Report for the Academic Year 1992-1993 - The Institute Libraries ...

THE SCHOOL OF NATURAL SCIENCES
ACADEMIC ACTIVITIES
Faculty
STEPHEN L. ADLER [New Jersey Albert Einstein Professor]
JOHN N. BAHCALL
FREEMAN J. DYSON
PIET HUT
FRANK WILCZEK
EDWARD WITTEN
STEPHEN ADLER's main activity this year has been work on the final stages
of his book on Quaternionic Quantum Mechanics, to be published by Oxford
University Press. During the summer of 1992 he began work on a chapter on
field theory, leading to some ideas for putting a Hamiltonian dynamics on a
manifold with non-commuting (i.e., operator valued) coordinates. This work
was put aside during August-October to permit further work on revisions.
Larry Horwitz, during his visit to the Institute during September and October
of 1992, reread the entire manuscript in its revised form and made a whole
series of useful suggestions for changes, which were incorporated. Starting in
November, Professor Adler resumed work on the field theory issue, and now a
chapter on this is virtually complete. It gives an extension of standard quantum
mechanics to systems with an invariance under general operator-valued gauge
transformations, using a a new type of Lagrangian and Hamiltonian based on a
total trace as the primary tool. A condensed account of these results has been
put out as a paper, since it will be a year and a half at least until the book is in
print. Work in progress includes a short final chapter on outlook and open issues,
and a review of the final three chapters with Larry Horwitz, who will again visit
the Institute during the fall of 1993. Professor Adler now expects the manuscript
to go to the publisher by November 1993.
As an outgrowth of his discussions with Professor Adler on quaternionic quantum
mechanics, Horwitz wrote a paper showing that a time operator, which
does not exist in complex quantum mechanics, exists in the quaternionic case
under rather general conditions. Horwitz is exploring further implications of
this, and has other investigations in progress on problems related to Professor
Adler's program.
Professor Adler has also been discussing aspects of computational physics with
Cyan Bhanot and with a Princeton graduate student, John Weckel, for whom he
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