Question

The Mandelstam variables s, t, and u are defined for the reaction A + B → C + D, by 

s = (P_A + P_B)²/c², t = (P_A − P_C)²/c², u = (P_A − P_D)²/c² 

where P_A, P_B, P_C, P_D are the relevant energy-momentum four vectors. Show that 

s + t + u = ∑m_j²(j = A, B,C, D)

Answer 1

s + t + u = (1/c²)[(P_A + P_B)² + (P_A − P_C)² + (P_A − P_D)²]