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For an elementary discussion without too many details, QFT is simple. We start from certain classical fields dictated by a Lagrangian. Learn about these a little using the fields form of Euler-Lagrange equations, quantize them using the operator methods of Quantum Mechanics - reducing the system to set of harmonic oscillators. At this point, we treat particles as the quantization of these fields viz. the excitations of the individual harmonic oscialltors they are made of. We then look at the propagator and comment on the causality issues. Adding interactions to this free theory tempts us to use perturbation theory to determine some physical observable, the scattering ammplitudes and cross-sections! The goal of this article is to lead upto these calculations and describe what Feynman diagrams are about, all in the context of the simplest field theory - scalar boson.
As a broad overview of classical aspects of QFT that this article series aims to be, it’s worth starting from the classification of fields we study in QFT.
Particles $\longleftrightarrow$ Fields $\longleftrightarrow$ Lorentz Group Representations
The fields, or their Lagrangians to be more precise must respect the Lorentzian and translation symmetries, which are grouped together as Poincare symmetry. With this, the fields we study essentially reflect the possible representations of the Poincare group!
| Field type | Spin |
|---|---|
| Scalar field | Spin 0 |
| Vector field | Spin 1 |
| Dirac field | Spin 1/2 |
| Symmetric tensor field | Spin 2 |
Tong.
Tong + Yogesh Set the context for pertubration theory, and Feynman diagrams.
Tong. Basically give the rules of drawing diagrams.
Give one hint where they are coming from.
Self-research.