The diffeomorphism field

Abstract

We revisit the dynamical action, developed in earlier studies [1][2][3], of the gravitational analog of Yang-Mills field, called the diffeomorphism field. We show an inconsistency in the construction of this action and solve it by a modification.The modified action becomes structurally similar to the Yang-Mills action. Then we explain the problems that arise from interpreting the diffemorphism field as a tensor. We leave out this interpretation, thereby also covariantization as a method to reach diffeomorphism invariance. By introducing corrections that involve affine connection coefficients we recover full diffeomorphism invariance in interactions of the diffeomorphism field with other fields. We also show that this approach maintains the spatial diffeomorphism invariance of the theory itself.

Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) polynomial affine gravity

“…Interesting proposals-in models other than the Polynomial Affine model of Gravity-could be found in Ref. [70,[74][75][76][77][78][79][80].…”

Dynamical projective curvature in gravitation

“…(2.49) is set to zero and the coordinate transformations are ignored, one sees that this parallels a Gauss Law constraint from a Yang-Mills theory where the onedimensional electric field E θ takes the place of Λ. In [16,[18][19][20][21][22][23] the authors argued that there was an analogous field theory related to the dual of the Virasoro algebra that, like Yang-Mills, could be written in any dimension. Then one could lift the onedimensional identity of D to a field theory in two-dimensions and higher.…”