Dear reader,
there is a physics problem where I couldn't understand what the solutions.
It is about the lorentz transformation of a bilinear spinor matrix element thing.
So the blue colored equation signs are the parts which I couldn't figure out how.
There must be some steps in between which...
I read this question
https://physics.stackexchange.com/questions/95970/under-what-conditions-is-a-vector-spinor-gamma-trace-free . Also I read Sexl and Urbantke book about groups. But I dont understand why spinors is irreducible if these are gamma-tracelees. Also I read many papers about higher...
Hello everybody!
I have a doubt in using the chiral projection operators. In principle, it should be ##P_L \psi = \psi_L##.
$$ P_L = \frac{1-\gamma^5}{2} = \frac{1}{2} \begin{pmatrix} \mathbb{I} & -\mathbb{I} \\ -\mathbb{I} & \mathbb{I} \end{pmatrix} $$
If I consider ##\psi = \begin{pmatrix}...
Homework Statement
Let ##\vec{e}\in\mathbb{R}^3## be any unit vector. A spin ##1/2## particle is in state ##|\chi \rangle## for which
$$\langle\vec{\sigma}\rangle =\vec{e},$$
where ##\vec{\sigma}## are the Pauli-Matrices. Find the state ##|\chi\rangle##
Homework Equations :[/B] are all given...
I'm studying QFT by David Tong's lecture notes.
When he discusses causility with real scalar fields, he defines the propagator as (p.38)
$$D(x-y)=\left\langle0\right| \phi(x)\phi(y)\left|0\right\rangle=\int\frac{d^3p}{(2\pi)^3}\frac{1}{2E_{\vec{p}}}e^{-ip\cdot(x-y)},$$
then he shows that the...
Homework Statement
I am given the Rashba Hamiltonian which describes a 2D electron gas interacting with a perpendicular electric field, of the form
$$H = \frac{p^2}{2m^2} + \frac{\alpha}{\hbar}\left(p_x \sigma_y - p_y \sigma_x\right)$$
I am asked to find the energy eigenvalues and...
Homework Statement
I am currently working on an exercise list where I need to calculate the second functional derivative with respect to Grassmann valued fields.
$$
\dfrac{\overrightarrow{\delta}}{\delta \psi_{\alpha} (-p)} \left( \int_{x} \widetilde{\bar{\psi}}_{\mu} (x) i \partial_{s}^{\mu...
Here it is a simple problem which is giving me an headache,
Recall from class that in order to build an invariant out of spinors we had to introduce a somewhat
unexpected form for the dual spinor, i.e. ߰ψ = ψ†⋅γ0
Then showing that ߰ is invariant depends on the result that (ei/4⋅σμν⋅ωμν)† ⋅γ0...
Context
The following is from the book "Ideas and methods in supersymmetry and supergravity" by I.L. Buchbinder and S.M Kuzenko, pg 56-60. It is about realizing the irreducible massive representations of the Poincare group as spin tensor fields which transform under certain representations of...
Okay, I have read on spinors here and there but I really don't understand geometrically or intuitively what it is. Can someone please explain it to me and how/when it is used? Thanks!
Hi, i dont find much about spinor spaces. I can think in that spaces like a vector space above the field of complex numbers (a complex vector space)?
sorry if what i saying is a non-sense, but i really want to understand better the math behind the concept of a spinor.
thanks
I have the following system of differential equations, for the functions ##A(r)## and ##B(r)##:
##A'-\frac{m}{r}A=(\epsilon+1)B##
and
##-B' -\frac{m+1}{r}B=(\epsilon-1)A##
##m## and ##\epsilon## are constants, with ##\epsilon<1##. The functions ##A## and ##B## are the two components of a...
In four dimensions, left and right chiral fermion can be written as
\psi_L=
\begin{pmatrix}
\psi_+\\
0
\end{pmatrix},\qquad
\psi_R=
\begin{pmatrix}
0\\
\psi_-
\end{pmatrix},
respectively, where \psi_+ and \psi_- are some two components spinors(Weyl spinors?). In this representation, the...
When I studied General Relativity using Misner, Thorne and Wheeler's "Gravitation", it was eye-opening to me to learn the geometric meanings of vectors, tensors, etc. The way such objects were taught in introductory physics classes were heavily dependent on coordinates: "A vector is a collection...
I was reading in this book: Supergravity for Daniel Freedman and was checking the part that has to do with Extremal Reissner Nordstrom Black Hole. He was using killing spinors (that I am very new to).
I was understanding the theory until he stated with the calculations:
He said that the...
Consider the Spinor object for an electron. Are the non-relativistic and relativistic (Dirac equation) Spinor objects, from a mathematical point-of-view, identical?
Thanks in advance.