Probabilistic foundations of general quantum theories and characterizations of representation space

Author

Salvadore J. Guccione Jr.

Abstract

"A program for re-structuring the mathematical foundations of general quantum theories along probabilistic lines suggested by Mielnik as opposed to the lattice theoretical approach due to Birkhoff and von Neumann is undertaken. In pursuing this program, some interesting characterizations of inner product spaces, generalized inner product spaces and uniformly convex spaces are given in terms of two-dimensional probability space structures imposed on the unit sphere. Next, an analysis of the variety of two-dimensional probability structures admissible on the unit sphere of a real Hilbert space is given and the difficulties in obtaining probability space structures of dimension greater than two in the normed linear space setting are discussed. Finally, it is shown, by imposing two-dimensional probability structures on abelian groups, that our probabilistic postulates imply a high degree of algebraic and geometrical structure on a given set of quantum states"--Abstract, page iii.

Advisor(s)

Stanojević, Časlav V., 1928-2008

Committee Member(s)

[illegible signature]
Penico, Anthony J., 1923-2011
Peacher, Jerry
Haddock, Glen

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1977

Pagination

v, 31 pages

Note about bibliography

Includes bibliographical references (pages 29-30).

Rights

© 1977 Salvadore J. Guccione , Jr., All rights reserved.

Document Type

Dissertation - Citation

File Type

text

Language

English

Subject Headings

Quantum theory -- MathematicsProbabilitiesConvexity spaces

Thesis Number

T 4255

Print OCLC #

5995623

Recommended Citation

Guccione, Salvadore J. Jr., "Probabilistic foundations of general quantum theories and characterizations of representation space" (1977). Doctoral Dissertations. 366.
https://scholarsmine.mst.edu/doctoral_dissertations/366