Questions tagged [equations-of-motion]
DO NOT USE THIS TAG just because the question contains an equation of motion!
84 questions
1 vote
2 answers
177 views
How can we read Feynman rules from the equations of motion?
Reading Feynman rules from a Lagrangian is a quite standard procedure. However I have seen papers (for example Appendix A of arXiv:2412.14858) where this is done from the Equations of Motion instead ...
- 21
3 votes
1 answer
137 views
The continuum limit of antiferromagnetic magnons
There is a lot of setup needed to ask this question, and numerous steps of which I'm not 100% sure, but my main question is contained in the last paragraph. Consider an antiferromagnetic quantum spin ...
0 votes
0 answers
97 views
The difference in the number of symmetries an action has and those that the on-shell action has (when the system is a manifold with a boundary)
I read that symmetry breaking is an indication that the solution of the equation of motion, the state, does not possess the same symmetry the action enjoys. Does this mean that in some physical ...
- 445
3 votes
2 answers
185 views
The contribution of higher-order derivatives on the equations of motion in QFT [closed]
I am currently preparing for a final on QFT and one of the old exam questions involves calculating the equations of motion (EOM) of a Lagrangian. Now this should be an easy question, but the ...
- 41
1 vote
1 answer
182 views
Inserting equations of motion into Lagrangian in QFT [duplicate]
In some QFT articles, like this one considering an effective theory, I see that the equations of motion (EOM) for certain fields are inserted into the Lagrangian to prove that two operators are ...
- 346
5 votes
2 answers
797 views
Confusion about Noether's Theorem
In classical mechanics, a transformation $q \rightarrow q + \delta q$ is a symmetry if the resultant change in the Lagrangian is a total derivative, $$ \delta L = \frac{dF}{dt}.$$ If we derive the ...
- 95
5 votes
2 answers
344 views
Splitting Scalar into Holomorphic and Anti-Holomorphic Parts
I am reading Tong’s string theory lecture notes. On page 78, he splits the 2d free scalar into left- and right-moving parts, seemingly using the classical equation of motion as justification. Why is ...
- 145
2 votes
0 answers
20 views
Gauge invariance using equations of motion [duplicate]
I am working with a lagrangian on a homework problem. I expect it to have some gauge invariance. I can show that the Lagranian is invariant under those (gauge) tansformations but I have to use ...
- 712
3 votes
0 answers
108 views
Consequences for symmetries of the equations of motion in QFT
In general, if a Quantum Field Theory is described by a Lagrangian $\mathcal{L}$, the symmetries of $\mathcal{L}$ lead to classically conserved currents along the equations of motion and Ward ...
- 392
0 votes
1 answer
126 views
To find the displacement of a rolling body
When calculating the displacement of a rolling body do we just calculate the displacement due to Vcom in a particular time t or additionally need to consider also the displacement that may be produced ...
- 111
1 vote
0 answers
203 views
Does the path integral approach to QFT have equations of motion? [duplicate]
In the canonical quantization approach for QFT, we deal with operators & their (anti)commutation relations. However, at the same time, we say that the field operators are the solutions of equation ...
- 494
1 vote
0 answers
204 views
Why does the ball in Galileo's double inclined plane experiment reach the same height?
Why does the ball in Galileo's double inclined plane experiment reach the same height? I know how to show it by energy conservation law but am unable to prove it by the equations of motion. Can anyone ...
- 91
2 votes
1 answer
450 views
Noether’s second theorem: about the action principle
Noether's second theorem is supposed to show that the invariance of the Lagrangian by the Lie group (infinite in dimension) of certain theories necessarily implies that the field equations proper to ...
- 150
0 votes
1 answer
110 views
Why for motion planning of quadrators the goal is to minimize the jerk/snap?
In motion planning for quadrators the optimization goal is sometimes to minimize the (norm squared of the) jerk and more often the (norm squared of the) snap. Can someone provide an intuitive and ...
- 41
3 votes
2 answers
199 views
Can the $\eta_{\mu\nu}\mathcal{L}$ term in canonical energy–momentum tensor be omitted?
From Noether theory we can define the canonical energy–momentum tensor as \begin{equation} T_{\mu\nu}\equiv\frac{\partial\mathcal{L}}{\partial(\partial^\mu\phi)}\partial_\nu\phi-\eta_{\mu\nu}\mathcal{...
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