Canonical Transformations in Quantum Mechanics

Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in principle, be realized quantum mechanically as a product of these transformations. It is found that the intertwining of two super-Hamiltonians is equivalent to there being a canonical transformation between them. A consequence is that the procedure for solving a differential equation can be viewed as a sequence of elementary canonical transformations trivializing the super-Hamiltonian associated to the equation. It is proposed that the quantum integrability of a system is equivalent to the existence of such a sequence.Comment: 27 pages, McGill 92-29 (revised version--several typos fixed in examples

An elegant solution of the n-body Toda problem

The solution of the classical open-chain n-body Toda problem is derived from an ansatz and is found to have a highly symmetric form. The proof requires an unusual identity involving Vandermonde determinants. The explicit transformation to action-angle variables is exhibited.Comment: LaTeX, 13 p

Clocks and Time

A general definition of a clock is proposed, and the role of clocks in establishing temporal pre-conditions in quantum mechanical questions is critically discussed. The different status of clocks as used by theorists external to a system and as used by participant-observers within a system is emphasized. It is shown that the foliation of spacetime into instants of time is necessary to correctly interpret the readings of clocks and that clocks are thus insufficient to reconstruct time in the absence of such a foliation.Comment: LaTeX, 19 p

“I Have a [Fair Use] Dream”: Historic Copyrighted Works and the Recognition of Meaningful Rights for the Public

Dr. Martin Luther King wrote and delivered his famous “I Have a Dream” speech more than fifty years ago. When he obtained copyright protection on the speech in 1963, Dr. King (and later his estate) would have expected the copyright to last a maximum of fifty-six years. That fifty-six-year copyright has become a ninety-five-year copyright, thanks to lengthy duration extensions enacted by Congress in the mid-1970s and late 1990s. As a result, the copyright on the “I Have a Dream” speech will not expire until the end of 2058. Because the Estate of Martin Luther King, Jr., Inc. and its affili- ates have closely guarded the speech in a copyright enforcement and li- censing sense, the public seldom sees more than snippets of one of the most highly regarded speeches in history. Greater public exposure to the full speech would serve important purposes of the sort recognized by Congress in the fair use section of the Copyright Act. However, those interested in borrowing from or otherwise using the speech have tended to drop their plans or have obtained a costly license from the King Estate or one of the affiliated entities—even when the users may had have a plausible right under the fair use doctrine to borrow from or use the speech without ob- taining a license. With the copyright on the speech not expiring until the end of 2058, there is a danger that the snippets-only nature of the pub- lic’s exposure to the speech will remain the status quo for more than another four decades. Infringement cases that have not been settled by the parties have yielded judicial rulings on whether the “I Have a Dream” speech was properly copyrighted, but no case has been litigated extensively enough to permit a court to address the defendant’s fair use defense. This Article proposes a fair use analysis appropriate for use by courts in the event that a user of the “I Have a Dream” speech departs from the usual tendency to obtain a license in order to avoid litigation and, instead, rests its fate on the fair use doctrine. The proposed analysis gives a suitably expansive scope to the fair use doctrine for cases dealing with uses of the speech or similarly historic works, given the important public purposes that could be served by many such uses. The Article also develops a test for use in determining whether a work is sufficiently historic, for purposes of the fair use analysis proposed here