GR as Gauge Theory

[fresh_42]

TL;DR

I found a dissertation from 1990 that attempted to model the general relativity theory as an $SO(3)$ gauge theory. What has happened to that idea?

While searching the internet for milestones in physics, mainly for those that led to the standard model, I came to ask myself why general relativity cannot be modeled by a gauge theory. Searching for "Relativitätstheorie als Eichtheorie" brought up a dissertation from 1990 titled: "Die Allgemeine Relativitätstheorie als $SO(3)$-Eichtheorie", "The General Relativity Theory as $SO(3)$ Gauge Theory".
https://arxiv.org/pdf/gr-qc/0310111

The author wrote:

This work is intended to provide an answer to both the successes and the problems of the general theory of relativity. Since the successes mentioned are based entirely on the (at least approximate) validity of Einstein's equations, these equations of motion must also retain their validity in the modified theory. On the other hand, the weak points of Einstein's theory explained above must also be taken into account, which means that the Einstein equations must be given a new interpretation within the framework of the modified theory. The three basic pillars of the modified theory of gravitation are briefly presented:

1. General Structure of the Theory
2. Energie-Impuls der Gravitation
3. The Vacuum

The dissertation is in German so I don't expect you to read it. On the other hand, it is now 35 years old, so my question is simple: What has happened to that idea and have there been further approaches, eventually with other gauge groups?

 

[PeterDonis]

I came to ask myself why general relativity cannot be modeled by a gauge theory.

It can be, in a sense, but the "gauge group" is not any compact group. See this Insights article by haushofer, which I believe gives a good discussion of the "mainstream" view among relativity physicists on this topic:

https://www.physicsforums.com/insights/general-relativity-gauge-theory/

 

[haushofer]

TL;DR Summary: I found a dissertation from 1990 that attempted to model the general relativity theory as an $SO(3)$ gauge theory. What has happened to that idea?

While searching the internet for milestones in physics, mainly for those that led to the standard model, I came to ask myself why general relativity cannot be modeled by a gauge theory. Searching for "Relativitätstheorie als Eichtheorie" brought up a dissertation from 1990 titled: "Die Allgemeine Relativitätstheorie als $SO(3)$-Eichtheorie", "The General Relativity Theory as $SO(3)$ Gauge Theory".
https://arxiv.org/pdf/gr-qc/0310111

The author wrote:


The dissertation is in German so I don't expect you to read it. On the other hand, it is now 35 years old, so my question is simple: What has happened to that idea and have there been further approaches, eventually with other gauge groups?

As Peter points out, the "standard approach" (afaik) is to treat GR as the gauge theory of the Poincaré algebra (i.e. the algebra describing the full isometry group of the vacuum) and impose constraints. These constraints eliminate unwanting transformations (the local translations) directly, and indirectly by making certain gauge fields dependent on other gauge fields (the spin connection becomes a dependent field). This procedure can be extended to other algebras, like N = 1 super Poincaré, giving N = 1 supergravity, the Bargmann algebra, which gives you Newton-Cartan theory, and even a stringy version of this Bargmann algebra which leaves you with a Newton-Cartan theory for strings. Note that all these algebras have an SO(3) subalgebra. I don't know why one would only use SO(3) to obtain GR, but for that I have to read the thesis, I guess :P

If you want more details, maybe you can find them in my PhD-thesis:

https://research.rug.nl/en/publications/newton-cartan-gravity-revisited