Given the functional:
a. find the canonical mementa and construct the Hamiltonian tensor components, and
b. write the Euler-Lagrange equations
Notation:
Now I think can do part a (soln below) but I am strugling with part b. Obviously if I have part a wrong then that would make part b "difficult"
Part a.
The canonical momentum is
The Hamiltonian tensor is
Part b.
The functional does not depend explicitly on the coordinates or on phi. So the Euler-Lagrange equations are:
and
I have tried all kinds of things but they always become computationally complex and that seems unlikely.