All Questions
64
questions
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answers
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Is there a straightforward simplified proof of energy conservation from time translation symmetry?
Electric charge conservation is easily proven from electric potential gauge symmetry, as follows:
The potential energy of an electric charge is proportional to the electric potential at its location.
...
- 12.1k
30
votes
6
answers
8k
views
Noether Theorem and Energy conservation in classical mechanics
I have a problem deriving the conservation of energy from time translation invariance. The invariance of the Lagrangian under infinitesimal time displacements $t \rightarrow t' = t + \epsilon$ can be ...
- 21.9k
3
votes
1
answer
82
views
Does quasi-symmetry preserve the solution of the equation of motion?
In some field theory textbooks, such as the CFT Yellow Book (P40), the authors claim that a theory has a certain symmetry, which means that the action of the theory does not change under the symmetry ...
- 91
3
votes
5
answers
939
views
What is the point of knowing symmetries, conservation quantities of a system?
I think this kind of question has been asked, but i couldn’t find it.
Well i have already know things like symmetries, conserved quantities and Noether’s theorem, as well as their role in particle ...
- 1,312
5
votes
1
answer
593
views
Does the Hamiltonian formalism yield more Noether charges than the Lagrangian formalism?
In Lagrangian formalism, we consider point transformations $Q_i=Q_i(q,t)$ because the Euler-Lagrange equation is covariant only under these transformations. Point transformations do not explicitly ...
- 145
1
vote
0
answers
54
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Doubt Regarding Noether's theorem for time-dependent systems
I'm having problems showing Noether's theorem when the lagrangian is time dependent. I'm trying to do it not using infinitesimal transformations from the beginning, but continuous transformations of a ...
- 207k
2
votes
1
answer
72
views
Some doubts about action symmetry
We know that Symmetry of the Lagrangian ($\delta L = 0$) always yields some conservation law.
Now, if $\delta L \neq 0$, that doesn't mean we won't have conservation law, because if we can show action ...
- 207k
28
votes
2
answers
9k
views
Invariance of Lagrangian in Noether's theorem
Often in textbooks Noether's theorem is stated with the assumption that the Lagrangian needs to be invariant $\delta L=0$.
However, given a lagrangian $L$, we know that the Lagrangians $\alpha L$ (...
- 82
1
vote
1
answer
137
views
In a simple case of a particle in a uniform gravitational field, do we have translation invariance or not?
Consider a system where a particle is placed in a uniform gravitational field $\vec{F} = -mg\,\vec{e}_{z}$. The dynamics of this are clearly invariant under translations. When we take $z\rightarrow z+...
- 207k
1
vote
0
answers
27
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Analytical mechanics: Noether charge as a generator with variating fields to time direction [duplicate]
Summary
I want to clarify how can I prove the fact that "the Noether charge generates the corresponding transformation" when the infinitesimal transformation of the fields contain the ...
- 207k
2
votes
1
answer
293
views
Geometrical intuition for Noether's Theorem
I have been reading some questions about the relation between Noether's Theorem and Lie Algebras and I wanted to get some intuition on it, but I didn't find what I really wanted. Also, the majority of ...
4
votes
0
answers
170
views
Noether's Theorem in non-conservative systems
In most books on classical mechanics, Noether's Theorem is only formulated in conservative systems with an action principle. Therefore I was wondering if it is possible to also do that in non-...
- 207k
5
votes
2
answers
775
views
Intuition behind the definition of Continuous Symmetry of a Lagrangian (Proof of Noether's Theorem)
Suppose there is a one-parameter family of continuous transformations that maps co-ordinates $q(t)\rightarrow Q(s,t)$ where the $s$ is the continuous parameter. Also, for when $s=0$ the transformation ...
- 1,989
0
votes
2
answers
85
views
How did Noether use the total time derivation to get her conservation of energy? [duplicate]
I was informed by @hft that by combining the total time derivation:
$$\frac{dL}{dt} = \frac{\partial L}{\partial x}\dot{x} +
\frac{\partial L}{\partial \dot{x}}\ddot{x} +
\frac{\partial L}{\partial t}$...
- 207k
-1
votes
2
answers
624
views
Conservation theorem for cyclic coordinates in the Lagrangian
Suppose $q_1,q_2,...,q_j,..,q_n$ are the generalized coordinates of a system.
$q_j$ is not there in the Lagrangian (it is cyclic).
Then $\frac{\partial L}{\partial\dot q_j}=constant$
In Goldstein, it ...
- 21.9k