Here are the rest of the topics with brief descriptions.

6) The Spin/Statistics Connection

States involving multiple identical particles involve a fundamental inability to distinguish between the particles. In three-dimensional space, it turns out that a state involving multiple identical particles must be symmetric or antisymmetric under particle swaps. Particles that swap symmetrically are called bosons, while particles that swap antisymmetrically are fermions. As we have seen, particles are partly categorized by their spin, and it turns out that relativity imposes the condition that integer spin particles are bosonic while half-integer spin particles are fermionic. The relationship between particle swapping properties and particle spin is called the spin-statistics connection. This term paper should explore why the connection is true at both a conceptual and more mathematical level.

7) The Spinor Helicity Formalism

There is a curious feature of four-dimensional spacetime: 4-vectors can be decomposed into pairs of two-component spinors. Over the last several years researchers have used this relationship to discover new formulations of four-dimensional quantum field theory and much more efficient methods for calculating scattering amplitudes and probabilities. This term paper explores the basic elements of this relationship and how it can be used to formulate theories of massless particles.

8) Supersymmetry

There are fermions and there are bosons. Supersymmetry refers to a whole class of symmetry transformations that exchange the one particle type with the other. You can show that any fermion-type particle can be described in terms of a supersymmetric world-line. On the other hand, supersymmetry relating different particle types in a four-dimensional theory has shaped theoretical and experimental research programs for decades. There are many directions that this term paper topic can go. I would expect any such paper to provide an elementary description of supersymmetry at the quantum level and explore some of the generic implications.

9) Bosonic Strings

The theory of bosonic strings is one of the simplest generalizations of particle-based quantum field theory. This term paper should explore the relationship between the world-line formalism of standard quantum field theory and the worldsheet approach to strings. In the course of doing so, it would be great if the paper could provide some arguments for why (a) the theory requires 26 dimensions for consistency and (b) why nevertheless, the existence of a tachyonic state renders the theory problematic.