The global approach to quantum field theory

Bryce DeWitt9780198510932, 0198510934, 019852790X, 0198527918

There exists an anomaly today in the pedagogy of physics. When expounding the fundamentals of quantum field theory physicists almost universally fail to apply the lessons that relativity theory taught them early in the twentieth century. Although they usually carry out their calculations in a covariant way, in deriving their culational rules they seem unable to wean themselves from canonical methods and Hamiltonians, which are holdovers from the nineteenth century and are tied to the cumbersome C + l)-dimensional baggage of conjugate momenta, bigger-than-physical Hilbert spaces, and constraints. There seems to be a feeling that only canonical methods are “safe”; only they guarantee unitarity. This is a pity because such a belief is wrong, and it makes the foundations of field theory unnecessarily cluttered. One of the unfortunate results of this belief is that physicists, over the years, have almost totally neglected the beautiful covariant replacement for the canonical Poisson bracket that Peierls invented in 1952.