On Sun, Dec 27, 2009 at 6:40 PM, <mcintosh@servidor.unam.mx> wrote:
Quoting Mike Stay <metaweta@gmail.com>:
Is there a general formula for "d/dz" in dimension D?
You are in good company with Paul Dirac and Oliver Heaviside. As long as D is finite, there is no problem, even with a multiply valued complex logarithm. It is the limit that hurts, and for which distribution theory was sort of invented. I recall that in the late forties, Aurel Wintner proved that there are no matrices A and B such that AB - BA = I, the unit matrix. Mark Kac must have read the paper, because he assigned it as a problem in the final examination for his Mathematical Methods course. However, the Physics Department did not disappear in a puff of smoke even if you called A and B p and q. But there *were* those who noticed that something was wrong.
That's good to know, thanks. I was trying to follow the sum-over-paths derivation of QM in the first chapter of Zee's "QFT in a nutshell" using spin states instead of position states and using the Hadamard transform to get a conjugate basis for the sum over paths. Has someone done quantum mechanics on discrete spacetime using the q-derivative? Sounds like something Louis Kaufmann would do. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com