Quantum field theories in classical spacetimes and particles

Research output: Contribution to journalArticle

Abstract

According to a Received View, relativistic quantum field theories (RQFTs) do not admit particle interpretations. This view requires that particles be localizable and countable, and that these characteristics be given mathematical expression in the forms of local and unique total number operators. Various results (the Reeh-Schlieder theorem, the Unruh Effect, Haag's theorem) then indicate that formulations of RQFTs do not support such operators. These results, however, do not hold for non-relativistic QFTs. I argue that this is due to the absolute structure of the classical spacetimes associated with such theories. This suggests that the intuitions that underlie the Received View's choice of mathematical representations of localizability and countability are non-relativistic. Thus, to the extent that such intuitions are inappropriate in the relativistic context, they should be abandoned when it comes to interpreting RQFTs.

Original languageEnglish (US)
Pages (from-to)98-106
Number of pages9
JournalStudies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
Volume42
Issue number2
DOIs
StatePublished - May 2011

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theorems
operators
formulations
Space-time
Quantum Field Theory
Particle
Operator
Intuition
Countability

Keywords

  • Classical spacetimes
  • Particles
  • Quantum field theory

ASJC Scopus subject areas

  • History and Philosophy of Science
  • Physics and Astronomy(all)
  • History

Cite this

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abstract = "According to a Received View, relativistic quantum field theories (RQFTs) do not admit particle interpretations. This view requires that particles be localizable and countable, and that these characteristics be given mathematical expression in the forms of local and unique total number operators. Various results (the Reeh-Schlieder theorem, the Unruh Effect, Haag's theorem) then indicate that formulations of RQFTs do not support such operators. These results, however, do not hold for non-relativistic QFTs. I argue that this is due to the absolute structure of the classical spacetimes associated with such theories. This suggests that the intuitions that underlie the Received View's choice of mathematical representations of localizability and countability are non-relativistic. Thus, to the extent that such intuitions are inappropriate in the relativistic context, they should be abandoned when it comes to interpreting RQFTs.",
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