 Solution

ID: past-exam-of-the-theoretical-physics-ii-course-of-the-university-of-cambridge/2015/paper-1/6/a/solution

The defining condition is

S L (2, C) = {S \in M_{2} (C) : det S = 1} .

The entries are complex and the matrices are invertible; products and inverses retain determinant one. There is no unitarity condition

S^{†} S = I

in general. Four complex entries subject to one complex determinant equation give three complex, or six real, local group parameters.

 New to topics? Read the docs here!