  New symmetry theorems are obtained for field theories formulated in Minkowski
spacetime, based on the recognition that such theories should be diffeomorphism
invariant. These theorems, which are in fact generalized Noether theorems, have
several nontrivial ramifications. One immediate consequence is the necessity to
re-evaluate some of the default characterizations of the original Noether
theorems as general statements - for instance, the statement that every global
invariance of the action gives rise to a conserved current. As it turns out,
this latter statement remains valid, but apparently only as a consequence of
both the generalized first and second Noether theorem (at any rate, it is very
far from clear how to avoid such a conclusion). A ramification of a more
constructive nature consists in a novel expression for the so-called Belinfante
stress-energy tensor, for which it is evident that it generalizes to the
correct stress-energy tensor within the context of general relativity. The
crucial symmetry property here is diffeomorphism invariance, rather than
Poincar\'e invariance. Using this new form for the stress-energy tensor, an
alternative route to general relativity also becomes available, which, in
contrast to many standard treatments, is intrinsically based on a variational
formulation - i.e. without the need to have prior knowledge of the form of
Einstein's equation. The connection of these results to related results
previously established in the literature (although in a completely different
context) will be pointed out where applicable.
