# How are the covariant Pauli matrices defined?

When doing calculations with Weyl spinors, terms like $\theta\sigma^\mu\theta^\dagger$ appear. I know that for 3+1 spacetime dimensions, $\sigma^\mu = (\textbf{1}, \sigma^i)$ with $i=1,2,3$ the usual Pauli matrices. But what if we consider 1+1 or even $D$+1 dimensions?

• What do you know about Clifford groups and algebras? – DanielC Sep 27 '17 at 7:58
• @DanielC I know the elements have to fulfill anti commutator relations $\{ \gamma^\mu,\gamma^\nu \} = 2\eta^{\mu\nu}\textbf{1}$. – Stephan Sep 27 '17 at 8:07
• You asked about the generalization to D spatial dimensions. I asked you for your mathematical background because I found a possible source to answer your question arxiv.org/abs/hep-th/0506011 – DanielC Sep 27 '17 at 8:29
• That's great, thank you very much! I guess I should rather say, my knowledge of Clifford algebras is somewhat limited. I can't find the answer to $\sigma^\mu$ in 1+1 dimensions in this paper.. – Stephan Sep 27 '17 at 8:37
• I will try to look this up. Namely, if there are spinors for SO(1,1). – DanielC Sep 27 '17 at 8:46