Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-07-01T08:52:29.186Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Choice of Algebra for Quantization

Published online by Cambridge University Press:  01 January 2022

Benjamin H. Feintzeig
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, I examine the relationship between physical quantities and physical states in quantum theories. I argue against the claim made by Arageorgis that the approach to interpreting quantum theories known as Algebraic Imperialism allows for “too many states.” I prove a result establishing that the Algebraic Imperialist has very general resources that she can employ to change her abstract algebra of quantities in order to rule out unphysical states.

Type
Research Article
Information
Philosophy of Science , Volume 85 , Issue 1 , January 2018 , pp. 102 - 125
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

†.

I would like to thank Hans Halvorson, Jim Weatherall, and two anonymous referees for helpful comments.

References

Alfsen, E., and Shultz, F.. 2001. State Spaces of Operator Algebras. Boston: Birkhauser.CrossRefGoogle Scholar
Arageorgis, A. 1995. “Fields, Particles, and Curvature: Foundations and Philosophical Aspects of Quantum Field Theory in Curved Spacetime.” PhD diss., University of Pittsburgh.Google Scholar
Beaume, R., Manuceau, J., Pellet, A., and Sirugue, M.. 1974. “Translation Invariant States in Quantum Mechanics.” Communications in Mathematical Physics 38:29–45.CrossRefGoogle Scholar
Bratteli, O., and Robinson, D.. 1996. Operator Algebras and Quantum Statistical Mechanics. Vol. 2. New York: Springer.Google Scholar
Clifton, R., and Halvorson, H.. 2001. “Are Rindler Quanta Real? Inequivalent Particle Concepts in Quantum Field Theory.” British Journal for the Philosophy of Science 52:417–70.CrossRefGoogle Scholar
Dixmier, J. 1977. C*-Algebras. New York: North-Holland.Google Scholar
Dubin, D., Hennings, M., and Smith, T.. 2000. Mathematical Aspects of Weyl Quantization and Phase. Singapore: World Scientific.CrossRefGoogle Scholar
Emch, G. 1972. Algebraic Methods in Statistical Mechanics and Quantum Field Theory. New York: Wiley.Google Scholar
Feintzeig, B. 2017a. “On Theory Construction in Physics: Continuity from Classical to Quantum.” Erkenntnis, forthcoming.CrossRefGoogle Scholar
Feintzeig, B. 2017b. “Toward an Understanding of Parochial Observables.” British Journal for the Philosophy of Science, forthcoming.Google Scholar
Haag, R. 1992. Local Quantum Physics. Berlin: Springer.CrossRefGoogle Scholar
Halvorson, H. 2001. “On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics.” Journal of Philosophical Logic 37:27–50.CrossRefGoogle Scholar
Halvorson, H. 2004. “Complementarity of Representations in Quantum Mechanics.” Studies in History and Philosophy of Modern Physics 35:45–56.CrossRefGoogle Scholar
Halvorson, H. 2006. “Algebraic Quantum Field Theory.” In Handbook of the Philosophy of Physics, ed. Butterfield, J. and Earman, J., 731–864. New York: North-Holland.Google Scholar
Kadison, R., and Ringrose, J.. 1997. Fundamentals of the Theory of Operator Algebras. Providence, RI: American Mathematical Society.Google Scholar
Kay, B., and Wald, R.. 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
Landsman, N. P. 1990. “C*-Algebraic Quantization and the Origin of Topological Quantum Effects.” Letters in Mathematical Physics 20:11–18.CrossRefGoogle Scholar
Landsman, N. P. 1998. Mathematical Topics between Classical and Quantum Mechanics. New York: Springer.CrossRefGoogle Scholar
Landsman, N. P. 2006. “Between Classical and Quantum.” In Handbook of the Philosophy of Physics, ed. Butterfield, J. and Earman, J., 417–553. New York: North-Holland.Google Scholar
Petz, D. 1990. An Invitation to the Algebra of Canonical Commutation Relations. Leuven: Leuven University Press.Google Scholar
Reed, M., and Simon, B.. 1980. Functional Analysis. New York: Academic Press.Google Scholar
Ruetsche, L. 2002. “Interpreting Quantum Field Theory.” Philosophy of Science 69 (2): 348–78..CrossRefGoogle Scholar
Ruetsche, L. 2003. “A Matter of Degree: Putting Unitary Inequivalence to Work.” Philosophy of Science 70 (5): 1329–42..CrossRefGoogle Scholar
Ruetsche, L. 2006. “Johnny’s So Long at the Ferromagnet.” Philosophy of Science 73 (5): 473–86..CrossRefGoogle Scholar
Ruetsche, L. 2011. Interpreting Quantum Theories. New York: Oxford University Press.CrossRefGoogle Scholar
Sakai, S. 1971. C*-Algebras and W*-Algebras. New York: Springer.Google Scholar
Summers, S. 1999. “On the Stone–von Neumann Uniqueness Theorem and Its Ramifications.” In John von Neumann and the Foundations of Quantum Physics, ed. Redei, M. and Stoeltzner, M., 135–52. Dordrecht: Kluwer.Google Scholar
Wald, R. 1994. Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Chicago: University of Chicago Press.Google Scholar