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P: 657
 Originally posted by matt grime I'm notm sure my interpretation is correct, but in differential forms, d^2 is identically zero. so d^4(x) is zero.
d^4x is shorthand for the invariant measure in Minkowski 4 space. it is the volume 4 form, not the exterior derivative applied 4 times.

you can explicitly show that it is invariant, just by applying the change of variables formula (involving a Jacobian, as turin correctly suggests).