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- W2158151788 abstract "The CPT theorem of quantum field theory states that any relativistic (Lorentz-invariant) quantum field theory must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that seems to arise when one puts the existence of this sort of theorem alongside a standard way of thinking about symmetries, according to which spacetime symmetries (at any rate) are associated with features of the spacetime structure. The puzzle is, roughly, 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—capable of admitting a temporal orientation—this seems to be an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: it is suggested that the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field. To avoid irrelevant technical details, the discussion is carried out in the setting of classical field theory, using a little-known classical analog of the CPT theorem. 1. Introduction2. The Connection between Dynamical Symmetries and Spacetime Structure3. A Puzzle about the CPT Theorem4. A Classical PT Theorem 4.1. Bell's theorem4.2. Auxiliary constraints5. Resolution of the Puzzle6. Galilean-Invariant Field Theories 6.1. Temporal orientation in Galilean spacetime6.2. Counterexample to the Galilean PT hypothesis7. Conclusions" @default.
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- W2158151788 date "2010-03-01" @default.
- W2158151788 modified "2023-09-27" @default.
- W2158151788 title "Towards a Geometrical Understanding of the CPT Theorem" @default.
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- W2158151788 doi "https://doi.org/10.1093/bjps/axp004" @default.
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