We often say the Lagrangian is a function of some coordinates and only their first derivatives, $$ \mathcal{L}(q,\dot{q}). $$ Even in quantum field theory, the fields are only differentiated once, $$ \mathcal{L}(\phi,\partial_\mu\phi). $$ I heard Leonard Susskind mention in his lectures never to include second derivatives, and that it leads to trouble. I am just wondering why?
Asked
Active
Viewed 50 times
