Foundations of Physics

, Volume 21, Issue 10, pp 1183–1236 | Cite as

The foundation of quantum theory and noncommutative spectral theory: Part II

  • Hans Kummer
Article
  • 56 Downloads

Abstract

The present paper comprises Sects. 5–8 of a work which proposes an axiomatic approach to quantum mechanics in which the concept of a filter is the central primitive concept. Having layed down the foundations in the first part of this work (which appeared in the last issue of this journal and comprises Sects. 0–4), we arrived at a dual pair 〈Y, M〉 consisting of abase norm space Y and anorder unit space M, being in order and norm duality with respect to each other. This is precisely the setting of noncommutative spectral theory, a theory which has been developed during the late nineteen seventies by Alfsen and Shultz. (2,3) In this part we add to the four axioms (Axioms S, DP, R, SP) of Sect. 3 three further axioms (Axioms E, O, L). These axioms are suggested by the work of Alfsen and Shultz and enable us to derive the JB-algebra structure of quantum mechanics (cf. Theorem 8.9).

Keywords

Quantum Mechanic Quantum Theory Norm Space Spectral Theory Dual Pair 

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References

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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Hans Kummer
    • 1
  1. 1.Department of Mathematics and StatisticsQueen's UniversityKingstonCanada

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