All Questions
Tagged with equations-of-motion symmetry
10 questions
5
votes
2
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628
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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 ...
2
votes
0
answers
15
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Gauge invariance using equations of motion [duplicate]
I am working with a lagrangian on a homework problem. I expect it to have some gauge invariance. I can show that the Lagranian is invariant under those (gauge) tansformations but I have to use ...
- 542
3
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0
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69
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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
3
votes
2
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598
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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
1
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1
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Equations of motion describing a great circle
I'd like to argue that equations of motions of the form
$$\ddot \varphi = 0 \quad \text{and} \quad \ddot\theta = \sin\theta\cos\theta\dot\varphi^2$$
describe a great circle.
I think the standard ...
- 1,235
5
votes
3
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425
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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
2
votes
2
answers
444
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Rotation as an example of symmetry in classical mechanics
I modified the question because it was confused.
On my book there is this mathematical definition of symmetry transformation:
"The equations of motion have a symmetry, if the solutions of the ...
- 1,978
13
votes
3
answers
655
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Why intuitively, do we define symmetries as transformations that map solutions of the equations of motion into other solutions?
Of course, strictly speaking, a symmetry is always a transformation that leaves a given object unchanged. But I'm curious why observable symmetries of physical systems are exactly those ...
- 10.3k
2
votes
3
answers
299
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Are symmetries in the equation necessarily symmetries in the corresponding solution(s)?
I wonder whether the symmetries in the equations (such as the heat equation, the wave equation, the Schrödinger equation, Maxwell equations) are reflected into their solution(s). I.e., assuming that ...
3
votes
3
answers
677
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Is it valid to replace the equations of motion inside a symmetry?
For example, this symmetry:
$$\delta q^{i}=\epsilon(q^{i}-2\dot{q}^{i}t)$$
it's derivative is:
$$\delta\dot{q}^{i}=-\epsilon(\dot{q}^i +2\ddot{q}^i t)$$
There appears $\ddot{q}^{i}$ in this ...
- 862