Hi,(adsbygoogle = window.adsbygoogle || []).push({});

There is clearly an analogous relationship between Yang-Mills theories and LQG, for example the covariant derivative, the field strength tensor, the field and its conjugate momentum etc...

I am wondering how far this analogy extends. Specifically, is the Lagrangian for LQG the following?

[tex]

\mathcal{L}=-\frac{1}{4}F^{\,i}_{ab}F^{\,ab}_{i}

[/tex]

where

[tex]

F^{\,i}_{ab}=\partial_a A_{b}^{i}-\partial_b A_{a}^{i}+\epsilon^{i}{}_{jk}A_{a}^{j}A_{b}^{k}

[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Field Strength Tensor in LQG

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**