Question

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-J aC, where L is the Lagrangian density. In tis exercise, you will verify that S is a Lorentz scalar if C is a Lorentz scalar. To do this, you want to verify that d'rd d2d is nvari- ant under Lorentz transformations. To do that, recall from your calculus 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. Show that Ar,A = η implies that detA = ±1, and that transformations that are continuously connected to the identity must have det 1.

Answer 1

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