Towards a geometrical understanding of the cpt theorem
British Journal for the Philosophy of Science 61 (1):27-50 (2010)
| 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 | |||||||||
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Similar books and articlesJonathan Bain (2010). Relativity and Quantum Field Theory. In V. Petkov (ed.), Space, Time and Spacetime.
John Earman & Doreen Fraser (2006). Haag's Theorem and Its Implications for the Foundations of Quantum Field Theory. Erkenntnis 64 (3):305 - 344.
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Hilary Greaves (2010). Towards a Geometrical Understanding of the Cpt Theorem. British Journal for the Philosophy of Science 61 (1):27-50.
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