Linked Questions

3
votes
1answer
622 views

Noether's Current in QFT with position dependent variations?

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'(...
2
votes
1answer
38 views

What is the definition of a symmetry of an action?

Symmetries of Lagrangians The definition of a symmetry of a theory is quite clear at the level of a Lagrangian. We say a Lagrangian $\mathcal{L}(\phi,\partial_\mu \phi)$ is symmetric under the ...
2
votes
1answer
57 views

Why is an action built from superfields guaranteed to be supersymmetric?

Given a superfield (in 0+1 spacetime + 2 superspace coordinates) $$X(t,\theta_1,\theta_2) = x(t) + \theta_i \psi_i(t) + \theta_1 \theta_2 F_{12}(t)\tag{1}$$ and given the standard supercharges ...
2
votes
1answer
332 views

Problem using Noether's theorem in time-dependent lagrangian

I have some problems calculating the conserved quantity for a lagrangian of the form $$ L = \frac{1}{2}m\dot{q}^2 - f(t) a q, $$ because I found the general problem too abstract, I tried at first ...
2
votes
1answer
240 views

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 ...
2
votes
1answer
452 views

The Lagrangian of a free particle in Landau & Lifshitz

In Landau & Lifshitz's derivation of the Lagrangian of a free particle in a galilean frame of reference one finds the following argument: the equations of motion in two galilean frames must be ...
2
votes
1answer
167 views

Elementary question about global supersymmetry of a worldsheet [closed]

I'm reading chapter 4 of the book by Green, Schwarz and Witten. They consider an action $$ S = -\frac{1}{2\pi} \int d^2 \sigma \left( \partial_\alpha X^\mu \partial^\alpha X_\mu - i \bar \psi^\mu \rho^...
2
votes
1answer
466 views

Does an on-shell symmetry necessarily change the Lagrangian by a total derivative?

This is a follow-up question to: Does a symmetry necessarily leave the action invariant? Qmechanic writes here: Here the word off-shell means that the Lagrangian eqs. of motion are not assumed to ...
1
vote
1answer
93 views

Symmetry modulo total derivative term in Noether's Theorem

I came across the proof of Noether's Theorem in David Tong's notes (page 14) on QFT. He writes something like, We say that the transformation $$\delta\phi(x) = \chi (\phi) \tag{1.34}$$ is a ...
1
vote
1answer
41 views

How do we define the quantity $Q$, in the conservation of energy? And what does it rely on?

Noether's theorem to me explains how a certain defined quantity (Q) is conserved (locally) in time due to the time translation symmetry, and to be more specific; if we had a ball that is placed in a ...
1
vote
1answer
111 views

Lagrangian of free particle - classical case

I have a question, more related to a mathematical aspect of physics, which seems I am not understanding very well. So, by applying Galilean transformation between two reference frames, which move at ...
1
vote
1answer
323 views

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 ...
1
vote
1answer
331 views

Variation of the Action under infinitesimal arbitrary transformations and Noether's Theorem

Let's consider an arbitrary infinitesimal transformation of the fields and their coordinates : $$x'^{\mu}= x^{\mu} + \delta x^{\mu} = x^{\mu} + \frac{\delta x^{\mu}}{\delta{\omega}^a}{\omega}^a\tag{1}...
0
votes
1answer
190 views

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 ...
2
votes
0answers
165 views

Are there (interesting) Poincare-invariant QFTs with non-invariant Lagrangian densities?

In all QFTs I know, the Lagrangian density is completely invariant under the Poincare group, $$ \mathcal L \to \mathcal L. $$ On the other hand, the action would be invariant even if the Lagrangian ...

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