Doctoral Dissertations
Probabilistic foundations of general quantum theories and characterizations of representation space
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 -- Mathematics
Probabilities
Convexity spaces
Thesis Number
T 4255
Print OCLC #
5995623
Link to Catalog Record
Full-text not available: Request this publication directly from Missouri S&T Library or contact your local library.
http://merlin.lib.umsystem.edu/record=b1067695~S5Recommended 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
Share My Dissertation If you are the author of this work and would like to grant permission to make it openly accessible to all, please click the button above.
