Question

Construct the 4x4 tENSOR (4-row ,J-colomn and also tre 4x4 tensoR 9PP. For te 13.30 Polari zation 4-Vector

construct the 4*4 tensor for the polarization 4 vector.

Answer 1

Given that: polarization 4 - vector, The polarization 4 - vectors for a particle moving in the z - direction given int - B for sigma^3_lambda = 1 E_lambda mu (P) elementof E_lambda v(P) E_1(E_P, 0, 0, Vertical-bar P Vertical-bar ) = (0 1 0 0) E_2(E_P, 0, 0, Vertical-bar P Vertical-bar ) = (0 0 1 0) E_3(E_P, 0,0, Vertical-bar P Vertical-bar ) = ( Vertical-bar P^rightarrow Vertical-bar /m 0 0 E_P/m) sigma^3_lambda = 1 E_lambda mu(P) E_lambda v(P) = E_1 mu E_1v + E_2 mu E_2v + E_3 mu E_3v If mu = v = E_1^2 mu + E_2^2 mu + E_3^2 mu \r\n (0 1 0 0) (0 1 0 0) + (0 0 1 0) + (0 0 1 0) + ( Vertical-bar P Vertical-bar /m 0 0 E_P/m) ( Vertical-bar P Vertical-bar /m 0 0 E_P/m) = [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] + [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] + [P^2/m^2 0 0 E_p^P/m^2 0 0 0 0 0 0 0 0 PE_P/m^2 0 0 E_P^2/m^2]