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Example text
17 36 1. A BRIEF HISTORY OF QUANTUM GAUGE FIELD THEORY operator equation because it would have been incompatible with the canonical commutation relations. Rather he proposed (although this is not very explicitly stated) to view the relation ∂ µ Aµ = 0 as a subsidiary condition which physical states must satisfy, thus ∂ µ Aµ (x)|phys = 0 for all x and t. Heisenberg and Pauli (see the footnote on page 174 of their second paper) gave a Lagrangian reformulation of Fermi’s approach, 2 − 12 (∂ µ Aµ )2 +L(minimal coupling of matter) and observed that the action L = − 14 Fµν yields the equations of motion if one takes Aµ = − 4π j , which agrees with their own approach c µ = 1.
15). 1), was proposed by Dirac in 1932 [65]. (In fact, even earlier Fermi had considered this approach [35]). ,xµN . The wave function satisfied general Dirac equations, but if one set all times tn equal to the same time t, one came back to Fermi’s and Dirac’s radiation theory. This so-called many-time formalism remains a combination of quantum mechanics for electrons and field theory for photons, but it can describe pair creation if one uses the concept of the Dirac sea. It was shown to be equivalent to earlier approaches [66], but because it was very complicated, equivalent to other approaches, and a mixture of quantum mechanics and field theory, it was soon abandoned by all physicists, including Dirac himself.
We discuss further historical aspects of path integrals in section 5. One advantage of his approach was that it no longer needed arbitrary spacelike surfaces for relativistic invariance. Another advantage was that the perturbation expansion of path integrals led to a formulation of quantum field theory in terms of simple space-time pictures, which became known as Feynman diagrams. Most importantly, the simple pictorial formulation combined with its manifestly relativistic invariance made it easy to perform calculations33 and to subtract divergences in an unambiguous way [88].