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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Is there a symmetry associated to the conservation of information?

Conservation of information seems to be a deep physical principle. For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory. We may wonder if there is an underlying ...
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Is there something similar to Noether's theorem for discrete symmetries?

Noether's theorem states that, for every continuous symmetry of an action, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
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What conservation law corresponds to Lorentz boosts?

Noether's Theorem is used to related the invariance under certain continuous transformations to conserved currents. A common example is that translations in spacetime correspond to the conservation of ...
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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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What's the interpretation of Feynman's picture proof of Noether's Theorem?

On pp 103 - 105 of The Character of Physical Law, Feynman draws this diagram to demonstrate that invariance under spatial translation leads to conservation of momentum: To paraphrase Feynman's ...
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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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Can Noether's theorem be understood intuitively?

Noether's theorem is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. ...
27
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What symmetry causes the Runge-Lenz vector to be conserved?

Noether's theorem relates symmetries to conserved quantities. For a central potential $V \propto \frac{1}{r}$, the Laplace-Runge-Lenz vector is conserved. What is the symmetry associated with the ...
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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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Swimming in Spacetime - apparent conserved quantity violation

My question is about the article Swimming in Spacetime. My gut reaction on first reading it was "this violates conservation of momentum, doesn't it?". I now realize, however, that this doesn't allow ...
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Why does charge conservation due to gauge symmetry only hold on-shell?

While deriving Noether's theorem or the generator(and hence conserved current) for a continuous symmetry, we work modulo the assumption that the field equations hold. Considering the case of gauge ...
18
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1answer
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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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What is the conserved quantity of a scale-invariant universe?

Consider that we have a system described by a wavefunction $\psi(x)$. We then make an exact copy of the system, and anything associated with it, (including the inner cogs and gears of the elementary ...
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Noether's theorem and gauge symmetry

I'm confused about Noether's theorem applied to gauge symmetry. Say we have $$\mathcal L=-\frac14F_{ab}F^{ab}.$$ Then it's invariant under $A_a\rightarrow A_a+\partial_a\Lambda.$ But can I say that ...
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3answers
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What is the symmetry which is responsible for preservation/conservation of electrical charges?

Another Noether's theorem question, this time about electrical charge. According to Noether's theorem, all conservation laws originate from invariance of a system to shifts in a certain space. For ...
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Noether charge of local symmetries

If our Lagrangian is invariant under a local symmetry, then, by simply restricting our local symmetry to the case in which the transformation is constant over space-time, we obtain a global symmetry, ...
15
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2answers
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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 ...
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Symmetrizing the Canonical Energy-Momentum Tensor

The Canonical energy momentum tensor is given by $$T_{\mu\nu} = \frac{\partial {\cal L}}{\partial (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L} $$ A priori, there is no reason to ...
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What is the symmetry which is responsible for conservation of mass?

According to Noether's theorem, all conservation laws originate from invariance of a system to shifts in a certain space. For example conservation of energy stems from invariance to time translation. ...
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If all conserved quantities of a system are known, can they be explained by symmetries?

If a system has $N$ degrees of freedom (DOF) and therefore $N$ independent1 conserved quantities integrals of motion, can continuous symmetries with a total of $N$ parameters be found that deliver ...
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Why does the classical Noether charge become the quantum symmetry generator?

It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this ...
12
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1answer
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Supersymmetric Noether theorem and supercurrents — invariance requirements

Consider $\mathcal{N}=1,d=4$ SUSY with $n$ chiral superfields $\Phi^i,$ Kaehler potential $K,$ superpotential $W$ and action ($\overline{\Phi}_i$ is complex conjugate of $\Phi^i$) $$ S= \int d^4x \...
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1answer
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Trick for deriving the stress tensor in any theory

In D. Tong's notes on string theory (pdf) section 4.1.1 he explains a trick for deriving the stress-energy tensor which arises from translations in the base manifold of the field theory (in this case ...
11
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Noether currents for the BRST tranformation of Yang-Mills fields

The Lagrangian of the Yang-Mills fields is given by $$ \mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu} D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+ \bar{c}^a(\partial\...
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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 ...
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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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Energy momentum tensor from Noether's theorem

in the book Quantum Field Theory by Itzykson and Zuber the following derivation for the stress-energy tensor is proposed (p.22): Assume a Lagrangian density depending on the spacetime coordinates $x$ ...
9
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Does the action and Lagrangian have identical symmetries and conserved quantities?

From the book Introduction to Classical Mechanics With Problems and Solutions by David Morin, page 236 states: Noether's Theorem: For each symmetry of the Lagrangian, there is a conserved quantity....
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More general invariance of the action functional

I will formulate my question in the classical case, where things are simplest. Usually when one discusses a continuous symmetry of a theory, one means a one-parameter group of diffeomorphisms of the ...
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Does Noether's theorem also give rise to quantities conserved over space?

Noether's theorem gives rise to quantities that are conserved over time. But does it also give rise to quantities that are conserved over space?
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Translation Invariance without Momentum Conservation?

Instead of the actual gravitational force, in which the two masses enter symmetrically, consider something like $$\vec F_{ab} = G\frac{m_a m_b^2}{|\vec r_a - \vec r_b|^2}\hat r_{ab}$$ where $\vec F_{...
8
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1answer
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Boundary currents for Asymptotic Symmetry Group (ASG)

In the context of asymptotic symmetry groups, what is a boundary current? Why is it called a "current"? Context: I'm reading Strominger's recent paper on Asymptotic symmetry group of Yang-Mills (...
8
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1answer
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Introduction to Gauge Symmetries: Good, Bad or Ugly?

I'm trying to come up with a good (as in intuitive and not 'too wrong') definition of a gauge symmetry. This is what I have right now: A dynamical symmetry is a (differentiable) group of ...
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Conjugate Variables, Noether's Theorem and QM

What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in Noether's theorem (e.g. time symmetry implies energy ...
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1answer
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Constants of motion vs. integrals of motion

Since the equation of mechanics are of second order in time, we know that for $N$ degrees of freedom we have to specify $2N$ initial conditions. One of them is the initial time $t_0$ and the rest of ...
8
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1answer
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Noether currents in QFT

I am trying to organize my knowledge of Noether's theorem in QFT. There are several questions I would like to have an answer to. In classical field theory, Noether's theorem states that for each ...
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2answers
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What is the symmetry associated with the local particle number conservation law for fluid?

According to Noether's theorem, every continuous symmetry (of the action) yields a conservation law. In fluid, there is a local particle number conservation law, which is $$\partial{\rho}/\partial{t}+...
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Damped oscillator: time-reversal, time-translation and dissipation

The equation of motion of a damped oscillator $$\frac{d^2x}{dt^2}+\gamma\frac{dx}{dt}+\omega_0^2x=0$$ which is invariant under time-translation $t\rightarrow t+a$, but not under time reversal $t\...
7
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Noether theorem with semigroup of symmetry instead of group

Suppose You have semigroup instead of typical group construction in Noether theorem. Is this interesting? In fact there is no time-reversal symmetry in the nature, right? At least not in the same ...
7
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1answer
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Why is color conserved in QCD?

According to Noether's theorem, global invariance under $SU(N)$ leads to $N^2-1$ conserved charges. But in QCD gluons are not conserved; color is. There are N colors, not $N^2-1$ colors. Am I ...
7
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1answer
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Noether theorem and classical proof of electric charge conservation

How to prove conservation of electric charge using Noether's theorem according to classical (non-quantum) mechanics? I know the proof based on using Klein–Gordon field, but that derivation use ...
7
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1answer
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Infinitesimal rotation of classical fields: why are rotation group representations important?

I understand that $SO(3)$ representations are important in quantum physics, because eigenspaces of the Hamiltonian are irreps of $SO(3)$ if it is part of the symmetry group. But I don't see the reason ...
7
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1answer
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Lie algebra of axial charges

Starting from the lagrangian (linear sigma model without symmetry breaking, here $N$ is the nucleon doublet and $\tau_a$ are pauli matrices) $L=\bar Ni\gamma^\mu \partial_\mu N+ \frac{1}{2} \partial_\...
7
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Is it intuitive that the conserved quantity from time symmetry is what we know as energy?

Is there an easy (aka intuitive) way to understand that the conserved quantity from time translation symmetry is just what we call energy? In other words, we use two definitions of energy. One is ...
6
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1answer
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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 $\alpha L$ (...
6
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2answers
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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 ...
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What is the symmetry that corresponds to conservation of position?

We know that conserved quantities are associated with certain symmetries. For example conservation of momentum is associated with translational invariance, and conservation of angular momentum is ...
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1answer
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Easy proof of Noether's theorem? [duplicate]

Where could I find an easy proof of Noether's theorem? I mean I know that the variation must be $ 0=\delta S = (EULER-LAGRANGE)+ (CONSERVED\, \, \, CURRENT) $ for the case of a particle $q(t)$. I ...
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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 $$\mathscr L_g=\frac 1{16\pi k}\sqrt{-g}R.$$ ...
6
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Noether's Theorem: Lie algebra, Lie groups

I've had a brief look through similar threads on this topic to see if my question has already been answered, but I didn't find quite what I was looking for, perhaps it is because I'm finding it hard ...