All Questions
Tagged with differentiation conventions
22
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What's the difference? $\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$
What's the difference? $$\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$$
In John Dirk Walecka's book 'Introduction to General Relativity',...
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Generator normalisation in the covariant derivative
A common convention for the definition of the covariant derivative in the SM is
$$
D_\mu = \partial_\mu - i g_s \frac{\lambda^a}{2}G^a_\mu - \cdots
$$
where $\lambda^a$ are the Gell-Mann matrices. In ...
- 11
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1
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Does the expression "$𝑑𝑠^2$..." mean the same thing as "$\Delta 𝑠^2$... "?
I reviewed this question but sometimes I'm unsure about delta ($\Delta$) versus differential ($d$) notation.
Does the expression "$ds^2=-c^2dt^2+a^2(t)[dr^2 + S_k^2(r)d\Omega^2 ]$" mean the ...
- 181
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4
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Newton's Law of Cooling: $\delta Q$ or $\mathrm{d}Q$?
In this popular answer, I invoked Newton's Law of Cooling/Heating:
$$\dot{q}=hA\Delta T\tag{1}$$
$$\dot{q}=\frac{\mathrm{d} Q}{\mathrm{d}t}\tag{2}$$
$$\dot{q}=\frac{\delta Q}{\mathrm{d}t}\tag{3}$$
$$\...
- 35.4k
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110
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Sign conundrum while deriving electrostatic potential
Consider a fixed, positive Point charge $q1$, kept at the origin. Another (positive) charge, $q2$, is being brought from $\infty$ to the point $(r,0)$, by an external agent slowly. We wish to ...
- 1,295
3
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2
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762
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How does the transformation of 4-derivative into a 4-momentum actually happen in a derivative coupling?
Consider a derivative coupling with $$\mathcal{L}_{int} = \lambda \phi_1 (\partial_\mu \phi_2) (\partial_\mu \phi_3),\tag{7.101}$$ and a scalar field
$$ \phi(x) = \int \frac{d^4p}{(2\pi)^3} \frac{1}{\...
- 59
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2
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Is it reasonable and common to interpret $dt$ as a time point (a point in time)? [duplicate]
I heard some one talked about the instantaneous and average velocities.
He was using $\Delta t$ to denote a time frame, $dt$ denote a time point.
average velocities $\bar{v} = \dfrac{\Delta s}{\...
- 123
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3
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606
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What does $\Delta$ stand for? [duplicate]
Newton’s first law states that $\Delta v=0$ unless acted on by an external force, $F_{\mathrm{net}}\neq0$.
Can someone explain to me what the $\Delta v$ symbol means?
- 21
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What is the meaning of $d$? [duplicate]
What is the meaning of $d$? Is is Delta? If it is Delta, why is it then not $\Delta$? I am still confused with that. Can someone help explain it to me?
user224451
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Operator $A$ only act on the neighboured state or operator but not the entire expression?
In state vector formalism $A|\psi(x)><u(x)|=(A|\psi(x)>)<u(x)|$, where $A$ only act on $|\psi(x)>$
However, in terms of wave formalism, suppose $A$ is the well known $\frac{d}{dx}$.
...
- 3,256
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1
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Planck Blackbody Radiation: Is this an error in the textbook?
the textbook I am reading describes two forms of equations of Blackbody Radiation.
$$d\rho(\nu, T) = d\rho_\nu(T)d\nu = \frac{8\pi h}{c^3}\ \frac{\nu^3d\nu}{e^{h\nu/k_BT}-1}\ . $$
Substituting $ c = \...
- 11
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1
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What is $δx$ used in physics? [duplicate]
I know that:
1) Change in $x$ ie., $Δx$, when $\lim Δx→0$, then $Δx$ is replaced by $dx$.
2) I also know that $∂x$ is used in partial derivative.
Then what is $δx$?
Is $dx$ and $δx$ is just the ...
- 103
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1
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110
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What is $\delta t$? [duplicate]
I'm confused whether it's difference between two times (i.e final and initial) or it represents very small time.
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Are indices conventionally raised inside or outside of partial derivatives in general relativity?
If $A_\mu$ is a one-form, then is there a widely accepted convention among physicists about whether the notation $$\partial_\mu A^\mu \tag{1}$$ means "the partial-derivative four-divergence of the ...
- 48.4k
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Why do we write $(v\cdot \nabla) v$ instead of $v \cdot (\nabla v)$ for $v_j \frac{\partial}{\partial x_j} v_i$ in the material derivative?
Suppose I have a steady flow and I want to find the rate of change of pressure of a bit of fluid. This depends on the velocity of the fluid and the pressure gradient,
$$\frac{\mathrm{d}P}{\mathrm{d} ...
- 53.2k