Sunday, July 20, 2014

[hep-th] A Simple Introduction to Particle Physics

A Simple Introduction to Particle Physics

This is a wonderfully written paper introducing the topic of particle physics to undergraduates. It approaches the subject leisurely in Part 1 by reviewing some important classical physics concepts. These include Noether's theorem, gauge transformations, and the Classical Electrodynamics Lagrangian $$ \mathcal{L_{EM}} = -\frac{1}{4} F_{\mu \nu}F^{\mu \nu} - J^{\mu}A_{\mu} $$

Following this, Part 2 introduces the algebraic concepts needed to be successful and harness a true understanding of particle physics. Using these foundations, the generators and Lie algebras for any group may be discovered. This portion of the paper is somewhat mathematically rigorous due to the generality of the discussion.

The fun really begins in Part 3 of the paper where Quantum Field Theory is finally introduced. The author starts with the typical derivation of the Klein-Gordon equation for spin-0 fields through the relativistic Hamiltonian. Moving forward Robinson et al. discuss spinors and why the irreducible representation of the Lorentz group turns out to be $ SU(2) \otimes SU(2) $. After discussing the Dirac sea of antiparticles and the correct QFT interpretation of antiparticles, we move on to discuss the Dirac Lagrangian for a particle in an electromagnetic field and the coupling of the particle's field (e.g. electron) with the gauge field (photon).

Once you reach the section on quantization the paper starts to pick up and get pretty difficult for a reader encountering particle physics for the first time. I suggest only skimming this section or looking up other resources if you have not had experience with this before.

Finally, some investigation of the Standard Model is done. The authors look at spontaneous symmetry breaking, the Higgs sector, and the quark sector. You will need to understand what was going on in the quantization section to keep up with their tempo here.

This is a fantastic paper that will introduce advanced undergraduates to the beauty and rigor of particle physics without assuming too much early on. The paper becomes difficult in the later portions of Part 3 so is pretty approachable. I hope you all enjoy this paper!

P.S. for those of you who highly enjoyed the paper, there is a second paper that goes much deeper into the geometrical approach to gauge theories. 
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