All Questions
Tagged with conservation-laws lagrangian-formalism
227
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Generalized momentum
I am studying Hamiltonian Mechanics and I was questioning about some laws of conservation:
in an isolate system, the Lagrangian $\mathcal{L}=\mathcal{L}(q,\dot q)$ is a function of the generalized ...
- 49
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1
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Does Noether's theorem apply to a strict on-shell symmetry of the action that holds on every integration region?
I've worked through different proofs of Noether's theorem and read various posts about it on this site. Some important takeaways, among others from this and this post by Qmechanic were
Every off-...
- 587
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62
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Symmetry transformation exact meaning
In whatever text/review I happen to come across (like for example From Noether’s Theorem to Bremsstrahlung: A pedagogical introduction to
Large gauge transformations and Classical soft theorems, ...
- 3,992
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Finding the Noether current
I'm currently reading "QFT for the gifted Amateur by Lancaster and Blundell, and in a lot of the problems I'm a bit unsure of how to do them, an example asked
"Consider a system ...
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1
answer
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How is Noether’s theorem actually applied?
Noether’s theorem roughly states that the existence of a symmetry group for a given system implies a conservation law for that system. All well and good, except that I’m shaky on exactly how you ...
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4
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Why exactly does time translation symmetry lead to conservation of energy? [duplicate]
As far as I know (and I don't know much), Noether's theorem claims that time translation invariance of the laws of physics leads to the conservation of energy. The way I understand it is that if we ...
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1
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Analogy of Euler-Lagrange-equation and Continuity equation
It seems to me that there is a link between the continuity equation
$$\nabla\rho u + \frac{\partial \rho}{\partial t} = 0$$
and the Euler-Lagrange equation for Lagrangian mechanics
$$\nabla_q L - \...
- 19
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What is the point of knowing symmetries, conservation quantities of a system?
I think this kind of question has been asked, but i couldn’t find it.
Well i have already know things like symmetries, conserved quantities and Noether’s theorem, as well as their role in particle ...
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Discrepance between gauge symmetry and Noether's first theorem
In QFT we're interested in the symmetries of our theory (encoded in the invariance of the Lagrangian under symmetries) because they let us study conserved currents of the theory by Noether's theorem.
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- 309
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95
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Conserved current transforming under adjoint
If we have a Lagrangian with a global internal symmetry $G$. Why do the conserved currents transform under the adjoint representation of $G$? Is it a general statement (if this is the case, how can we ...
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The meaning of stress tensor conservation in general relativity [duplicate]
In general relativity one has the Hilbert stress-energy tensor defined as
$$T^{\rm matter}_{ab} = -\frac{2}{\sqrt{-g}}\frac{\delta S_{\rm matter}}{\delta g^{ab}}~,$$
which is covariantly conserved i.e ...
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Deriving conserved currents from variation of action
I am reading An Modern Introduction to Quantum Field Theory by Maggiore. I have difficulty following the calculation of $\delta ( d^4 x)$ and $\delta (\partial_\mu \phi_i)$. Also, wonder whether the ...
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Q1.1(a) Sakurai Advanced Quantum Mechanics For energy-momentum tensor [closed]
I need to prove that the energy-momentum tensor density is defined as:
\begin{equation}
\mathcal{T}_{\mu\nu}=-\frac{\partial \phi}{\partial x_\nu}\frac{\partial\mathcal{L}}{\partial(\frac{\partial \...
- 111
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Sufficient condition for conservation of conjugate momentum
Is the following statement true?
If $\frac{\partial \dot{q}}{\partial q}=0$, then the conjugate momentum $p_q$ is conserved.
We know that conjugate momentum of $q$ is conserved if $\frac{\partial L}{\...
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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 ...
