4
votes
1answer
115 views

On a trick to derive Noether current

Suppose, in whatever dimension and theory, the action $S$ is invariant for a global symmetry with a continuous parameter $\epsilon$. The trick to get the Noether current consists in making the ...
1
vote
1answer
80 views

What is meant by a local Lagrangian density?

What is meant by a local Lagrangian density? How will a non-local Lagrangian look like and what is the problem that we do not consider such Lagrangian densities?
1
vote
1answer
38 views

Integrating out fields from classical systems

Has anyone ever heard of integrating out fields from classical Lagrangians if they are quadratic?
2
votes
2answers
387 views

Symmetry of Euler-Lagrange equations and conservation laws

Continuous symmetry of the action implies a conservation law, but what if equations of motion have a continuous symmetry? Does it imply a conservation law? Also is symmetry of equations of motion ...
2
votes
1answer
123 views

Total energy is extremal for the static solutions of equation of motions

In physics total energy is extremal for the static solutions of equation of motions. Can anyone explain this sentence to me?