# Questions tagged [equations-of-motion]

DO NOT USE THIS TAG just because the question contains an equation of motion!

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### 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 ...
• 123
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### 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 ...
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### 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 ...
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### 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 ...
1 vote
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### 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 ...
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### 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 ...
131 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 ...
45 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 ...
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### 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 T_{\mu\nu}\equiv\frac{\partial\mathcal{L}}{\partial(\partial^\mu\phi)}\partial_\nu\phi-\eta_{\mu\nu}\mathcal{...
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1 vote
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### Why the classical Euler-Lagrange equation is assumed when deriving the Noether's conserved current?

As known, in QFT, the conserved currents, such as the energy-momentum tensor, can be derived from the Noether's theorem and expressed as the product of the field operators. These conserved currents ...
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### Conceptual question about Euler-Lagrange equations in Quantum Field Theory

So I've started going down the QFT rabbit hole aided by Schwartz's book "Quantum Field Theory and the Standard Model". On chapter 7, the first method used to find the position-space Feynman ...
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234 views

### Using EOM in QED Lagrangian [duplicate]

Let's have the QED Lagrangian. $$\mathcal{L} = -\frac{1}{4} F_{\mu\nu}F^{\mu\nu} + \bar{\Psi}(i\partial_\mu \gamma^\mu - m)\Psi + g\bar{\Psi}A_\mu \gamma^\mu \Psi.\tag{1}$$ The equations of motion are:...
130 views

### Schwarzschild's null-geodesic new form or an error?

My question is whether or not this form (radial acceleration of a photon) $$\ddot{r}=\frac{L^2}{r^4}(r-3M)$$ is correct ? Recall the standard set of second-order ODE for the Schwarzschild metric (for ...
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1 vote
44 views

### Test charge in 2+1 dimensions

Given a Chern-Simons theory,as in this resource(page 4), in 2+1 dimensions we can define the electric and magnetic fields as $$E_i=-\partial_iA_0-\partial_0A_i\;\;\;B=\epsilon^{ij}\partial_iA_j$$ ...
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### Equations of Motion and Minimization of Spacetime Interval

I'm trying to show that the extrema of a path in spacetime, as given by the spacetime interval (or length if just considering space) is the one that solves the equations of motion. Let a path be given ...
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### Relation between equations of the form "Derivative" $f=0$

I'm currently taking an introductory course in QFT, and I've noticed that lots of equations in physics take the form of "Derivative" of a funcition equal 0. Some examples being the wave ...
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### Euler-Lagrangian equation of motion of quantum fields in QFT

A canonical way of doing quantum field theory is by starting with some Lagrangian, for example, that of free scalar field $$L=\frac{1}{2}\partial_{\mu}\phi \partial^{\mu}\phi-\frac{1}{2}m\phi^2$$ Then ...
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362 views

### What is the difference between 'Equation of motion' and 'Transport equation'?

I think this is a simple question with a not so easily explained answer. What is the difference between the Equation of motion and Transport eq? Is Navier stokes equation an 'Equation of motion' or a '...
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### What the role of classical equation of motion in quantum field theory?

I've learnt quantum field theory for a semester but I still can't understand the role of classical equation of motion in QFT. I have looked up for several books. They all discuss classical field ...
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### Paradox in the Kinematic SUVAT Equations of Motion

The 5 equations of motion have been chosen such that from the 5 variables of motion: $s$, $u$, $v$, $a$ and $t$; each equation, exclusively omits one of these. This allows us to only ever require the ...
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### Motion of charged particle in uniform magnetic field and a radially symmetric electric field

This question posted by me on MSE talks about a physics problem. This is what it was: (I hope someone can help me with this) Consider a region of 2-dimensional space with a uniform magnetic field of ...
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