Chapter 3
Quantum field theory
Quantum mechanics describes nature as absurd from the point of view of common sense. And yet it fully agrees with experiment. So I hope you can accept nature as She is — absurd. — Richard Feynman
The standard model is a quantum field theory (QFT). It describes the universe as a collection of fields associated with the various elementary particles. At each point in spacetime, there is a random probability for these fields to interact and create or destroy their respective particles.
This means we have an electron field, a photon field, a Higgs field, etc. spread across the universe, and all electrons, photons, and Higgs bosons are identical quantum excitations of these. The interactions of the electron and photon fields, for example, are what we experience as electromagnetism.
As Feynman says, this may all sound absurd. Fields are highly unintuitive, “unphysical” concepts. It can be hard to imagine that particles, matter, and indeed all of us, are simply a collection of quanta probabilistically popping out and dropping back into an abstract cosmic sea.
Not only that, historically, QFT often appeared intractable and even nonsensical, yielding results such as negative energy and infinite mass particles. Its development underwent multiple periods of stagnation and ardent opposition, including by Richard Feynman who suggested in 1945 that field theory be abandoned altogether [95] before changing his mind and making seminal contributions to quantum electrodynamics.
Yet, through the collective efforts of generations of physicists, QFT can now explain nearly every observed phenomenon in particle physics, up to the highest experimental energies. Moreover, it has made some of the most staggering and precise predictions in the history of physics, all of which proved to be in complete agreement with experiment. These range from the calculation of the electron’s magnetic moment up to 12 significant digits, to the prediction of the Higgs boson 50 years before its discovery. Its unprecedented experimental success is why we believe “it is the language in which the laws of Nature are written” (Tong SM [76]).
In this chapter, we first introduce classical and quantum field theory for free particles in Section 3.1, before discussing their interactions and connection to physical observables in Section 3.2. We then detail gauge theories and the beautiful connection between symmetries, QFT, and the forces of nature, in Section 3.3. We conclude with a description of the Higgs mechanism, which is of particular relevance to this dissertation, in Section 3.4. Further background on classical mechanics and mathematical details of quantization, interactions, and spinors can be found in Appendix A.1.1.