January 2011 – February 2011

For clarity, the author’s page numbering is ignored; any page numbers referenced below are those from the scanned PDF documents.

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