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Towards a geometrical understanding of the CPT theorem

Greaves, Hilary (2007) Towards a geometrical understanding of the CPT theorem. [Preprint]

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    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 (rather than quantum) field theory, using a little-known classical analog of the CPT theorem.


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    Item Type: Preprint
    Keywords: CPT, PCT, TCP, symmetry, symmetries, field theory, space-time, spacetime
    Subjects: Specific Sciences > Physics > Classical Physics
    Specific Sciences > Physics > Symmetries/Invariances
    Specific Sciences > Physics > Relativity Theory
    Specific Sciences > Physics > Quantum Field Theory
    Depositing User: Hilary Greaves
    Date Deposited: 27 Nov 2007
    Last Modified: 07 Oct 2010 11:15
    Item ID: 3676
    URI: http://philsci-archive.pitt.edu/id/eprint/3676

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