2. Consider a two body collision process: a+b=c+d with Pa, Pb. Pc: Pa denoting the four...

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2. Consider a two body collision process: a+b=c+d with Pa, Pb. Pc: Pa denoting the four momenta of the particles a, b, c, d respectively. (a) (4 points) Construct all possible Lorentz invariant quantities and show that there can only be two independent quantities (be specific by stating the relevant expression). (b) (3 points) For elastic scattering process of identical particles a + a⇒a+a, show that the variable t = -2p² (1-cos 0) where p is the magnitude of momentum of particle in the centre of momentum frame and is the scattering angle. 2. Consider a two body collision process: a+b=c+d with Pa, Pb. Pc: Pa denoting the four momenta of the particles a, b, c, d respectively. (a) (4 points) Construct all possible Lorentz invariant quantities and show that there can only be two independent quantities (be specific by stating the relevant expression). (b) (3 points) For elastic scattering process of identical particles a + a⇒a+a, show that the variable t = -2p² (1-cos 0) where p is the magnitude of momentum of particle in the centre of momentum frame and is the scattering angle.