$$A+B \rightarrow C+D$$

can be expressed in a covariant form as:

$$F= 4 \sqrt{ (p_A^\mu p_{B \, \mu})^2 - m_A^2 m_B^2}$$

where $p_{A(B)}$ are the four-momenta of particles $A(B)$, and $m_{A(B)}$ their masses.

Write the expressions for $F$ in the case of:

(a) A collinear (head on) collision;

(b) A collision between a beam particle and a fixed target (see class notes!).