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The C* Axioms and the Phase Space Fomalism of Quantum Mechanics

Chapter

Abstract

In 1972, “Algebraic Methods in Statistical Mechanics and Quantum Field Theory” was published by Gerard Emch [8], giving the axioms for a physical system in an algebraic setting using the language of Irving Segal [19], and then continuing to obtain the C*-algebraic formalism for a physical system. Of these axioms, only the fifth contained an assumption that was questionable in its physical content. Bearing in mind that for each observable A and state φ, one obtains a distribution of values for the observed results of measurement, we have:

Axiom 5: For any element A in the set of observables \(\mathfrak{A}\) and any non-negative integer n, there is at least one element, denoted A n , in \(\mathfrak{A}\) such that (i) the set of dispersion-free states for A n is contained in the set of dispersion-free states for A, (ii) < φ; A n > = < φ; A > n for all φ in the set of dispersion-free states for A. (Here < φ; B > is the expectation of B in state φ.)

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© Hindustan Book Agency 2007

Authors and Affiliations

  1. 1.University of DenverDenverUSA

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