February 2012-July 2012: An Algebraic Approach to Gauge Gravity (Part I)

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 February 2012 – July 2012: https://gaugegravity.com/wp-content/uploads/2020/01/1-Notebook-2-7-2012.pdf

An Algebraic Gauge Approach to Gravity (Part I): Work here is concurrent with Notebook: April 2012 – May 2012.

(p. 1) A consideration of Kleinert’s novel gauge theory.

(p. 11) So there is a fantastically interesting tension between the relativistic philosophy and the Hamiltonian one–If we want a uniform dynamics in which all observables are treated uniformly and evolve according to FODE.

(p. 15) The study I have initiated on the measurability of the electromagnetic field, with the goal of generalizing to the torsion field of teleparallel gravity is quite substantial.

(p. 15-16) Why has the Bohr-Rosenfeld analysis become forgotten? Bohr and Rosenfeld exhibit the basis for the physical interpretation of quantum electrodynamics … Today we start with renewed confidence in the importance of pursuing the Bohr-Rosenfeld analysis. Not only can this lead to insights in teleparallel gravity, but also to the foundations of quantum theory. Bohr reproduces his classic thoughts on non-relativistic quantum theory in the relativistic field theory framework: 1) Application to interpretation of (teleparallel) gauge gravity. 2) Application to formulation of quantum mechanics.

The relationship between the real and reciprocal spaces is absolutely beautiful. It is the physical basis for the tension between the unitarity and covariance requirement of QFT.

(p. 24-25) Relationship between non commutativity and gravity: Szabo et. al. have written a nice paper discussing the fact that Non commutative U(1) gauge theory contains teleparallel gravity. Ref: 01050492v2 25 May 2001. This is quite an old paper but it may be helpful for my concept of gauge gravity.

(p. 24-25) A novel conception of gauge gravity

(p. 26) As for a technical project to begin with now I’d like to extend the Bohr-Rosenfeld analysis to the gravitational field. This should be viable due to the rewriting of the field in its teleparallel form. We really only need the theory of a background field acting upon massive test bodies to replicate the Bohr-Rosenfeld field results. Ideally we should end up with uncertainty relations for the torsion field in exactly the same way that Bohr-Rosenfeld found results for the electrodynamic field strengths.

(p. 81-83) A Review and Summary