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### Different derivations of first Noether's theorem [duplicate]

I'm my current studies in Noether's theorem, the two that I liked the most are joshphysics answer to this Phys SE. post, and the derivation in chapter $4$ of An Elementary Introduction to Classical ...
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### Noether Theorem and Energy conservation in classical mechanics

I have a problem deriving the conservation of energy from time translation invariance. The invariance of the Lagrangian under infinitesimal time displacements $t \rightarrow t' = t + \epsilon$ can be ...
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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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Setup Consider a mapping $F$ that takes every point $x$ on the manifold $M$ to the point $x'$ on the same manifold. Under this mapping the field $\phi(x)$ evaluated at the point $x$ changes to $\phi'(... 1answer 1k views ### Energy momentum tensor from generalized Noether current Proceeding like here, let us consider$N$independent scalar fields which satisfy the Euler-Lagrange equations of motion and are denoted by$\phi^{(i)}(x) \ ( i = 1,...,N)$, and are extended in a ... 1answer 272 views ### What is the most general expression of Noether's current in classical field theory? Peskin & Schroeder's expression of the Noether current If a (quasi-)symmetry is defined as a transformation that changes the action by a surface term i.e. $$S\to S'=S+\int d^4x \partial_\mu K^\mu(\... 1answer 213 views ### How to use general expression for Noether's current to get the energy-momentum conservation law? The most general form of the Noether's current (see here and here) is given by$$j^\mu(x)=\sum\limits_a\frac{\partial \mathscr{L}}{\partial(\partial_\mu\phi_a)}\delta\phi_a -\theta^{\mu\nu}\delta x_\... 2answers 163 views ### Why is there an extra term in definition of Noether current for spacetime translations? I am reading Schwartz's Quantum Field Theory textbook. In chapter 3, Schwartz first defines the conserved current for a symmetry$\phi \rightarrow \phi + \delta \phi$that depends on a parameter$\...
Version 1: An infinitesimal variation on the fields $\phi\mapsto\phi'$ is said to be a symmetry if $\delta \mathcal{L}:=\mathcal{L}(\phi',\partial\phi')-\mathcal{L}(\phi,\partial\phi)$ is a total ...
When I looked at the Noether's theorem(here, we discuss the field case), there are two ways to derive it. One way is to assume that the variation of Lagrange $\delta L$ is exactly equal to derivative ...