Quantum field theory, in its present incarnation, makes crucial use some gauge degrees of freedom that are ultimately superfluous, in the sense that they wind up getting symmetrized out. Such, at least, is my understanding of the point of view of Arkani-Hamed and Trnka in their new paper on The Amplituhedron. They propose a reformulation which, at least for one toy theory, results in a major simplification.
Via the Lumonator.
I can't quite decide whether reading it will just make me feel stupider or not.
Update: Peter Woit has a nice post on this and related matters, and
Sean Carroll has a guest post from Lance Dixon, one of the pioneers in new methods for calculating amplitudes in QCD.