Tagged Questions
0
votes
1answer
39 views
Relativistic Lagrangian transformations
I need to study the relativistic lagrangian of a free particle.
It's
$\ L= - m c^2 \sqrt[2]{1- \frac{|u|^2}{c^2}} $ I need to study the translation, boost and rotation symmetry. I say it doesn't ...
2
votes
2answers
137 views
Does a constant factor matter in the definition of the Noether current?
This is a very basic Lagrangian Field Theory question, it is about a definition convention. It takes much more time to typeset it than answering, but here it is:
Consider a field Lagrangian with only ...
1
vote
2answers
111 views
In Noether's theorem, what is a “classical solution of the equations of motion”?
I'm reading a book which states that:
for each generator of a global symmetry transformation, there is a
current $j^{\mu}_{a}$ which, when evaluated on a classical solution
of the equations of ...
2
votes
1answer
58 views
Obtaining the conserved current of the Lagrangian making the parameter depending on $x$
To calculate the conserved current due to an internal symmetry of the system (expressed by the Lagrangian density) we can proceed as follows: if it is invariant under
$\delta \phi = \alpha \phi$, ...
2
votes
1answer
188 views
Application of Noether's theorem
Consider one parameter transformation: $y = y ( \tilde{y}, \alpha)$ such that lagrangian satisfies: $\tilde{L}(\tilde{y}, \alpha) = L(y ( \tilde{y}, \alpha))$. We say that equation is invariant ...
4
votes
2answers
306 views
How to apply Noether's theorem
Say I have a point transformation:
$$x' ~=~ (1 +\epsilon)x,$$
$$t' ~=~ (1 +\epsilon)^2t,$$
and Lagrangian
$$ L ~=~ \frac{1}{2}m\dot{x}^2 - \frac{\alpha}{x^2}.$$
How do I go out about showing ...
2
votes
1answer
153 views
Why has the trace of the energy-momentum tensor to vanish for conserved scaling currents to exist?
In this paper, the authors say that the trace of the energy-momentum tensor has to vanish to allow for the existence of conserved dilatation or scaling currents, as defined on p 10, Eq(22)
$$ ...
1
vote
1answer
144 views
Improved energy-momentum tensor
While still dealing with this issue, I've stumbled upon this answer to a question asking about the conserved quantity corresponding to a scaling transformation. It mentions that in accordance with ...
3
votes
1answer
261 views
How do you know if a coordinate is cyclic if its generalized velocity is not present in the Lagrangian?
Goldstein's Classical Mechanics says that a cyclic coordinate is one that doesn't appear in the Lagrangian of the system, even though its generalized velocity may appear in it (emphasis mine). For ...
1
vote
1answer
90 views
Cyclic co-ordinates implying the constant velocity motion of center of mass of a system of particles
I'm reading the section on Central Force in my textbook (Goldstein's Classical Mechanics has a similar argument in the chapter titled "The Central Force Problem", first section), where we have the ...
3
votes
1answer
317 views
Noether current for the Yang-mills-higgs lagrangian
I am trying to calculate the Noether's current, more specifically, the energy density of the Yang-mills-Higgs Lagrangian. Please refer to the equations in the Harvey lectures on Magnetic Monopoles, ...
8
votes
2answers
76 views
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 ...
16
votes
1answer
211 views
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 ...
4
votes
1answer
512 views
invariance of lagrangian in Noether's theorem
Noether's theorem needs the lagrangian to be invariant.
However, given a lagrangian $L$, we know that the lagrangians $\alpha L$ (where $\alpha$ is any constant) and $L + \frac{df}{dt}$ (where $f$ is ...
7
votes
3answers
405 views
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 ...
13
votes
6answers
2k views
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. ...
3
votes
2answers
450 views
Is there a conserved quantity that enforces planar orbits in central force motion?
From what I remember, one of the first steps in finding the equations of motion for an orbiting body is to argue that the body's motion has to be restricted to a plane, because the central force has ...
