Lectures on quantum field theory

de Paul Adrian Maurice Dirac · Publicada por primera vez en 1966

" Dirac's life-long (1948-1984) and relentless pursuit for a quantum electrodynamics with a logical footing" In the 1950’s in his search for a better QED, Paul Dirac developed the Hamiltonian theory of constraints (Cand J Math 1950 vol 2, 129; 1951 vol 3, 1) based on lectures that he delivered at the 1949 International Mathematical Congress in Canada. Although Dirac, like Einstein, would never jump on the band wagon, it is not simply true that he was not aware of particles called mesons ( see Farmelo G 2009 "The Strangest Man", London Faber & Faber). Dirac (1951 “The Hamiltonian Form of Field Dynamics” Cand Jour Math, vol 3 ,1) had also solved the problem of putting the Tomonaga-Schwinger equation into the Schrödinger representation ( See Phillips R J N 1987 “Tributes to Dirac” p31 London:Adam Hilger) and given explicit expressions for the scalar meson field (spin zero pion or pseudoscalar meson ), the vector meson field (spin one rho meson), and the electromagnetic field (spin one massless boson,photon) . Dirac had met Feynman in 1961 and the two physicists talked about the non-existence of an equation “similar to the relativistic equation of the electron” describing a meson which apparently Feynman was supposed to be working on! Feynman started the conversation with the question “It must be good to have invented that equation ”. J C Polkinghorne admitted how wrong he was about Dirac and contemporary particle physics in an article in Kursunoglu & Wigner (Ed) 1990 "Reminiscences about a great physicist" p228 Cambridge:CUP..quote... “All very clever”, we thought to ourselves, " but Dirac would probably not know a pion if he saw one”. The last laugh is where it ought to be, with the great and insightful not tossed about by every wind of physical fashion but profound in his understanding of the quantum field theory that he had invented. I realize now ,with hindsight, that I heard Dirac talk about monopoles and the quantum mechanics of constrained and of extended systems and the difficulties of quantizing gravity, all topics of the highest contemporary interest, to which he contributed the unique clarity and force of his understanding... unquote. In 1956 C N Yang and T D Lee suggested that when particles interact weakly nature might choose to break the perfect symmetry between left and right, the so called parity symmetry (Framelo, 2009). Gravitational and electromagnetic interactions are ambidextrous. Dirac had foreseen the possibility that parity symmetry might be broken in his paper “Forms of relativistic dynamics” (1949 Rev Mod Phys 21 392) in which he states that “I do not believe there is any need for physical laws to be invariant under these reflections (in space and time), although the exact physical laws of nature so far known (gravity and electromagnetism) do have this invariance.” In a paper “Long range forces and broken symmetries” (1973 Proc Roy Soc 333 403 ) he discusses an important feature of Weyl’s geometry that leads to a breaking of the C (charge conjugation) and T (time reversal) symmetries with no breaking of P (parity change) or CT. The breaking of the C and T symmetries is a rare event and has been observed for the K-meson. The Weyl interpretation of of the electromagnetic field as influencing the geometry of space and not something embedded in Riemannn space implies symmmetry breaking. In the late 50’s he applied the Hamiltonian methods he had developed to cast Einstein’s general relativity in Hamiltonian form (Proc Roy Soc 1958,A vol 246, 333,Phys Rev 1959,vol 114, 924) and to bring to a technical completion the quantization problem of gravitation and bring it also closer to the rest of physics according to Salam and DeWitt. In 1959 also he gave an invited talk on "Energy of the Gravitational Field" at the New York Meeting of the American Physical Society later published in 1959 Phys Rev Lett vol 2, 368. In 1964 he published his “Lectures on Quantum Mechanics” (London:Academic) which deals with constrained dynamics of nonlinear dynamical systems including quantization of curved spacetime. He also published a paper entitled “Quantization of the Gravitational Field” in 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics. In 1963 he apparently found from his old notes a rather novel method -using the Hamiltonian formalism that he had already used in 1958 to discuss the energy of gravitational waves and the gravitational polarization of spin 2 - of deriving the Schwinger term and the Lamb shift (1056.17MHz) without recourse to the usual “joining technique” of utilizing Bethe’s non-relativistic result adopted by a number of workers-including Weisskopf and French, Feynman and Schwinger-in quantum electrodynamics. The troublesome vacuum polarisation terms created problems for Feynman (1022.89 MHz) and Schwinger (1016.11 MHz) ; they calculated the Lamb shift without vacuum polarization and again with vacuum polarization which stretegies d