All you need to know about the Dirac equation

Abstract

A very brief introduction is given to all that is needed to appreciate the formal structure of the Dirac equation and why–without destroying this structure–it cannot be reduced to a Pauli-Schrödinger type equation.

Keywords:

• relativistic quantum mechanics
• Dirac equation
• electronic structure
• group theory
• magnetism
• quantum mechanical calculation
• theoretical

Acknowledgements

I would very much like to acknowledge the influence of my former teachers Per-Olov Löwdin (Uppsala, together with Harold MacIntosh), Simon Altmann (Oxford) and Walter Kohn (Santa Barbara). While Per-Olov raised my interest in ‘formal structures’, it was Simon who completely indoctrinated me with group theory as a formal tool to view ‘structures’. And Walter taught me to keep the right distance to my own research.

Notes

Notes

1. for a discussion of classical relativistic dynamics see, e.g. the book by Messiah 6.

2. This is exactly the algebra of creation and annihilation operators for fermions.

3. Because of the block-diagonal form of the Dirac matrix β.