# Hi, I'm Luke Burns

I program a bunch and study physics a bunch. I recently attended the Recurse Center, where I built a p2p event emitter, toyed with a model for open peer review, studied some category theory, and worked on an extension of the Dirac equation. All of my work is on Github.

Below is a list of projects I've been working on recently. Each project has a Github repository with a full version history, TeX source, open issues, and a most recent pdf build. You're welcome to open an issue, or fork and submit a pull request with improvements.

Maxwell's equations from a bounded current (pdf) It is shown that Maxwell's equations follow directly from the ansatz "an electric current density is a conserved, integrable, and bounded timelike vector field in spacetime."

Gauging duality symmetry of the generalized Maxwell equations (pdf) It is shown that duality symmetry of the generalized Maxwell's equations (with magentic sources) can be gauged. Because the newly introduced gauge field is indistinguishable from an electromagnetic gauge field, it is suggested that the coupling could describe non-linear interactions between electromagnetic fields.

An extension of the Dirac equation (pdf) A minimal extension of the Dirac equation is shown to describe a pair of massless, electrically charged fermions. Solutions exhibit rotation in the particle's spin plane, analogous to the zitterbewegung of massive Dirac theory and identical to electric and magnetic fields of circularly polarized electromagnetic waves.

An introduction to geometric algebra (pdf)

Is it possible to construct spinor valued gauge fields? (pdf)