Bain, Jonathan Quantum field theories in classical spacetimes and particles. (English) Zbl 1228.81256 Stud. Hist. Philos. Sci., Part B, Stud. Hist. Philos. Mod. Phys. 42, No. 2, 98-106 (2011). Summary: 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. Cited in 3 Documents MSC: 81T99 Quantum field theory; related classical field theories Keywords:quantum field theory; particles; classical spacetimes PDFBibTeX XMLCite \textit{J. Bain}, Stud. Hist. Philos. Sci., Part B, Stud. Hist. Philos. Mod. Phys. 42, No. 2, 98--106 (2011; Zbl 1228.81256) Full Text: DOI References: [1] Arageorgis, A.; Earman, J.; Ruetsche, L., Fulling non-uniqueness and the Unruh effect: A primer on some aspects of quantum field theory, Philosophy of Science, 70, 164-202 (2003) [2] Araki, H., Mathematical Theory of Quantum Fields (1999), Oxford University Press: Oxford University Press Oxford [3] Bain, J., Against particle/field duality: Asymptotic particle states and interpolating fields in interacting QFT (or: Who’s afraid of Haag’s Theorem?), Erkenntnis, 53, 375-406 (2000) · Zbl 0970.81037 [4] Bain, J., Theories of Newtonian gravity and empirical indistinguishability, Studies in History and Philosophy of Modern Physics, 35, 345-376 (2004) · Zbl 1222.83006 [5] Bär, C., Localization and semibound energy—A weak unique continuation theorem, Journal of Geometry and Physics, 34, 155-161 (2000) · Zbl 0969.58007 [6] Bratteli, O.; Robinson, D., Operator Algebras and Quantum Statistical Mechanics 1 (1987), Springer: Springer New York [7] Christian, J., Exactly soluble sector of quantum gravity, Physical Review D, 15, 4844-4877 (1997) [8] Clifton, R.; Halvorson, H., Are Rindler Quanta Real? Inequivalent particle concepts in quantum field theory, British Journal for the Philosophy of Science, 52, 417-470 (2001) · Zbl 1002.81003 [9] Earman, J.; Fraser, D., Haag’s theorem and its implications for the foundations of Quantum field theory, Erkenntnis, 64, 305-344 (2006) · Zbl 1107.81004 [10] Fraser, D., The fate of “Particles” in quantum field theories with interactions, Studies in History and Philosophy of Modern Physics, 39, 841-859 (2008) · Zbl 1223.81027 [11] Fraser, D. (2006). Haag’s theorem and the interpretation of quantum field theories with interactions. Ph.D. thesis, University of Pittsburgh.; Fraser, D. (2006). Haag’s theorem and the interpretation of quantum field theories with interactions. Ph.D. thesis, University of Pittsburgh. [12] Halvorson, H., Reeh-Schlieder defeats Newton-Wigner: On alternative localization schemes in relativistic quantum field theory, Philosophy of Science, 68, 111-133 (2001) [13] Halvorson, H.; Clifton, R., No place for particles in relativistic quantum theories?’, Philosophy of Science, 69, 1-28 (2002) [14] Horuzhy, S. S., Introduction to Algebraic Quantum Field Theory (1990), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht, (translation of Russian edition (1986)) [15] Lévy-Leblond, J.-M., Galilean quantum field theories and a Ghostless Lee Model, Communications in Mathematical Physics, \(4, 157-176 (1967)\) · Zbl 0163.22104 [16] Lévy-Leblond, J.-M., Galilei group and Galilean invariance, (Loebl, E., Group Theory and its Applications, Vol. II (1971), Academic Press: Academic Press New York), 221-299 [17] Malament, D., Defense of Dogma: Why there cannot be a relativistic quantum mechanics of (Localizable) particles, (Clifton, R., Perspectives on Quantum Reality (1996), Kluwer: Kluwer Dordrecht), 1-10 [18] McCabe, G., The Structure and Interpretation of the Standard Model (2007), Elsevier: Elsevier Amsterdam [19] Requardt, M., Spectrum condition, analyticity, Reeh-Schlieder and cluster properties in non-relativistic Galilei-invariant quantum theory, Journal of Physics A, 15, 3715-3723 (1982) [20] Saunders, S. (1992). Locality, complex numbers, and relativistic quantum theory, PSA \(:\)Proceedings of the Biennial Meeting of the Philosophy of Science Association; Saunders, S. (1992). Locality, complex numbers, and relativistic quantum theory, PSA \(:\)Proceedings of the Biennial Meeting of the Philosophy of Science Association [21] Segal, I.; Goodman, R., Anti-locality of Certain Lorentz-invariant operators, Journal of Mathematics and Mechanics, 14, 629-638 (1965) · Zbl 0151.44201 [22] Streater, R., Why should anyone want to axiomatize quantum field theory?, (Brown, H.; Harre, R., Philosophical Foundations of Quantum Field Theory (1988), Clarendon Press: Clarendon Press Oxford), 137-148 [23] Streater, R.; Wightman, A., PCT, Spin and Statistics, and All That (1964/1989), Princeton University Press: Princeton University Press Princeton · Zbl 0135.44305 [24] Strohmaier, A. (1999) The Reeh-Schlieder property for the Dirac field on static spacetimes. Available at 〈lanl.arxiv.org/abs/math-phy/9911023; Strohmaier, A. (1999) The Reeh-Schlieder property for the Dirac field on static spacetimes. Available at 〈lanl.arxiv.org/abs/math-phy/9911023 [25] Strohmaier, A., The Reeh-Schlieder property for quantum fields on stationary spacetimes, Communications in Mathematical Physics, 215, 105-118 (2000) · Zbl 0983.81038 [26] Verch, R., Antilocality and a Reeh-Schlieder theorem on manifolds, Letters in Mathematical Physics, 28, 143-154 (1993) · Zbl 0798.58065 [27] Wallace, D. (2001) The emergence of particles from bosonic quantum field theory. Available at 〈lanl.arxiv.org/abs/quant-ph/0112149; Wallace, D. (2001) The emergence of particles from bosonic quantum field theory. Available at 〈lanl.arxiv.org/abs/quant-ph/0112149 [28] Wald, R., Quantum Field Theory in Curved Spacetimes and Black Hole Thermodynamics (1994), Chicago University Press: Chicago University Press Chicago · Zbl 0842.53052 [29] Weinberg, S., The Quantum Theory of Fields, Vol. 1 (1995), Cambridge University Press: Cambridge University Press Cambridge This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.