International Journal of Theoretical Physics

, Volume 34, Issue 12, pp 2395–2407 | Cite as

Effect algebras and tensor products of S-sets

  • Stanley Gudder
Article

Abstract

An S-set is an algebraic structure that generalizes an effect algebra. Unlike effect algebras, the tensor product of two S-sets always exists and this tensor product can be concretely represented. Morphisms are used to study relationships between S-sets and effect algebras. The S-set tensor product is employed to obtain information about effect algebra tensor products.

Keywords

Field Theory Elementary Particle Quantum Field Theory Tensor Product Algebraic Structure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aerts, D., and Daubechies, I. (1975). Physical justification for using tensor products to describe quantum systems as one joint system,Helvetica Physica Acta,51, 661–675.Google Scholar
  2. Dvurečenskij, A. (1995). Tensor product of difference posets,Transactions of the American Mathematical Society,347, 1043–1057.Google Scholar
  3. Dvurečenskij, A., and Pulmannová, S. (1994). Difference posets, effects, and quantum measurements,International Journal of Theoretical Physics,33, 819–850.Google Scholar
  4. Dvurečenskij, A., and Riečan, B. (1994). Decompositions of measures on orthoalgebras and difference posets,International Journal of Theoretical Physics,33, 1387–1402.Google Scholar
  5. Foulis, D. (1989). Coupled physical systems,Foundations of Physics,19, 905–922.Google Scholar
  6. Foulis, D., and Bennett, M. K. (1993). Tensor products of orthoalgebras,Order,10, 271–282.Google Scholar
  7. Foulis, D., and Bennett, M. K. (1994). Effect algebras and unsharp quantum logics,Foundations of Physics,24, 1325–1346.Google Scholar
  8. Foulis, D., and Randall, C. (1980). Empirical logic and tensor products, inInterpretations and Foundations of Quantum Theories, A. Neumann, ed., Wissenschaftsverlag, Bibliographisches Institut, Mannheim.Google Scholar
  9. Gudder, S., and Greechie, R. (1996). Effect algebra counterexamples,Mathematica Slovaca (to appear).Google Scholar
  10. Kôpka, F. (1982). D-posets and fuzzy sets,Tatra Mountains Mathematical Publications,1, 83–87.Google Scholar
  11. Kôpka, F., and Chovanec, F. (1994). D-posets,Mathematica Slovaca,44, 21–34.Google Scholar
  12. Navara, M., and Pták, P. (n.d.). Difference posets and orthoalgebras, to appear.Google Scholar
  13. Pulmannová, S. (1985). Tensor product of quantum logics,Journal of Mathematical Physics,26, 1–5.Google Scholar
  14. Wilce, A. (n.d.). Perspectivity and congruence in partial abelian semigroups, to appear.Google Scholar
  15. Zecca, A. (1978). On the coupling of quantum logics,Journal of Mathematical Physics,19, 1482–1485.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Stanley Gudder
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of DenverDenver

Personalised recommendations