All Questions
64
questions
-1
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0
answers
81
views
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.
...
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 ...
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 ...
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 ...
1
vote
0
answers
54
views
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 ...
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 ...
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+...
1
vote
0
answers
27
views
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 ...
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-...
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 ...
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:
$$\frac{dL}{dt} = \frac{\partial L}{\partial x}\dot{x} +
\frac{\partial L}{\partial \dot{x}}\ddot{x} +
\frac{\partial L}{\partial t}$...
-1
votes
2
answers
624
views
Conservation theorem for cyclic coordinates in the Lagrangian
Suppose $q_1,q_2,...,q_j,..,q_n$ are the generalized coordinates of a system.
$q_j$ is not there in the Lagrangian (it is cyclic).
Then $\frac{\partial L}{\partial\dot q_j}=constant$
In Goldstein, it ...
2
votes
3
answers
480
views
Lagrangian first integral
I want to extremize $$\int dt \frac{\sqrt{\dot x ^2 + \dot y ^2}}{y}.$$
I have thought that, since the Lagrangian $L(y, \dot y, \dot x)$ is $t$ dependent only implicitly, that i could use the fact ...
2
votes
3
answers
191
views
Noether‘s theorem: Why can function be dependent of $\dot{q}$?
We define a continuous symmetry in Lagrangian mechanics as follows:
$$\delta L\overset{!}{=}\epsilon\frac{\mathrm{d}}{\mathrm{d} t} f(q,\dot{q}, t)$$
Where $\epsilon\in\mathbb{R}$ is a parameter in ...