# Solutions to first order equation with Clifford algebra elements

1. Nov 18, 2014

### gentsagree

In the same way one can show that $\nabla^{2}\theta=0$ has only one smooth solution, namely $\theta=0$, I would like to show that

$$\gamma^{i}\partial_{i}\epsilon=0$$ has only one smooth solution, where $\gamma^{i}$ is a Dirac gamma matrix (or an element of the Clifford algebra), and $\epsilon$ is a spinorial quantity (which may or may not be relevant to finding a smooth solution, I am not sure).

Also can anyone recommend a book that treats formally (and clearly, possibly) a procedure for finding unique/smooth solutions to equations.

Thanks.

2. Nov 23, 2014