7
votes
4answers
222 views

Does the action and Lagrangian have identical symmetries and conserved quantities?

From the book Introduction to Classical Mechanics With Problems and Solutions by David Morin, page 236 states: Noether's Theorem: For each symmetry of the Lagrangian, there is a conserved ...
4
votes
1answer
182 views

Derivation of Noether's theorem - A problem with physical significance

My question is about the field theoretic version of Noether's theorem. I am deeply troubled by one of the hypotheses of the theorem. As it is the standard textbook for Lagrange mechanics, I'll follow ...
2
votes
3answers
769 views

Noether's current expression in Peskin and Schroeder

In the second chapter of Peskin and Schroeder, An Introduction to Quantum Field Theory, it is said that the action is invariant if the Lagrangian density changes by a four-divergence. But if we ...
4
votes
2answers
497 views

How to apply Noether's theorem

Say I have a point transformation: $$x' ~=~ (1 +\epsilon)x,$$ $$t' ~=~ (1 +\epsilon)^2t,$$ and Lagrangian $$ L ~=~ \frac{1}{2}m\dot{x}^2 - \frac{\alpha}{x^2}.$$ How do I go out about showing ...
8
votes
2answers
146 views

More general invariance of the action functional

I will formulate my question in the classical case, where things are simplest. Usually when one discusses a continuous symmetry of a theory, one means a one-parameter group of diffeomorphisms of the ...