MATH425 – Quantum Field Theory

Abstract

Quantum Field Theory is the unification of special relativity with quantum mechanics. First attempts at this failed because physicists tried to keep the number of particles constant. For energies much smaller than the rest mass, i.e. $E\ll mc^{2}$, this is a reasonable approximation. However, once we thinking about high-energy processes we can create new particles. Once this idea was accepted, the development of Quantum Field Theory was still somewhat rocky. This changed when in 1948 Julian Schwinger calculated the anomalous magnetic moment of the electron. The following decades are followed are the story of the success of Quantum Field Theory. The Quantum Field Theory prediction of the anomalous magnetic moment of the electron is to this day the most precise test of a theory in all of science:

I will not be able to show you how this is calculated. But I hope that, over the coming weeks and months, I can give you an idea of the underpinnings of this calculation.

We will begin by studying a relativistic classical scalar field with the Klein-Gordon equation. Next, we will quantise this field, first without interactions and then with using perturbation theory. In the end, we will study decay and scattering as well as higher-order corrections.

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