61 questions linked to/from Invariance of Lagrangian in Noether's theorem
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### Conserved quantity of a relativistic free Lagrangian for a Lorentz boost

Let $$L~=~-mc^2\sqrt{1- \frac{|\textbf{v}|^2}{c^2} },$$ where $\textbf{v}$ is the usual velocity of the particle in a fixed inertial frame. Then, this is the Lagrangian for a relativistic free ...
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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 is dependence on derivatives not a problem in the definition of canonical energy-momentum tensor?

Let $\mathcal L(\phi,\partial\phi)$ be a Lagrangian for a field $\phi$. It is known that the Lagrangian $\mathcal L$ and the Lagrangian $\mathcal L+\partial_\mu K^\mu$ produces the same physics, ...
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### Alternative symmetries for the Maxwell Lagrangian?

I'm wondering about how to show that $A_a\rightarrow A_a+\alpha\partial_0A_a$, with $\alpha$ infinitesimal, is an infinitesimal symmetry of $\mathcal L=-\frac14F_{ab}F^{ab}$. F_{ab}\...
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### Do total derivatives have anything to do with central extensions?

I recently got interested in the Galilean group and its central extension and found a paper "Quantization on a Lie group: Higher-order Polarizations" by Aldaya, Guerrero and Marmo. Before asking my ...
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### Conservation of energy for a class of Lagrangians with explicit time dependence

I have read in my book that if $\frac{\partial L}{\partial t}=0$, then the quantity $L-\frac{\partial L}{\partial \dot{q}} \dot{q}$ is conserved, and we call it the energy of the system. But if ...
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