*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: ** **https://gaugegravity.com/wp-content/uploads/2019/08/Notebook-1-2-2011.pdf**

**Gravitational Theory and Quantum Theory: Implications**

**(p. 01)** Implications of Gravitational Theory for Quantum Theory. Here we *assume* that gravity is a generalized gauge theory of the type I have partially developed.

**(p. 03)** So, is the momentum algebroid any of the famous algeboids?** … **Let’s guess that we are dealing with the structure detailed in Ch. 6 of deSilva’s notes, *Geometric Models of Non-Commutative Algebras*.** **

**(p. 07)** The question is: Should electrodynamics be associated with the classical field, or should it be considered a quantum effect associated with the wave function?

**(p. 08)** We wish to think of dynamics as being based on Lie Algebra considerations, and we first review mechanics on this basis, using Santilli as a fundamental reference. ** **

**(p. 12)** The Hamiltonian ** **

**(p. 14)** I cannot accept the modern direction. One must construct a Generalized Gauge Theory and a *corresponding generalization of Quantum Theory* to be consistent with *groupoids*. How can we we generalize Quantum Theory to be completely groupoid consistent?

**(p. 16)** It looks like the Birkhoffian generalization of Mechanics **is** related to Algebroid symmetry.

**(p. 17)** Santilli’s Birkhoffian generalization of quantum and classical mechanics seems to have striking similarities to my generalized gauge theory based on Algebroid/Groupoid symmetries as opposed to the more restrictive group symmetry.

**(p. 23)** Displacement Algebra: when the C’s are structure functions; Gauge Algebra: where the D’s are structure constants.

**(p. 24)** In an effort to make a theory that is more local than S-matrix theory, we must introduce something like a “local” operator for place. In the scheme of QFT one has no such operator Physically.