Student Colloquium: Joe Lesnefsky
Have you ever seen ⊗ and been confused? I know I have. Tensor products, ⊗, are constantly used in physics and rarely, if ever, explained to any degree of mathematical rigour. In fact, it seems that conventional notation is designed to conceal ⊗. Continuing Martin Winslow's IN YOUR FACE lecture series on mathematical physics, I intend to elucidate the elusive ⊗ by introducing some category theory, free groups, and group presentations. Additionally, I propose a generalized method utilizing appropriate presentations of free categories to custom build useful mathematical objects subject to physical constraints. Demonstrating this method, I will look its applications to the Dirac equation and the multi-linear tensor functor ⊗. Finally I will expose commonly concealed ⊗'s in other conventional physics such as Lorentz tensors, the completeness relation, and spin algebras.