5 - Introduction to relativistic quantum field theory: propagators, interactions, and all that

Summary

We start this chapter with a brief history of quantum field theory. In the 1920s, Dirac attempted to quantize the electromagnetic field (see Chapter 8). This attempt was the beginning of the history of quantum field theory. Then, in 1926, M. Born, W. Heisenberg, and P. Jordan invented canonical quantization, which we will use in Chapters 6 and 7 in order to quantize the Klein–Gordon field and the Dirac field, respectively, that will bring us from relativistic quantum mechanics to relativistic quantum field theory. Next, in 1927, Dirac created and presented the first reasonably complete theory of quantum electrodynamics (QED), and in the following year, 1928, he formulated the Dirac equation (cf. Chapter 3). In addition, in 1928, E.Wigner found that the quantum field describing electrons, or other (spin-1/2) fermions, had to be expanded using anticommuting creation and annihilation operators due to the Pauli exclusion principle. After World War II, in the 1940s, H. Bethe, F. Dyson, R. Feynman, J. Schwinger, and S.-I. Tomonaga solved the socalled ‘divergence problem’ through renormalization (see Chapter 13). This was the start of the modern theory of QED. In the 1950s, C.-N. Yang and R. Mills generalized QED to gauge theories – known as Yang–Mills theories – which we will discuss classically (i.e. without quantization) in Chapter 9.