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### Is the converse of Noether's first theorem true: Every conservation law has a symmetry?

Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is the converse true: Any conservation law of a physical ...
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### Equivalence between Hamiltonian and Lagrangian Mechanics

I'm reading a proof about Lagrangian => Hamiltonian and one part of it just doesn't make sense to me. The Lagrangian is written $L(q, \dot q, t)$, and is convex in $\dot q$, and then the Hamiltonian ...
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### Is there a kind of Noether's theorem for the Hamiltonian formalism?

The original Noether's theorem assumes a Lagrangian formulation. Is there a kind of Noether's theorem for the Hamiltonian formalism?
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### 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 $\alpha L$ (...
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### What does a symmetry that changes the Lagrangian by a total derivative do to the Hamiltonian $H$?

A tiny symmetry transformation may change the Lagrangian $L$ by a total time derivative of some function $f$. This is a basic fact used in the proof of Noether's theorem. How can we see the effect of ...
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### Prove that Noether's Theorem produces generators of the symmetry

Suppose we have a classical Lagrangian $L(q,\dot{q})$. Here $q = q(s,t)$ is a generalized coordinate as a function of time and some parameter $s$ corresponding to a transformation. If this is a ...
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### Proving that Noether charge generates symmetries in the Lagrangian formalism

I know that similar questions have been asked on this site before, but I haven't been able to find the answer to my specific question. I want to show that the Noether charge defined in Lagrangian ...
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### Why are some symmetries invisible to the configuration space Lagrangian $L(q, \dot q,t)$?

Usually, when people talk about Lagrangians they are talking about a function of configuration space variables $q_i$ and their time derivatives $\dot q_i$. This is a function $L = L(q_i, \dot q_i,t)$. ...
I have been trying to understand the Legendre transformation (in mechanics, in the hyperregular case: when the Legendre transformation is one-to-one) and the correspondence between symmetry $\to$ ...
A first integral in Lagrangian formalism is defined as a function which is constant along the solutions $(q,\dot{q})$ where $q$ are the generalized coordinates; while a first integral in Hamiltonian ...