Just a couple of comments on this thread: 1) Noether's Theorem is not a "rubric". It is an extremely powerful tool in mathematical physics. It explains where the laws of conservation of energy and momentum come from, amongst other things like lepton number and baryon number. It is actually quite beautiful and fascinating. 2) The Feynman Path Integral is usually written in terms of a continuity. In this case the classical path dominates the path integral since the non-classical paths are added to the path integral with a weight determined by a complex exponential that oscillates as it deviates from the classical path. Thus the classical path dominates the path integral in most cases. 3) On the other hand, I remember learning in graduate school (and this was a long time ago) that in fact if you dig deeper into the FPI you find that the paths that truly dominate are non-continuous (and maybe nowhere differentiable, I don't remember this part clearly) gaussian drunkard's walks around the classical path. I learned this from a guy named Jon Bagger who at the time was researching conformal field theory. Maybe my learning is now out of date. Rowan. On Fri, Jan 27, 2012 at 8:39 PM, Bill Gosper <billgosper@gmail.com> wrote:
I used to nonrigorously crank out conjectural identities (doubtless all now conquered by holonomics) by closing rectangular contours with non-integer sides, using the standard trick Prod(M,a,b) := Prod(M,a,oo).Prod(M,b+1,oo)^-1 . --rwg
DWilson>
I would wonder if a grid of matrices with path invariance could be generalized to a continuous surface of matrices with path invariance? This would require some notion of matrix product along a continuous path. If this were possible, perhaps we could formulate some smooth generalization for multinomial expressions and continued fractions. Better at imagining these things than doing them. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun