It's interesting maliaidas, when you compare mathematical structures/conceptions that contain infinity and how their use has evolved in the modern scientific MDR.

In standard calculus If you have an integral that does not converge at its limits you have an indefinite integral and regard the result as undefined while if it does converge you can call it an improper integral and can use the result.

Nina Byers wrote a very informative paper in 1998 titled "E. Noether’s Discovery of the Deep Connection Between Symmetries and Conservation Laws:". Unfortunately

the normal arXiv link in the PDF of the paper links to a different paper called "Dimensional Reduction" for some reason so try

http://xxx.lanl.gov/abs/physics/9807044.

On the other hand, in standard calculus, you can also have a sub function of a higher level function that cycles between + infinity and - infinity

(symmetric) over one cycle, you can then regard this as an improper integral and use the result even if the sub function does not converge (and may be indefinite in isolation).

If there's a failure of a principle local energy conservation which is different at higher scales then the default energy conservation symmetry comes from a controlling

function that is universal in scope from the bb to the end of the universe? Can you break your symmetries if your highest level controlling function only ever has one

cycle, nearly one cycle or nearly half a cycle?

Charles Dodgson had a slightly different take on that one with Alice in Wonderland and Through the Looking Glass. The thing I always liked was that his tales took the

reader from 'reality' into either wonderland or the looking glass world, examined and took part in the strange goings on, and always returned them back to 'reality' at the end of the story. That's why I wonder if the Dirac equation etc from 10 years later in 1928, where m is rest mass and h_bar is the reduced Planck constant, requires another step, i.e. to transform from an infinite wonderland coordinant system back to a finite 'reality' coordinant system where h = h_bar * 2 * Pi. To me the 2 * Pi represents the minimum one full cycle required to qualify what would be an infinite indefinite integral as an improper integral (regardless of what its polar coordinants were) and retain the integrity of the functional symmetry's underpinning the model.