How to derive Nielsen equation from Lagrange equation?

[AlephClo]

How to derive Nielsen equation from Lagrange equation

 

[BvU]

Isn't google your friend ? What did you find so far ?

 

[AlephClo]

I have done couple hours of research and tried to derive it myself. The best that I found is this, but I do not understand where the commutator come from. It does not seem to be the Poisson braket commutator applied to T either (A,B) = AB-BA . Nor that I understand where the (2) relationship comes from. Thank you

 

[BvU]

The best that I found is this

It was the first one I found too. But: Not good enough then, ... (*)
What about the second one in the list I got ?

Except where it says $=0$ one should read $= Q_j$

(*) And yes, the commutator [A,B] means: first B then A minus first A then B.

 

[AlephClo]

Thank you BvU.