Below is a partial list the term paper topics for class with some very brief thoughts about how the topic connects to the course:

1) Lagrangian formulation of QM/QFT and Path Integrals

We’ve been describing quantum theory (and eventually we will describe QFT) from a Hamiltonian perspective. An alternate way to formulate things is using Lagrangians, which is convenient when developing a quantum theory from an already known formulation of a classical theory (quantization). The paper I’m envisioning here would basically explore this alternate formulation.

2) History of QFT

QFT was not built by any one individual. It was built over a period of years with some of the key steps occurring even as people like Schrodinger, Heisenberg, and Dirac were struggling with the formulation of non-relativistic quantum mechanics. The scope of possibilities for this topic is pretty broad. One way or another, I’d like there to be some discussion of technical issues that folks ran into in the early development.

3) Feynman Diagrams

Feynman diagrams are the bread-and-butter tools that folks use when organizing their calculations for scattering amplitudes. I’d expect this paper to at least describe where Feynman diagrams come from (i.e. how the basic diagrams come from certain terms in the Lagrangian density of a theory) and the basic rules for combining them and translating them into a mathematical expression. You can even use such diagrams to do ordinary integrals, which may be a nice toy-example to explicitly lay out in your paper.

4) The Standard Model

In our course, we’ve spent a great deal of time discussing the combination of relativity with the principles of quantum theory. Among the key topics has been how the non-interacting single-particle theories work when the particles possess non-zero spin. The Standard Model of particle physics is built from these basic ingredients. At minimum, I’d expect a description of the different particle types and how they fit together into the framework of the Standard Model.

5) Linearized Gravity from QFT

What happens when you write down a quantum theory consisting of a massless spin 2 particle? Well, if you’re careful about extending the Hilbert space to maintain manifest Lorentz symmetry and then determining the constraints that identify the physical subspace of states you discover gravity—almost. In fact, you are forced to write down the linear approximation to the equations of general relativity. I would expect this term paper basically describes this construction in detail.