Linked Questions

2
votes
1answer
40 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 ...
3
votes
2answers
83 views

Confusion about Noether's theorem

In my field theory class we recently derived Noether's theorem: We consider a infinitessimal transformation $\phi \to \phi + \epsilon \,\delta\phi$ of our field which preserves action i. e. $\delta S =...
2
votes
2answers
103 views

Is this a gauge symmetry?

Imagine a hypothetical action: $$S=\int \left(\frac{\partial}{\partial t}\phi(x,t)\right)^2 d^3x dt$$ Now we have a symmetry of the action: $$\phi(x,t)\rightarrow \phi(x,t)+\chi(x).$$ At time $t$, $\...
4
votes
2answers
121 views

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 ...
5
votes
3answers
216 views

In what sense are the equations of motion conserved by symmetries?

I am studying variational principles and I have been reading this set of notes by Townsend. In the first paragraph of Section 9, Townsend defines what it means for a transformation to be a symmetry of ...
1
vote
1answer
97 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 ...
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 ...
8
votes
2answers
373 views

Why are symmetries in phase space generated by functions that leave the Hamiltonian invariant?

Hamilton's equation reads $$ \frac{d}{dt} F = \{ F,H\} \, .$$ In words this means that $H$ acts on $T$ via the natural phase space product (the Poisson bracket) and the result is the correct time ...
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 ...
3
votes
2answers
143 views

What's the name of the symmetry $ L \to L + \frac{d \Lambda}{dt}$?

In the Lagrangian formulation of Classical Mechanics, we have the freedom to add a total time derivative of an arbitrary function $\Lambda$ to the Lagrangian: $$ L \to L + \frac{d \Lambda}{dt} . $$ ...
5
votes
2answers
151 views

Deriving special relativity free particle Lagrangian using infinitesimal boost?

At the very beginning of Landau and Lifshitz Mechanics they derive the form of the Lagrangian for a free particle in Newtonian mechanics. I want to see how to do the analogous derivation in special ...
4
votes
1answer
99 views

Why are some symmetries invisible to the configuration space Lagrangian $L(q, \dot q,t)$?

Usually, when people talk about Lagrangians they are talking about a function of configuration space variables $q_i$ and their time derivatives $\dot q_i$. This is a function $L = L(q_i, \dot q_i,t)$. ...
5
votes
3answers
229 views

What does a symmetry that changes the Lagrangian by a total derivative do to the Hamiltonian $H$?

A tiny symmetry transformation may change the Lagrangian $L$ by a total time derivative of some function $f$. This is a basic fact used in the proof of Noether's theorem. How can we see the effect of ...
4
votes
1answer
227 views

Constrained Hamiltonian systems: spin 1/2 particle

I am trying to apply the Constrained Hamiltonian Systems theory on relativistic particles. For what concerns the scalar particle there is no issue. Indeed, I have the action \begin{equation} S=-m\int ...
2
votes
1answer
338 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 ...

15 30 50 per page
1
2 3 4 5