All Questions
Tagged with equations-of-motion noethers-theorem
8 questions
5
votes
2
answers
630
views
Confusion about Noether's Theorem
In classical mechanics, a transformation $q \rightarrow q + \delta q$ is a symmetry if the resultant change in the Lagrangian is a total derivative,
$$ \delta L = \frac{dF}{dt}.$$
If we derive the ...
5
votes
3
answers
425
views
In what sense are the equations of motion conserved by symmetries?
I am studying variational principles and I have been reading this set of notes by Townsend. In the first paragraph of Section 9, Townsend defines what it means for a transformation to be a symmetry of ...
- 51
3
votes
2
answers
118
views
Can the $\eta_{\mu\nu}\mathcal{L}$ term in canonical energy–momentum tensor be omitted?
From Noether theory we can define the canonical energy–momentum tensor as
\begin{equation}
T_{\mu\nu}\equiv\frac{\partial\mathcal{L}}{\partial(\partial^\mu\phi)}\partial_\nu\phi-\eta_{\mu\nu}\mathcal{...
- 41
3
votes
2
answers
599
views
Deriving conserved charges from the equations of motion
It is very well established how to derive conserved charges associated to the symmetries of Lagrangian using the Noether's theorem. Also in the Hamiltonian formulation, we know how to derive the ...
- 1,140
3
votes
0
answers
69
views
Consequences for symmetries of the equations of motion in QFT
In general, if a Quantum Field Theory is described by a Lagrangian $\mathcal{L}$, the symmetries of $\mathcal{L}$ lead to classically conserved currents along the equations of motion and Ward ...
- 382
2
votes
1
answer
221
views
Noether’s second theorem: about the action principle
Noether's second theorem is supposed to show that the invariance of the Lagrangian by the Lie group (infinite in dimension) of certain theories necessarily implies that the field equations proper to ...
- 121
1
vote
2
answers
670
views
Showing the invariance of the equations of motion
It is strange to me that for a symmetry which involves $\dot{x}$, there seems to always appear a term with $\dddot{x}$ in the variation of the equations of motion, which doesn't makes much sense. I ...
- 862
1
vote
1
answer
101
views
Why the classical Euler-Lagrange equation is assumed when deriving the Noether's conserved current?
As known, in QFT, the conserved currents, such as the energy-momentum tensor, can be derived from the Noether's theorem and expressed as the product of the field operators. These conserved currents ...
- 163