October 2011-December 2011: Non-Generated Diffeomorphisms (Part II)

Author Commentary Below: A few notations from this notebook, to indicate topics covered. Author’s page numbering is ignored, any page numbers referenced below are from the scanned PDF documents.

Notebook October 2011 – December 2011: https://gaugegravity.com/wp-content/uploads/2020/01/Notebook-10-12-2011.pdf

Non-Generated Diffeomorphisms (continued); Plus A Few Thoughts on Generalized Gauge Theory

(p. 15-16) So, since I’ve made the interpolating function, it would seem that a sufficient constraint on so that it lies on a 1-parameter group containing the identity is that . If this constraint is relaxed we must deal with a more complicated computation. Already at the level of m+n=3, there is an addition to the differential equation that determines . It does, however, seem that only the are non-zero. So, the solution is:

(p. 17) It seems that one must retain products of 𝒷’s. We can check whether the approximation was sensible by checking the group law for the final function. In addition it is not too hard to find the exact solution, all we have in the RHS of the differential equation is sums of exponentials..

(p. 19) Now we set to zero any quantity quadratic in the 𝒷’s . That means that 𝓹 must be equal to 1.

(p. 24) We have discovered an interpolating function in the case that we can ignore all quadratic terms in the perturbation. the question is: does this give us the right to ignore the perturbation for all 𝓽?

(p. 25) More on the Unitarity problem of non-commutative QFT and the finding of a good set of uncertainty relations.

(p. 28-30) Small perturbation of a small rotation on a 1-parameter subgroup.

A Few Thoughts on Generalized Gauge Theory, November-December 2011: https://gaugegravity.com/wp-content/uploads/2019/08/Notebook-11-2011-1-2012.pdf

(p. 6) The principle novelty of Hawking’s argument is that “the Black Hole” is firmly placed in the interaction region and is therefore not accessible to experiment. Hawking assumes that all that can be measured about the Black Hole is available on the boundary.Suppose we have a shell of matter in-falling to create a Black Hole

(p. 7) If Hawking is correct, the observers at infinity have no measurement paradox. What about the observer in the bulk that can experimentally determine whether or not a Black Hole has actually formed. Such an observer may then report to the boundary observers.