Particles, Cutoffs and Inequivalent Representations

Fraser and Wallace on Quantum Field Theory

Abstract

We critically review the recent debate between Doreen Fraser and David Wallace on the interpretation of quantum field theory, with the aim of identifying where the core of the disagreement lies. We show that, despite appearances, their conflict does not concern the existence of particles or the occurrence of unitarily inequivalent representations. Instead, the dispute ultimately turns on the very definition of what a quantum field theory is. We further illustrate the fundamental differences between the two approaches by comparing them both to the Bohmian program in quantum field theory.

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Notes

  1. 1.

    Wallace and Timpson [6, p. 707] also emphasize the non-fundamental character of particles in QFT. In contrast to [3, 4], they even seem to advocate AQFT as a guide to fundamental ontology (pp. 711–712). This reinforces the claim that an AQFT-fueled refusal of particles at the fundamental level is fully compatible with a commitment to particles as non-fundamental entities.

  2. 2.

    Note that, despite its name, QFT does not straightforwardly support a field ontology either [7].

  3. 3.

    This does not mean, however, that no ontological lessons can be drawn from an effective theory like CQFT. We will return to this point in Sect. 5.

  4. 4.

    See [8], which also privileges AQFT on ontological grounds.

  5. 5.

    See [9, 10] for a recent version of scientific realism based on this idea. Section 9.3 of the latter work also contains a deeper investigation of the interplay between experimental and theoretical considerations in the interpretation of QFT.

  6. 6.

    Fraser might disagree with our characterization of this kind of evidence as theoretical, as she claims that “this unification project is also empirical, broadly construed, insofar as there is indirect empirical support for special relativity and its theoretical principles and for non-relativistic quantum theory and its theoretical principles” [2, p. 131]. However, given that there is indirect empirical support for general relativity as well, Wallace’s above-mentioned arguments also count as “empirical” in this sense.

  7. 7.

    The reader interested in historical aspects of the theory should refer to [12] and [13].

  8. 8.

    See [3, pp. 50–52] for different ways to address the problem of Poincaré non-covariance from the perspective of CQFT.

  9. 9.

    These two approaches have clearly a different scope and in some sense Bohmian QFT is less ambitious than AQFT, but far more empirically successful, since it is built to be empirically equivalent to CQFT as explained above.

  10. 10.

    A possible proposal could be to cast the existing Bohmian QFTs in the framework of Wightman’s axioms as it has been suggested by Nino Zanghí (personal communication).

  11. 11.

    It is interesting to consider that both in Bell’s first pilot-wave model [19] as well as in the Dirac Sea formulation of BQFT [20] bosons are not part of the ontology, fermions are sufficient in order to explain and describe observed phenomena. Bosons are instead part of the ontology in the Bell-type QFT, where they receive the same particle status as the fermions. For a detailed technical and conceptual expositions of these ideas see [21].

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Acknowledgements

VL is grateful to the Swiss National Science Foundation for financial support (Project No. 169313).

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Correspondence to Andrea Oldofredi.

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Egg, M., Lam, V. & Oldofredi, A. Particles, Cutoffs and Inequivalent Representations. Found Phys 47, 453–466 (2017). https://doi.org/10.1007/s10701-017-0069-4

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Keywords

  • Algebraic quantum field theory
  • Particle physics
  • Renormalization
  • Unitarily inequivalent representations