# Tagged Questions

A theorem that relates continuous symmetries (continuous transformations that don't affect the value of the lagrangian) to quantities conserved in time.

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### Noether's theorem in general relativity

Noether's theorem yields a conservation law for every symmetry. Is that independent of the Lagrangian i.e. when $\mathcal{L}\neq T-V$? In general relativity the integral that is minimised will be the ...
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### Gauge redundancies and global symmetries [closed]

It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
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### Generalise Noether's theorem [closed]

I'm not sure how to generalise Noether's theorem. For this L, I think $B\cdot\dot{x}$ is conserved so I tried to relate F and K to this and try to show that that was conserved but got no where. any ...
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### When can a global symmetry be gauged?

Take a classical field theory described by a local Lagrangian depending on a set of fields and their derivatives. Suppose that the action possesses some global symmetry. What conditions have to be ...
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### Why can't energy be created or destroyed?

My physics instructor told the class, when lecturing about energy, that it can't be created or destroyed. Why is that? Is there a theory or scientific evidence that proves his statement true or ...
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### Understanding Noether's theorem rigorously

I've known about Noether's theorem for some time and reading some things about it recently I've realised I haven't completely understood it. In that case I've been trying to understand a more rigorous ...
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### Is the Noether charge always a Hermitian operator?

Noether's theorem tells us that to every continuous symmetry of the Lagrangian there corresponds a conserved current $j^\mu$. From the time component of this current, we can then define the Noetherian ...
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### Noether's theorem for space translational symmetry

Imagine a ramp potential of the form $U(x) = a*x + b$ in 1D space. This corresponds to a constant force field over $x$. If I do a classical mechanics experiment with a particle, the particle behaves ...
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### Expression of Noether current corresponding to Lorentz transformation of scalar fields

I find the derivation of Noether current given in the post http://physics.stackexchange.com/a/56905/45429 very clear. However, following a similar logic, I am having problems deriving the Noether ...
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### Isolated system and mutual interaction potential

We know that the total linear momentum of a closed (isolated) system is conserved due to homogeneity of space (Landau and Liftshitz, page 15, Mechanics). Hence for an isolated system of two bodies ...
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My question has a few parts, I know from Noether that if there is a symmetry in a Hamiltonian, there is a conservation law. What would be the conservation law associated with $SU(2)$ symmetry? $... 2answers 142 views ### Does the conservation of the Wronskian follow from Noether's principle? Noether's principle is the paradigm that symmetries of Hamiltonian and Lagrangian systems correspond to conservation laws of various kinds. Consider a one-dimensional harmonic oscillator $$\tag{*} \... 1answer 88 views ### Deeper principles in classical mechanics While teaching introductory physics, my professor explained that the conservation of linear momentum, conservation of energy and conservation of angular momentum are based on deeper principles in ... 1answer 79 views ### What is the reason behind why energy must always be conserved, apart from observation? [duplicate] I know that we see in experiments (physical and thought) that energy is always transformed into something else, but what propels our universe to behave this way? What is happening at small levels that ... 0answers 25 views ### How can intuitively guess what conserved quantities has the system that I am studying? I'm taking a course in Classical Electrodynamics and in one problem my teacher introduced us to a triplet of fields (\phi^a) invariant under internal rotations, i.e. transformations like:$$\phi'^... 0answers 46 views ### Recovering a symmetry transformation from a conserved charge I'm going through some notes on how to apply the Hamiltonian formalism to systems with gauge invariance and I found a derivation of Noether's theorem I had never seen before. The idea is roughly that ... 0answers 38 views ### Free Complex scalar field and conservation principle In a free complex scalar field, the difference between the number of Particles and antiparticles is conserved. This constarint can be satisfied with a simultaneous creation of equal number of ... 1answer 498 views ### Does time invariance conclude conservation of energy? [closed] I find it hard to understand that time-translation invariance necessarily implies conservation of energy. As I understand it, Noether's theorem says that there is an energy conservation because the ... 1answer 99 views ### What symmetry gives you charge conservation? This is a popular question on this site but I haven't found the answer I'm looking for in other questions. It is often stated that charge conservation in electromagnetism is a consequence of local ... 2answers 71 views ### Variation of a Lagrange density Symmetries So I am reading Goenner's Spezielle RelativitÃ¤stheorie and I am currently in chapter Â§4.9.1 Variation under Inclusion of Coordinates p. 129. So basically we have: $$\delta W_\zeta=\int d^4x' \mathcal{... 0answers 53 views ### What kind of conservation law is energy conservation in thermodynamics? As I understand it, Noether's theorem is an important result that allows us to show when certain kinds of conservations arise. Is energy conservation in thermodynamics a result of Noether's theorem? ... 1answer 95 views ### Are there conserved quantities in field theory which don't arise from Noether's Theorem? In some QFT texts one writes down the number operator N for free theories, such that when acting on an n-particle state |n\rangle we have$$N|n\rangle=n|n\rangle$$In free theories this is a ... 1answer 64 views ### Is spin angular momentum conserved? According to the Noether theorem, we only have the conserved quantity$$J+S,$$where J is the orbital angular momentum and S is the spin angular momentum. But I am always impressed that the spin ... 2answers 183 views ### Pass to globally conserved currents from locally conserved currents in curved spacetime Let us begin with a Lagrangian of the form$$\mathscr L= \frac 12 \sqrt{-g}g^{\mu\nu}\partial_\mu\phi(x)\partial_\nu\phi(x)+\mathscr L_g,$$where$$\mathscr L_g=\frac 1{16\pi k}\sqrt{-g}R.$$... 1answer 67 views ### Einstein tensor as a conserved current? As is well-known, the traditional" conserved quantities (energy, momentum...) are Noether currents whose conservation depends on the existence of various Killing fields in Minkowski space. In ... 2answers 86 views ### How to describe time-shifts in Noether's theorem in Hamiltonian formalism As was described in, for example, this post, one can formulate Noether's Theorem also in Hamiltonian Mechanics. Symmetries are then represented by vector fields generated by observables whose Poisson ... 2answers 819 views ### A kind of Noether's theorem for the Hamiltonian formalism How can I (conveniently?) show that an invariance of the Lagrangian and Hamiltonian (i.e. the kinetic as well as the potential energy are independently invariant) will lead to a conservation law using ... 1answer 61 views ### Conserved currents from Noether's theorem I'm not sure if I understand the concept correctly. Given an infinitesimal transformation$$\phi \rightarrow \phi + \alpha \Delta\phi$$the change in the Lagrangian density \mathcal{L}(\phi,\... 2answers 299 views ### What symmetry is associated with conservation of Lipkin's zilch? The 'zilch' of an electromagnetic field is the tensor$$ Z^{\mu}_{\ \ \ \nu\rho}=^*\!\!F^{\mu\lambda}F_{\lambda\nu,\rho}-F^{\mu\lambda}\,{}^*\!F_{\lambda\nu,\rho} \tag1$$given in terms of the ... 3answers 3k views ### Noether's current expression in Peskin and Schroeder In the second chapter of Peskin and Schroeder, An Introduction to Quantum Field Theory, it is said that the action is invariant if the Lagrangian density changes by a four-divergence. But if we ... 0answers 109 views ### Noether's theorem and translations I'm a bit confused about Noether's theorem (or about calculus of variations in general) when it comes to the translational symmetry$x^\mu\mapsto {x'}^\mu=x^\mu-a^\mu$. My professor just wrote that if ... 1answer 70 views ### How is it possible to vary time without affect the coordinates or their derivatives? In the context of Noether's theorem , the Hamiltonian is the constant of motion associated with the time-translational invariance of the Lagrangian. Time-translational invariance is equivalent to the ... 1answer 59 views ### Why Conserved Current Should Not Need Renormalization? May be this is trivial but I need to understand why the renormalization of conserved current is not necessary ? As for example, in this paper, they demand (2$^{nd}$paragraph of the 2$^{nd}\$ column in ...
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What's a good book (or other resource) for an advanced undergraduate/early graduate student to learn about symmetry, conservation laws and Noether's theorems? Neuenschwander's book has a scary review ...