Towards a Geometrical Understanding of the CPT Theorem

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The CPT theorem states that any relativistic QFT must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that arises when one puts the existence of this theorem alongside a standard way of thinking about symmetries, according to which spacetime symmetries are associated with features of the spacetime structure. The puzzle is that the existence of a CPT theorem seems to show that it is not possible for a well- formulated theory that does not make use of a preferred frame or foliation to make use of a temporal orientation. Since a manifold with only a Lorentzian metric can be temporally orientable, this is an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field.


A presentation at the Philosophy of Quantum Field Theory Workshop, which was held at The University of Western Ontario on April 24-26, 2009

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