Advanced Quantum Mechanics Schwabl · Problem 6.12

The Coulomb Potential

Physics — Quantum Mechanics · pauli-fundamental-theorem-dirac-matrices

Problem

Prove Pauli's fundamental theorem for Dirac matrices: For any two four-dimensional representations

\gamma_\mu

and

\gamma_\mu'

of the Dirac algebra both of which satisfy the relation

\{\gamma_\mu, \gamma_\nu\} = 2g_{\mu\nu}

there exists a nonsingular transformation

M

such that

\gamma_\mu' = M\gamma_\mu M^{-1}\,.

M

is uniquely determined to within a constant prefactor.