Spinors: Lorentz Group

We take here as the physically relevant definition that spinor fields are elements of the spaces of the fundamental representations of the Lorentz Group. Hence we begin with an informal (and therefore non-rigorous) discussion of the structure and the various representations of this physically important group. In particular, this lecture includes a discussion of the fundamental and general representations of the Lorentz group as well as the special cases of self-dual and real representations. This will clarify what precisely is meant by the term “spinor,” and permit analogies between the notions of self-dual tensors and Weyl spinors as well as real antisymmetric tensors and Majorana spinors. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.