Abstract
A quantum logic structure for quantum mechanics which contains the concepts of a physical space, localizability, and symmetry groups is formulated. It is shown that there is an underlying Hilbert space which mirrors much of this axiomatic structure. Quantum fields are defined and shown to arise naturally from the quantum logic structure. The fields ofHaag andWightman are generalized to this theory and an attempt is made to find a local equivalence for these fields.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Bibliography
Haag, R., andB. Schroer: J. Math. Phys.3, 248 (1962).
Haag, R., andD. Kastler: J. Math. Phys.5, 848 (1964).
Segal, I.: Mathematical problems of relativistic physics. New York: American Math. Soc. 1963.
Piron, C.: Helv. Phys. Acta37, 439 (1964).
Jauch, J., andC. Piron: Helv. Phys. Acta36, 827 (1963).
Jauch, J.: Foundations of quantum mechanics. Reading, Mass.: Addison-Wesley 1968.
Mackey, G.: The mathematical foundations of quantum mechanics. New York: W. A. Benjamin 1963.
Zierler, N.: Pacific J. Math.12, 1151 (1961).
Bodiou, G.: Theory dialectique des probabilities. Paris: Gauthier-Villars 1964.
Gunson, J.: Commun. Math. Phys.6, 262 (1967); and the first reference in 2 of this bibliography.
MacLaren, M.: Argonne National Laboratory Report, ANL-7065 (1965).
Gudder, S.: Rev. Mod. Phys.40, 229 (1968).
Pool, J.: Baer *-semigroups and the logic of quantum mechanics (1968) (preprint).
Newton, T., andE. Wigner: Rev. Mod. Phys.21, 400 (1949).
Wightman, A.: Rev. Mod. Phys.34, 845 (1962).
Jauch, J., andC. Piron: Helv. Phys. Acta40, 559 (1967).
Mackey, G.: Amer. J. Math.73, 576 (1951);
Ann. Math.55, 101 (1952);58, 193 (1953).
Gudder, S.: J. Math. Phys.8, 1848 (1967).
Varadarajan, V.: Comm. Pure Appl. Math.15, 189 (1962).
Pool, J.: Report SUI-63-17 (1963), State Univ. of Iowa.
Ramsey, A.: J. Math. Mech.15, 227 (1966).
Gudder, S.: Trans. Am. Math. Soc.119, 428 (1965).
-- Can. Math. J. (to appear).
Wightman, A.: PCT spin and statistics, and all that. New York: W. A. Benjamin 1964.
Gudder, S.: Pacific J. Math.19, 81 (1966).
Misra, B.: Helv. Phys. Acta38, 189 (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gudder, S. On the quantum logic approach to quantum mechanics. Commun.Math. Phys. 12, 1–15 (1969). https://doi.org/10.1007/BF01646431
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01646431