Spacetime symmetries and the CPT theorem

Abstract

This dissertation investigates various aspects of the CPT theorem, exploring the nature of spacetime symmetries and the role of time reversal. It proposes a novel conception of time reversal, “geometric time reversal,” which is argued to be more suitable for specific theoretical applications than the existing “active” and “passive” interpretations. The dissertation then examines the quantum nature of the CPT theorem by presenting a classical analogue for tensor fields, suggesting that the CPT theorem for spinors is essentially quantum-theoretic, while the CPT theorem for tensor fields holds in both classical and quantum contexts. Finally, the work addresses the apparent conflict between the CPT theorem and the standard understanding of spacetime symmetries based on background spacetime structure, proposing a resolution for tensor field theories.