Advanced Quantum Mechanics Schwabl · Problem 6.11

The Coulomb Potential

Physics — Quantum Mechanics · gamma-matrix-commutant

Problem

Show that if a 4×44 \times 4 matrix XX commutes with all γμ\gamma^\mu, then this matrix XX is proportional to the unit matrix. Hint: Every 4×44 \times 4 matrix can, according to Problem 6.1, be written as a linear combination of the 16 matrices Γa\Gamma^a (basis!).

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