Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-15T11:10:13.712Z Has data issue: false hasContentIssue false
  • English
  • Français

Interpreting Quantum Field Theory

Published online by Cambridge University Press:  01 January 2022

Laura Ruetsche
Laura Ruetsche*
Affiliation:
Department of Philosophy, University of Pittsburgh
*
Send requests for reprints to the author, Department of Philosophy, 1001 Cathedral of Learning, University of Pittsburgh, Pittsburgh, PA 15260; ruetsche@pitt.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

The availability of unitarily inequivalent representations of the canonical commutation relations constituting a quantization of a classical field theory raises questions about how to formulate and pursue quantum field theory. In a minimally technical way, I explain how these questions arise and how advocates of the Hilbert space and of the algebraic approaches to quantum theory might answer them. Where these answers differ, I sketch considerations for and against each approach, as well as considerations which might temper their apparent rivalry.

Type
Research Article
Information
Philosophy of Science , Volume 69 , Issue 2 , June 2002 , pp. 348 - 378
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Thanks to those who have commented on earlier versions of this essay, particularly Gordon Belot, Rob Clifton, and John Earman.

References

Arageorgis, Aristidis (1995), Fields, Particles, and Curvature: Foundations and Philosophical Aspects of Quantum Theory on Curved Spacetime. Ph.D. Dissertation. Pittsburgh, PA: University of Pittsburgh.Google Scholar
Arageorgis, Aristidis, Earman, John, and Ruetsche, Laura (2002), “Weyling the Time Away: The Non-Unitary Implementability of Quantum Field Dynamics on Curved Spacetime and the Algebraic Approach to Quantum Field Theory”, Studies in the History and Philosophy of Modern Physics, forthcoming.CrossRefGoogle Scholar
Baez, John, Segal, Irving, and Zhou, Zhengfang (1992), Introduction to Algebraic and Constructive Quantum Field Theory. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Belot, Gordon, Earman, John, and Ruetsche, Laura (1999), “The Hawking Information Loss Paradox: Anatomy of a Controversy”, The Hawking Information Loss Paradox: Anatomy of a Controversy 50:189–229.Google Scholar
Bratelli, Ola, and Robinson, Derek (1987), Operators, Algebras and Quantum Statistical Mechanics, Vol. 1, 2nd edition. New York, NY: Springer-Verlag.CrossRefGoogle Scholar
Clifton, Rob, and Halvorson, Hans (2001), “Are Rindler Quanta Real?”, Are Rindler Quanta Real? 52:417–470.Google Scholar
Cushing, James (1987), “Foundational Problems in and Methodological Lessons from Quantum Field Theory”, in Brown, H., and Harre, R., (eds.), Philosophical Foundations of Quantum Field Theory, Oxford, UK: Clarendon Press, 25–42.Google Scholar
Emch, C. G. (1972), Algebraic Methods in Statistical Mechanics and Quantum Field Theory. New York, NY: John Wiley.Google Scholar
Frisch, M. (2000), “(Dis-)Solving the Puzzle of the Arrow of Radiation”, (Dis-)Solving the Puzzle of the Arrow of Radiation 51:381–410.Google Scholar
Fulling, S. A., Sweeny, M., and Wald, R. M. (1978), “Singularity Structure of the Two-Point Function in Quantum Field Theory in Curved Spacetime”, Singularity Structure of the Two-Point Function in Quantum Field Theory in Curved Spacetime 63:257–264.Google Scholar
Gel'fand, I. M., and Vilenkin, N. (1964), Generalized Functions, vol. IV. New York, NY: Academic Press.Google Scholar
Haag, Rudolf (1992), Local Quantum Physics. New York, NY: Springer-Verlag.CrossRefGoogle Scholar
Hajicek, P. (1978), “Observables for Quantum Fields on Curved Spacetime”, in Blueler, K., Petry, H. R., and Reetz, A. (eds.), Differentials and Geometrical Methods in Mathematical Physics II. Lecture Notes in Mathematics 676. New York, NY: Springer-Verlag, 535–565.Google Scholar
Helfer, A. D. (1996), “The stress-energy tensor”, The stress-energy tensor 13:L129–L134.Google Scholar
Huggett, N. (2000), “Philosophical Foundations of Quantum Field Theory”, Philosophical Foundations of Quantum Field Theory 51:617–637.Google Scholar
Isham, C. J. (1984), “Topological and Global Aspects of Quantum Theory”, in DeWitt, B. and Stora, R. (eds.), Les Houches Session XL 1983: Relativity, Groups, and Topology, New York, NY: Elsevier, 1061–1290.Google Scholar
Kaku, M. (1993), Quantum Field Theory: A Modern Introduction. New York, NY: Oxford University Press.Google Scholar
Kay, B. (1978), “Linear Spin-Zero Quantum Fields in External Gravitational and Scalar Fields”, Linear Spin-Zero Quantum Fields in External Gravitational and Scalar Fields 62:55–70.Google Scholar
Kay, B., and Wald, R. M. (1991), “Theorems on the Uniqueness and Thermal Properties of Stationary, Nonsingular, Quasifree States on Spacetimes with a Bifurcate Killing Horizon,” Physics Reports 207:49–136.CrossRefGoogle Scholar
Morgan, M. S. and Morrison, M. (eds.) (1999), Models as Mediators. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Reichenbach, Hans (1938), Experience and Prediction. Chicago, IL: University of Chicago Press.Google Scholar
Robinson, D. W. (1966), “Algebraic Aspects of Relativistic Quantum Field Theory”, in Chretien, M. and Deser, S. (eds.), Axiomatic Field Theory. NY: Gordon and Breach, 391–516.Google Scholar
Segal, I. (1967), “Representation of Canonical Commutation Relations”, in Lurcat, F. (ed.), Cargese Lectures in Theoretical Physics. NY: Gordon and Breach, 107–170.Google Scholar
Summers, S. J. (2001), “On the Stone-von Neumann Uniqueness Theorem and its Ramifications”, in Redei, M. and Stölzner, M. (eds.), John von Neumann and the Foundations of Quantum Mechanics. Dordrecht: Kluwer.Google Scholar
Teller, P. (1995), An Interpretative Introduction to Quantum Field Theory. Princeton, NJ: Princeton University Press.Google Scholar
Torre, C. J., and Varadarajan, M. (1998), “Functional evolution of free quantum fields”, Functional evolution of free quantum fields 16:2651–2668.Google Scholar
Van Fraassen, B. C. (1989), Laws and Symmetry. Oxford: Oxford University Press.CrossRefGoogle Scholar
Van Fraassen, B. C. (1991), Quantum Mechanics: An Empiricist View. Oxford: Clarendon Press.CrossRefGoogle Scholar
Wald, R. M. (1984), General Relativity. Chicago, IL: University of Chicago Press.CrossRefGoogle Scholar
Wald, R. M. (1994), Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Chicago, IL: University of Chicago Press.Google Scholar