Towards a geometrical understanding of the CPT theorem

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

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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.

Available Versions of this Item

• Towards a geometrical understanding of the CPT theorem (deposited 27 November 2007) [Currently Displayed]
  • Towards a geometrical understanding of the CPT theorem (deposited 20 April 2009)