I have made an attempt at this exercise: Is the following alright?:
If we take ##\mathcal{E}=\mathbb{R}##, and ##\gamma:\mathcal{E}\rightarrow \mathbb{R}^2## defined by ##\gamma u=(x(au),au)##, for ##u\in \mathcal{E}=\mathbb{R}##, then ##\gamma_∗...
I have made an attempt at this exercise: Is the following alright?:
If we take ##\mathcal{E}=\mathbb{R}##, and ##\gamma:\mathcal{E}\rightarrow \mathbb{R}^2## defined by ## \gamma u= (x(au),au),## for ##u\in \mathcal{E}=\mathbb{R}##,
then...
I am trying to study "religiously" the book by Sachs and Wu, but I am finding the Exercises very much of a challenge. Does anyone know if there exists a source for solutions one can consult when stuck?
As $f\circ f^{-1}=\textrm{id}$, we obtain $(Df)(f^{-1}(x))\cdot (Df^{-1})(x)=\textrm{id}$, and so we see that $(Df)(f^{-1}(x))$ is an invertible matrix, and also $(Df^{-1})(x)=((Df)(f^{-1}(x)))^{-1}$, and by Cramer's Rule,
we see that the $(i,j)$th entry of $Df^{-1}(x)$ is given by a...
Actually, I now realize that the Chain Rule does help, and probably the "0" in the hint is a typo, and is probably meant to be an identity, with the partial derivative replaced by derivative of as a map from R^d to R^d.
Then f o f^{-1}=id , the Chain Rule , and the Inverse Function Theorem...
I am studying Choquet-Bruhat's Introduction to General Relativity, Black Holes and Cosmology, and I don't follow the hint in Exercise I.2.1:
Exercise I.2.1 Let U,V be open subsets of R^d. Prove that a C^1 diffeomorphism f:U-->V with f of class C^k is a C^k diffeomorphism.
Hint: ##\partial (f...
Hi,
In a p-p collision, where a we look at u ubar → γ → f fbar, where f is a fermion,
what channels are available for f? Is f also allowed to be the top quark?
In an analogous process where the γ is replaced for example by the Z0 boson,
the book by Kane takes f to be all except the top...
Hello,
I am struggling to see why for a fermionic field $\psi$, one has the time ordered contraction $<0|T(\psi(x)\psi(y))|0>$. Could someone offer an outline/hints to see this please? Thanks!
Yes, my understanding was that S^1 is the 4x4 matrix with the 2x2 matrices (1/2)*sigma^1 as its diagonal blocks.
Then if what Zeidler's claim is true, this S^1 ought to kill the 4x1 column vector u appearing in the wave function, but it does not.
What am I doing wrong? Thanks!
@dextercioby: Yes, thanks for the suggestion. I should have done it the first time round, but the notation is rather heavy, and it is hard to type it all. So I have uploaded the images of 3 relevant pages. :) I wonder it it will help. Thanks!
Hello!
I am studying Zeidler's QFT Volume II, and I have a query on page 808:
It is claimed that
S Ψ^+_{p,s} = (sk)Ψ^+_{p,s} when p=p^3 k.
I tried my hand at deriving this, but when we write S=S^1i+S^2j+S^3k,
then the S^3k term acting on Ψ^+_{p,s} does give skΨ^+_{p,s},
but I don't see...