A General Approach to Gravity and Its Quantization

Quantum Theory, Birkhoffian Generalization of QT, Generalized Gauge Theory (3-4 2012)

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.

(p. 13) Coleman-Mandula may be evaded due to the Groupoid (vs.group) structures. I have a strong feeling that this is correct. What is the irreducibility concept for groupoids/algebroids?

(p. 27) On the deepest level the gauge potential is the function that determines the parallel transport of vectors in the Lie Algebra.

(p. 29) So it appears that in the case of gravity, the field strength plays also the role of connection. This in fact is the reason that the theory looks a bit Abelian: the connection (torsion) is invariant.

(p. 33) In our case, we have a Lie Algebroid symmetry. We follow the discussion on p. 119 of Weinstein’s Geometric Models paper, and extend the discussion of the Chinese Authors.

(p. 66) The reason for the brief excursion through the bremsstrahlung is to understand the requirement of quantum theory. The universe is not scale invariant, so an ‘Atom’ the size of the solar system is quasi-stable due to the suppression of large accelerations in that system that suppress the bremsstrahlung . As the system shrinks, one requires quantum corrections to stabilize the system. What is totally amazing is that the system loses its time dependence. Something happens to the meaning of “t” in the shrinking of the system.

(p. 82) Let’s…consider an expansion of quantum theory in light of Algebroid symmetry.

(p. 86-87) So there has been a substantial shift… We previously thought of … a conception that is close to Newton’s conception of absolute space… The new view is much closer to a relational understanding. In this picture spacetime is the web of relationships…between all objects …. This is quite a satisfactory improvement from the philosophical side.

(p. 91) New meaning of local gauge invariance.

(p. 92) The notion of parallelism is a physical concept, meaning it must be gauge invariant. I think the commutative diagram picture is quite appropriate for the general case in which there may ultimately be no underlying spacetime…