Constructing conformally invariant equations using Weyl geometry

Details Constructing conformally invariant equations using Weyl geometry Constructing conformally invariant equations using Weyl geometry

2011-09-12

arxiv.org/abs/1109.2579v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, no figures

Scientific paper

A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can build in the framework of this geometry. Indeed, working in a Weyl space, using the Weyl covariant derivative and the intrinsic Weylian geometrical tensors, all conformally homogeneous operators will be conformally invariant, as will the equations they determine. A Weyl space is defined by two independent objects: the metric tensor $g_{\mu\nu}$ and the Weyl vector $W_{\mu}$. A simple procedure allows us to go from a Weyl space into a Riemann space by imposing the Weyl vector to be a gradient. Under some conditions, the Weylian conformally invariant equations reduce to Riemannian conformally invariant equations. This method is applied to construct some conformally invariant scalar field equations, check the conformal invariance of Maxwell equations and recover the Eastwood-Singer conformal gauge fixing condition.

Affiliated with

Also associated with

No associations

Rating

Constructing conformally invariant equations using Weyl geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Constructing conformally invariant equations using Weyl geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constructing conformally invariant equations using Weyl geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-60816