All Questions
Tagged with differentiation notation
224 questions
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Calculating motion of equation in tensor form
for the Lagrangian density $$\mathscr{L}=\frac{1}{2}(\partial_{\mu}A^{\mu})^2$$
how can I get this $$\frac{\partial{\mathscr{L}}}{\partial(\partial_{\mu}A_\nu)}=(\partial_\rho A^\rho)\eta^{\mu\nu}$$
...
- 213k
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What does the zero in the differential operator $\partial_0$ mean?
I have noticed the differential operator $\partial_0$ in a lot of equations whilst studying quantum field theory. I am used to the notation $\partial_x$ meaning $ \frac{d}{dx} \\\\ $ etc. but just a ...
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Usage of delta operator [duplicate]
So I've always thought that "$\Delta$" when applied to an n-tuple or scalar was the change of that n-tuple or scalar relative to a previous state in time and proportional to the amount of time or $\...
- 213k
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What is the difference between $\frac{DA^\mu}{D\lambda}$ and $\frac{DA^\mu}{d\lambda}$?
I earlier asked this question How can you have $\frac{DA^\mu}{d\tau}$? I am now wondering:
What is the difference between $\frac{DA^\mu}{D\lambda}$ and $\frac{DA^\mu}{d\lambda}$?
In the linked ...
CommunityBot
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How can you have $\frac{DA^\mu}{d\tau}$?
If a covariant derivative is given by:
$$D_\nu A^\mu=\partial_\nu A^\mu +\Gamma^\mu_{\nu \lambda} A^{\lambda}$$
Then how does $\frac{DA^\mu}{d\tau}$ make any sense? Since there are no 'differentials' ...
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3
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Difference between $|d{\bf r}|$ and $d|{\bf r}|$
What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other?
My question might seem stupid to some and will probably get downvoted but I have ...
- 2,410
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Acceleration derivative
I am reading Morris Kline's "Calculus" and I fail to understand this notation:
We have acceleration to which an object $r$ feet from the center of the earth (and above the earth) is subject. If we ...
- 213k
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How is $\delta s$ different than $ds$? [duplicate]
Specifically I'm reading Dirac's General Relativity and he says essentially:
$$ \delta Q = \frac{\partial Q}{\partial x^\mu} \delta x^\mu $$
But what's the difference between this and:
$$ dQ = \...
CommunityBot
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What is the meaning of symbols $\delta f$ and $\delta^2f$?
Professor was using these symbols to derive the continuity equation. He defined the infinitesimal mass as $\delta^2m=\rho \delta V$ and the mass that leaves some closed boundary $\partial V$ as $\...
- 213k
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Electric current notation
Depending on the source, I sometimes read $\frac{\delta q}{dt}$ , $\frac{dq}{dt}$ or even $\frac{\delta q}{\delta t}$ (rare)
Wich one is the correct notation ?
In theory we are to know if a ...
- 661
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Meaning the symbol, $W$ and $dW$
What's the difference between $W$ and $dW$? They are both work done and have similar formulae (same dimension). But I don't know the difference between them.
$dW$ here ISN'T power.
- 213k
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Indexed Gradient operator on trigonometric functions
$$\nabla_{i}\nabla_{j}\Big(\frac{\sin(kR)}{R}\Big)$$ Where $R$ is the distance between particle $i,j$. And $k$ is a constant
I took $\nabla_{i}=\frac{\partial}{\partial R_{i}}$ and $\nabla_{j}=\frac{\...
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Computation of $T^{\mu\nu}$ from Lagrangian density $\mathscr{L} $
I am trying to understand how upper and lower indices are connected when computing the energy-momentum tensor. In particular, I found the simple problem where the Lagrangian density is given as
$$\...
- 19.5k
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What is the meaning of following expression $C=\frac{\delta Q}{dT}$ mathematically?
Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics):
Many text books (even Wikipedia) writes wrong expressions (from ...
- 213k
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Is there a difference in handwritten nabla $\vec{\nabla}$ with an overset arrow and typeset nabla $\nabla$?
According to some physicist at KIT it is usual to write the following when using pen and paper:
whereas in typeset texts you write $\nabla$.
Is that true? Are there sources for this convention?
- 213k
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Dot product of vector and its derivative with respect to time? How does $L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$? [closed]
How does:
$$L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$$
where L is a vector (I dunno how to make it bold in the equation).
How do they reach to this right hand side equation?
And what is ...
- 60.3k
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A confusion about notation in Goldstein
On treating systems of particles, Goldstein starts with the consideration that whenever there are $k$ particles on a system, the $i$-th one obeys the relation
$$\dfrac{d}{dt}{\bf p}_i = {\bf F}_i^{(e)...
- 213k
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Conventions regarding partial derivatives
Look at this expression:
$$\frac{\partial}{\partial t} (V-\mathbf{v}\cdot\mathbf{A}).$$
This expression occurs in Griffiths EM book (4th ed, p.444). $V=V(\mathbf{r},t)$is the scalar potential, $\...
- 2,367
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What is the difference between $\nabla _{\sigma} $ and $ \nabla^{\sigma}$?
What is the difference between:
$\nabla _{\sigma} $ and $ \nabla^{\sigma}$?
I've been told that the first is the covariant derivative, however I'm just starting a course on spacetime geometry and ...
- 14.9k
2
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3
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Ordering of differential operators
If we write something like:
$\partial_a X_{\mu} \partial^a X^{\mu}$
Does that mean the first derivative is only applied to the first X?
($\partial_a X_{\mu})( \partial^a X^{\mu}$)
Or is the ...
CommunityBot
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Higgs mechanism in QED
I'm trying to understand the Higgs mechanics. For that matter, I'm exploring the possibility of giving mass to the photon in a gauge-invariant way. So, if we introduce a complex scalar field:
$$ \phi=...
- 213k
3
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2
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Feynman's subscript notation
Consider this vector calculus identity:
$$
\mathbf{A} \times \left( \nabla \times \mathbf{B} \right) = \nabla_\mathbf{B} \left( \mathbf{A \cdot B} \right) - \left( \mathbf{A} \cdot \nabla \right) \...
- 213k
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Notation for differential operators and wave function math
I know that $[\frac {d^2}{dx^2}]\psi$ is $\frac {d^2\psi}{dx^2}$ but what about this one $[\frac {d^2\psi}{dx^2}]\psi^*$? Is it this like $\frac {d^2\psi\psi^*}{dx^2}$ or this like $\frac {\psi^*d^2\...
- 5,753
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What are $\partial_t$ and $\partial^\mu$?
I'm reading the Wikipedia page for the Dirac equation:
$\rho=\phi^*\phi\,$
......
$J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$
with the conservation of probability ...
- 13.9k