Question

In the theory of relativity a particle of mass m and position moving in R3 is described by the Lagrangian t1 where the speed of light c is a constant and a dot denotes differentiation with respect to time. Compute the equations of motion. Show that, if T is an anti-symmetric matrix, i.e. T =-TT, then verify that it is conserved. Compute the conjugate momentum p and energy E and verify that they are conserved. Show that Evaluate the energy for the cases = Q and → c.

Answer 1

l./ ㄜ丞〉〉.dt Not ㄒㄒㄨ

と 2

2 dlt 阪' dlt 1-

MU -尸 서치 1