Speaker
Description
First, I describe the motivation of this work and then introduce a simple toy model which is useful to understand the essential point of our theorem.
Next, I show that the following two sets of equations are equivalent if the gauge fixing is complete:
One is the Euler-Lagrange equations derived from the original action supplemented with the gauge-fixing conditions, and the other is the Euler-Lagrange equations derived from the gauge-fixed action with Lagrange multipliers.
Finally, I provide an application of the theorem to the case of homogeneous isotropic universe in scalar-tensor theories.
Summary
Regardless of the long history of gauge theories, it is not well-recognized under which condition gauge fixing at the action level is legitimate.
We address this issue from the Lagrangian point of view, and prove the following theorem on the relation between gauge fixing and Euler-Lagrange equations:
In any gauge theory, if a gauge fixing is complete, i.e., the gauge functions are determined uniquely by the gauge conditions, the Euler-Lagrange equations derived from the gauge-fixed action are equivalent to those derived from the original action supplemented with the gauge conditions.
