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Results tagged with homework-and-exercises
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user 21270
Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.
27
votes
1
answer
17k
views
Lorentz Invariant Integration Measure [closed]
When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by
$$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$
How can I show that …
- 3,053
0
votes
0
answers
91
views
Coordinate Transformation in Mass-Pulley Problems
Let's say we want to determine the tension $T$ of the rope in the setup above.
For the mass $m_1$, in $XOY$ coordinate system, Newton's 2nd law yields
$$m_1 a_1 \, \hat{x} = T \, \hat{x} - m_1 g …
- 3,053
0
votes
1
answer
187
views
Parametric equations of a hypersurface
In light-front QFT, in the Minkowski space, we define a hypersurface, $\Sigma_+ : x^3+ x^0 = 0 $. How can I write its parametric equations?
- 3,053
3
votes
How do I evalute $\langle n|x^2 |n\rangle$ using the annihilation and creation operators?
I am assuming that the question is in the context of $1D$ simple harmonic oscillator.
If you consult any introductory quantum mechanics textbook, you will see that $\hat{x}$ can be written as $K(\ha …
- 3,053
2
votes
1
answer
306
views
Derivatives with Two Indices in Electromagnetic Lagrangian [duplicate]
I was reading about the derivation of Maxwell's equations from an electromagnetic Lagrangian density from Sean Carroll's Spacetime and Geometry: An Introduction to General Relativity. The Lagrangian d …
- 3,053
4
votes
2
answers
2k
views
Unitary spacetime translation operator
Srednicki writes: We can make this a little fancier by defining the unitary spacetime translation operator
$$ T(a) \equiv \exp(-iP^\mu a_\mu/ \hbar) $$
Then we have
$$ T(a)^{-1} \phi(x) T(a) = \ …
- 3,053
1
vote
1
answer
388
views
Derivation of Equation 2.27 from Peskin & Schroeder
In Section 2.3, Peskin & Schroeder discusses the quantization of real scalar field in Schrodinger picture. He writes Eq. (2.25) as follows.
$$\phi(\textbf{x}) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sq …
- 3,053
0
votes
Relation between Green’s functions and connected Green’s functions
From the given expression for $C_n$ we can write,
$$C_n = \left[ \frac{\partial^n W(J)}{\partial J^n}\right]_{J=0},$$
where $W(J) = \ln Z(J) = \ln \left[\sum_{n=0}^{\infty}\frac{1}{n!} J^n G_n\right]$ …
- 3,053
1
vote
2
answers
170
views
Relation between Green’s functions and connected Green’s functions [closed]
I attempt to understand the $0$-dimensional QFT from these QFT lecture notes by Ronald Kleiss from 2019. The author defines the generating function $Z(J)$ and its logarithm in the following way.
$$Z(J …
- 3,053
0
votes
4
answers
9k
views
Limitation of Gauss's Law
We can use Gauss's law to find out the electric field $\vec{E}(\vec{r})$ due to an infinite cylinder of charge.
But if the cylinder is of finite length then it is said that $|\vec{E}(\vec{r})|$ is …
- 3,053
-2
votes
2
answers
409
views
Tension Forces between Different Blocks [closed]
For the mass $m_1$,
$$m_1\textbf{a}_1 = \textbf{T}_1$$
For the mass $m_2$,
$$m_2\textbf{a}_2 = \textbf{T}_2 + (-\textbf{T}_1)$$
For the mass $m_3$,
$$m_3\textbf{a}_3 = T_2 \hat{y} - m_3 g \hat{y}$ …
- 3,053