Joseph F.
Johnson
Assistant
Professor
B.S., Haverford College, 1977.
Ph.D., M.I.T., 1983


Research
Interests
My research interests are in the foundations of physical probability.
I use statistical concepts such as the autocorrelation of a time series
to define probability in terms of physically more basic concepts.
This has applications to turbulence and emergent order.
This led to a publication on the problem in the axiomatics of Quantum Mechanics
which Wigner called Quantum Duality, although it is now more usually
called Quantum Measurement.
The simplest rigorous, noncircular proof that d(cos x) =  sin x at the Math Department .
The influential paper by H. S. Green in 1958 on quantum measurement, zipped postscript. "Observation in Quantum Mechanics,"
Nuovo Cimento vol. 9 (1958) no. 5, pp. 880889.
Pages 12 pages 34 pages 56 pages 78 pages 910
An interesting list of papers on this hot topic of Quantum Information, maintained by the Italian national research centre on Quantum Computers.
A notebook of todo articles and topics of a Quantum Statistician at Michigan.
J. S. Bell's trenchant critique of the notion of Quantum Measurement, which, specifically, is what I have addressed and tried to answer. .
Selected
Publications
 Lie Algebra Cohomology and the Resolution of Certain HarishChandra
Modules, Mathematische Annalen, vol. 267 (1984), pp. 377393
 Endoscopic groups and stable packets of certain derived Functor
Modules, with Jeffrey Adams in: The Selberg Trace Formula and
Related Topics, Hejhal, Sarnak, and Terras, eds., Contemporary
Mathematics vol. 53 (1986), pp. 110
 Endoscopic Groups and Packets of nonTempered Representations,
with Jeffrey Adams, Compositio Mathematica, vol. 64 (1987), pp.
271309
 Stable Base Change C/R of Certain Derived Functor Modules, Mathematische
Annalen, vol. 287 (1990), pp. 467493
 Character Identities between Different Real Reductive Lie Groups,
Accepted, Advances in Mathematics
 Galoistwisted EulerPoincare Characteristics of Complex Algebraic
Groups, Crelle's Journal, vol. 568 (2004), pp. 122.
 Thermodynamic Limits, Quantum Entanglement, and NonCommutative Probability, in, Quantum Theory and Symmetries III, edited by Argyres et al., Singapore, 2004, pp. 133143.
 Statistical Mechanics of Amplifying Apparatus , in, Proc. VIII Internat. Wigner Symposium, NYC 2003, edited by Catto and Nicolescu, to appear.
 Some New Cases of Khintchine's Conjectures in Statistical Mechanics, Revista Investigación Operacional, vol. 33, no. 3 (2012), pp. 99113.
Outline of undergraduate Ordinary Differential Equations.
Not completely unconnected is my research on the relations between Social Justice and Economic Theory. This is a resumé of the book, as yet unpublished .
