Past exam of the theoretical physics II course of the University of Cambridge / 2015 / Paper 1 / 6 / a

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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.

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