Alright, I understand that there are redundant degrees of freedom in the Lagrangian, and because transformations between these possible "gauges" can be parametrized by a continuous variable, we can form a Lie Group.(adsbygoogle = window.adsbygoogle || []).push({});

What I am not so firm upon is how Lie Algebras, specifically, the Lie Algebra of the group generators, relates to this. I understand that a Lie Algebra is basically a vector space over a field with a binary operation, but I don't see how this can be used to analyze the corresponding Lie group.

Essentially, how do we go from gauge group to gauge field?

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

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!

# Relation between Lie Algebras and Gauge Groups

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