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

Preview

PDF tgu_v2.pdf Download (363kB)

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.

---

Export/Citation:

EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL

Social Networking:

Share |

---

Item Type:	Preprint
Creators:	Creators Email ORCID Greaves, Hilary
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 15:15
Item ID:	3676
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Symmetries/Invariances Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Quantum Field Theory
Date:	November 2007
URI:	https://philsci-archive.pitt.edu/id/eprint/3676

Available Versions of this Item

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

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item