Question

number 3 needed!!

2. Equations of motion respect relativity if the action is relativistically invariant. Sup pose that the action can be written as S = JdtL and L = JofrC, where L is the Lagrangian density. In this exercise, you will verify that S is a Lorentz scalar if C is a Lorentz scalar. To do this, you want to verify that dd°dis ivari ant under Lorentz transformations. To do that, recall from your caleulus class how under changes of variables, the integration measure picks up a factor of the Jacobian determinant. Verify that the Jacobian determinant forA is equal to 1 for a boost along the x-axis and also for a rotation around the axis. Sow that AT'A = η implies that det A-: 1, and that transformations that are continuously connected to the identity must have det A-1 3. Using the fact that j"(cp, J) transforms as a 4-vector, and the result of the previous question, argue that electric Carge Q = Jd3zp is Lorentz invariant.

Answer 1

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