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-3
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0answers
21 views

Converting the derivative into a particular form

I have found the derivative which is $$dy/dx = \frac{-2x(x+1)}{(x+2)^5}$$ However how would you express this derivative in the above form.
0
votes
0answers
39 views

Can I Wick-contract terms with derivatives with terms without derivatives?

Consider for example the QCD three point vertex, can I contract a gluon field with the gluon field with a derivative in the vertex?
-1
votes
1answer
22 views

Forced damped harmonic motion, angular frequency at which amplitude is maximum. differentiation [closed]

How would I differentiate this with respect to the driven angular frequency (equating to zero) in order to obtain the max value of the amplitude in terms of these components?
0
votes
2answers
57 views

Variation of square root of determinant of metric, $\delta g$ [closed]

I am trying to calculate $$ \frac{\partial \sqrt{- g}}{\partial g^{\mu \nu}},$$ where $g = \text{det} g_{\mu \nu}$. We have $$ \frac{\partial \sqrt{- g}}{\partial g^{\mu \nu}} = - \frac{1}{2 ...
1
vote
2answers
50 views

What does it mean to differentiate a spinor-valued field?

Peskin and Schroeder, equation 3.28, states that the Klein-Gordon equation $$(\partial^2+m^2)\psi=0 \tag{3.28}$$ is a valid choice of equation for a Dirac spinor field. Their explanation makes sense ...
1
vote
0answers
49 views

Covariant derivative and tensor symmetries [migrated]

Suppose we have a tensor field $T^{ab}$ such that $T^{ab} = T^{ba}$ everywhere. Then from the definition of the Riemannian covariant derivative in terms of a map between tensors, why must we then have ...
7
votes
2answers
198 views

How does uncertainty/error propagate with differentiation?

I have a noisy temperature (T) vs. time (t) measurement and I want to calculate dT/dt. If I approximate $dT/dt = \Delta T/\Delta t$ then the noise in the derivative gets too high and the derivative ...
1
vote
1answer
79 views

Geometric meaning of spin connection

A very short question: Does the spin connection that we encounter in General Relativity $$\omega_{\mu,ab}$$ have a geometric meaning? I am supposing it does because it comes from mathematical terms ...
0
votes
1answer
46 views

Issues with the chain rule in derivatives in chiral perturbation theory [duplicate]

I realize that this is a purely math question, which however has arisen in a physics computation. The reason to post it here is that I want a fast dirty answer. Not something cluttered with ...
0
votes
2answers
75 views

Changing coordinates in partial derivatives, re: Hydrogen atom

At around 11:35 in this video https://www.youtube.com/watch?v=q99ygFeWGv4 the instructor is using a "standard way of changing coordinates" in partial derivatives relating to the new variables of ...
13
votes
5answers
664 views

What does it mean for a physical quantity if its mixed second partial derivatives are not equal?

This goes for every problem (either in electromagnetism or fluid dynamics) that has to do with vector fields. Say we have a fluid flowing in a closed circular pipe (or an electromagnetic field, the ...
1
vote
0answers
17 views

Dependence of scattering amplitudes on Mandelstam variables

It is well-known that scattering amplitudes in QFT are tensors, hence e.g. scalar amplitudes /written in momentum space/ depend only on the Mandelstam variables of the external momenta, involved in ...
0
votes
3answers
89 views

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
votes
3answers
297 views

How do I know what variable to use for the chain rule?

In my textbook the tangential acceleration is given like this: $$a_t=\frac{dv}{dt}=r\frac{dw}{dt}$$ $$a_t=rα$$ I understand that the chain rule is applied here like this: ...
3
votes
1answer
53 views

Gradient in the Frenet-Serret coordinate

I was simply thinking that the gradient in the Frenet-Serret coordinate at a particular point is similar to the gradient in the Cartesian coordinate. I simply assumed that Frenet space is an ...
1
vote
4answers
391 views

Why is $F=-\nabla V$?

I came across this equation $$F=-\nabla V$$ where $V$ is potential energy. I do understand that $$F(r)=-\frac{dV}{dr}.$$ Hence does this mean the nabla operator in this case means derivative? Because ...
-3
votes
3answers
116 views

Derivative of kinetic energy [closed]

I read that the derivative of kinetic energy=$F\cdot v$. I tried to differentiate (1/2) mv^2 with respect to time but each time I am getting $m*v$ and not $m*a*v$ which solves to $F*v$. My efforts are ...
0
votes
3answers
47 views

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 ...
0
votes
2answers
83 views

Physical meaning of divergence

While reading the section on Hamiltonian mechanics in Taylor's Classical mechanics, I realized that I didn't fully understand what he was saying when he was explaining why ...
0
votes
1answer
25 views

Taking a derivative in a dynamic mass balance?

I'm practicing for a transport phenomena exam and I came across this question: A mothball with a diameter of 1.0 cm is hung (by a thread) in stationary air. Mothballs consist of pure naphthalene. ...
-1
votes
1answer
26 views

How is this trigonometric substitution achieved for this simple capacitor circuit equation?

In a simple circuit with one capacitor and one AC source, where the equation of the source voltage is v(t) = Acos(ωt), I was trying to follow how they found the ...
1
vote
0answers
60 views

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 = ...
4
votes
3answers
132 views

Is there a way to see that $ \nabla_\mu g_{\nu \rho} = 0 $ without explicit computation, where $\nabla_\mu$ refers to the covariant derivative?

In books, it is usually said that this is a consequence of the fact that parallel transport preserves dot product. How ?
0
votes
1answer
56 views

How do I set when the object isn't moving

I started studying instantaneous velocity derivatives using only now. It may seem stupid but really I'm not sure whether that's right: I have an equation: $$x (t) = 1.5t - 9,75t³$$ To set the time ...
1
vote
1answer
95 views

Covariant derivative ordering

I was working on a problem involving Bianchi identities, in a particular case I have to take the covariant derivative of the following, which indeed is the Ricci tensor in linearised limit ...
2
votes
1answer
63 views

How can the D'Alembertian of a field be interpreted intuitively?

The D'Alembertian operator is defined as $$ \Box = g^{\nu\mu}\nabla_\nu\nabla_\mu $$ For the Minkowski metric in Cartesian coordinates that is $$ \Box=\frac{1}{c^2}\frac{\partial^2}{\partial t^2} - ...
1
vote
1answer
52 views

Partial derivatives of chiral superfields with respect to scalar components in the superpotential

I am following some notes on supersymmetry by Matteo Bertolini and I need some clarification. Chapter five deals with sypersymmetric Lagrangians and the superpotential is introduced. It is stated ...
0
votes
1answer
105 views

Classical Mechanics, The Theoretical Minimum: error in answer to partial derivatives exercise? [closed]

I'm reading Leonard Susskind's Classical Mechanics, The Theoretical Minimum, and I'm on the interlude on partial derivatives. There is an exercise that asks you to find all of the first and second ...
1
vote
0answers
41 views

Specific heat at constant volume

Me and my friend came across this derivation is some lecture notes of our thermal physics module. We have been trying to calculate the partial differential of the internal energy but cannot get the ...
0
votes
0answers
85 views

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 ...
1
vote
2answers
94 views

Total time derivative of magnetic vector potential $A$

I am looking at this document, which tries to establish the Lagrangian of the Lorentz force. Everything is fine, but I don't see why: $$\frac{dA_i}{dt}=\frac{\partial A_i}{\partial t}+\frac{\partial ...
1
vote
1answer
118 views

Proof for Negele and Orland equation (2.34)

The equation (2.34) of Negele and Orland has $$\mathcal H_\text{A}(\hat{\mathbf p},\hat{\mathbf x}) = \frac{1}{2m}\left(\hat {\mathbf p} - \frac e c \mathbf A(\hat{\mathbf x})\right)^2.\tag{2.34a}$$ ...
3
votes
1answer
81 views

Why is the gauge potential $A_{\mu}$ in the Lie algebra of the gauge group $G$?

If we have a general gauge group whose action is $$ \Phi(x) \rightarrow g(x)\Phi(x), $$ with $g\in G$. Then introducing the gauge covariant derivative $$ D_{\mu}\Phi(x) = ...
1
vote
1answer
52 views

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 ...
14
votes
4answers
488 views

Lie derivative vs. covariant derivative in the context of Killing vectors

Let me start by saying that I understand the definitions of the Lie and covariant derivatives, and their fundamental differences (at least I think I do). However, when learning about Killing vectors I ...
0
votes
1answer
76 views

Varying wrt metric [closed]

I saw people write $\frac{\partial( F^{ab} F_{ab})}{\partial g^{ef}}$ as $\frac {\partial (g^{ca}g^{db}F_{cd}F_{ab})}{\partial g^{ef}}$ in a way that exposes the dependence on the metric. but ...
2
votes
2answers
81 views

Lack of rigour in usual derivation of Work-Energy Theorem

The derivation of the Work-Energy theorem usually goes as follows: You define the work done on a particle under net force $\vec{F}$ as $$W=\int\limits_C \vec{F}\cdot\mathrm{d}\vec{r}$$ And then you ...
2
votes
2answers
103 views

Differential operators in curvilinear coordinates

In the appendix A of Griffith's Electrodynamics text, he cites Spivak's Calculus on Manifolds as a reference more a more complete treatment of taking the gradient, curl, divergence, and Laplacian in ...
0
votes
2answers
56 views

Eulerian mass conservation on a stream line to Lagrangian mass conservation

if the density of a fluid particle is conserved on a streamline, $$\frac{d\rho}{dt}=0.$$ Why does this mean $$\frac{\partial \rho}{\partial t}+(\mathbf{v}\cdot\nabla)\rho=0$$ is true everywhere? Why ...
1
vote
0answers
73 views

How is Infinitesimal coordinate transformation related to Lie derivatives?

I am reading the book "Gravitaion and Cosmology" by S. Weinberg. In section 10.9, while discussing Lie derivatives of tensors of different ranks, he makes a general comment: The effect of an ...
1
vote
1answer
59 views

Lagrangian formalism (demonstration)

My question is about the multiplicity of the Lagrangian to a Physics system. I pretend to demonstrate the following proposition: For a system with $n$ degrees of freedom, written by the ...
1
vote
1answer
79 views

What is the function type of the generalized momentum?

Let $$L:{\mathbb R}^n\times {\mathbb R}^n\times {\mathbb R}\to {\mathbb R}$$ denote the Lagrangian (it should be differentiable) of a classical system with $n$ spatial coordinates. In the action ...
0
votes
1answer
54 views

Show $\frac{\partial T}{\partial \dot q_j} = m_i \dot r_i^T\frac{\dot r_i }{\partial \dot q_j} $ [closed]

This is a basic result in lagrangian mecanics. Let $T$ be the kinetic energy, $r_i$ be the position of the $i^{th}$ particle in the system I need to show $$\frac{\partial T}{\partial \dot q_j} = ...
5
votes
1answer
257 views

Physical intuition/interpretation of fractional derivatives/integrals?

Oftentimes, when the derivative and integral operations are introduced within the realm of physics, we are taught some physical interpretation of them: Velocity is the derivative of position ...
2
votes
1answer
64 views

Estimating divergence of set of vectors

I have a set of points where directions and intensities of a flow are given (in 3D). Is it possible to estimate the divergence of the flow defined by those vectors? I only need a rough estimate and I ...
0
votes
1answer
43 views

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.
0
votes
1answer
66 views

Lie derivative in this paper [closed]

In this paper http://arxiv.org/abs/1210.2332 it says in (3.19) p. 8 that $$L_{V}z^A =0$$ but I don't know much about Lie derivatives except what I saw now through wikipedia ...
0
votes
1answer
74 views

I need help with divergence and gradient? [closed]

$$A_z = \mu{\frac{e^{-jBr}}{4\pi r}}∫I(z')e^{jBz'\cos\theta}dz'$$ Midway into my question, I want to compute: $$-j\left( \frac{\nabla(\nabla\cdot A) }{w\mu\varepsilon} \right).$$ Symbols like $ w, ...
0
votes
1answer
76 views

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 ...
0
votes
1answer
84 views

Geodesic equation

I have a technical question about the geodesic equation. Assume we have a frame $(E_{1},E_{2},E_{3},E_{4})$ (not necessarily a coordinate frame). Assume we have a parametrized curve $\gamma(s)\in M$ ...