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 January 2011 – February 2011: https://gaugegravity.com/wp-content/uploads/2019/08/Notebook-1-2-2011.pdf
Gravitational Theory and Quantum Theory: Implications
(p. 01) 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.