# Is gravity a gauge theory?

## Main Question or Discussion Point

I have a project this year called "Is gravity a gauge theory?". From my understanding, it is. But I was wondering if someone could quickly explain to me the way/ways of showing this and perhaps some papers or books that would be particularly useful.

Thanks.

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tom.stoer
There are many attempts to formulate gravity as a gauge theory; the most famous one has been introduced by Ashtekar in the context of quantum gravity, but it makes sense to study this approach w/o any quantization.

The idea is usually to reformulate gravity such that one has a connection one-form that appears as the fundamental field. Then the connection can be treated similar to an el.-mag. 4-potential, whereas the canonical conjugate field is similar to an electric field.

To do this one factorizes the metric in a more fundamental object, the so-called tetrad field or vierbein which becomes the canonical conjugate field to the connection. Formally via this product ansatz the local Lorentz (or Poincare) symmetry is gauged; they act as a "generalized local rotations" of tangent space vectors; the effect of this transformation is absorbed by a gauge transformation of the connection itself.

In that sense gravity is a local gauge symmetry induced by the Lorentz or Poincare transformation.

But there are major differences as well, not related to the algebraic properties of the gauge symmetry, but especially to the dynamical structure of the theory. One observes immediately that gravity has a different Lagrangian which cannot be written in the usual form as "field-strength-tensor squared". And gravity has an additional symmetry, so-called 4-diffeomorphism invariance which results in additional structures not known from ordinary gauge theories.

George Jones
Staff Emeritus