4
votes
0answers
75 views

Dirac equation in curved spacetime - found second derivatives of the metric, violation of the principle of equivalence?

I am working on the Dirac equation on curved spacetime. A Foldy-Wouthuysen transformation was applied to obtain the semiclassical limit of the equation to study the dynamics of the spin of the ...
0
votes
0answers
34 views

How to find an action of $(\hat {\sigma} \cdot \hat {\mathbf L} )$ on spherical spinors?

Let's have the spherical spinors $\psi_{j, m, l = j \pm \frac{1}{2}}$, $$ Y_{j, m, l = j \pm \frac{1}{2}} = \frac{1}{\sqrt{2l + 1}}\begin{pmatrix} \pm \sqrt{l \pm m +\frac{1}{2}}Y_{l, m - \frac{1}{2}} ...
1
vote
2answers
156 views

Which of these two different forms of spin-orbit interaction is correct?

I am seeing the spin-orbit interaction in two different ways: $\lambda [\mathbf{p} \times \nabla V]\cdot \sigma$ $\lambda [\nabla V \times \mathbf{p}]\cdot \sigma$ I don't see how these two ...
2
votes
1answer
120 views

Spin tensor and Lorentz group operator in bispinor case

For infinisesimal bispinor transformations we have $$ \delta \Psi = \frac{1}{2}\omega^{\mu \nu}\eta_{\mu \nu}\Psi , \quad \delta \bar {\Psi} = -\frac{1}{2}\omega^{\mu \nu}\bar {\Psi}\eta_{\mu \nu}, ...
1
vote
1answer
222 views

Negative probability and spin-0 scalar field in Klein-Gordon equation

Klein-Gordon equation in quantum field theory is known to suffer from the possibility of negative probability. So, the question is, despite this, Klein-Gordon describes spin-zero field. So, how can ...
3
votes
4answers
1k views

Why would Klein-Gordon describe spin-0 scalar field while Dirac describe spin-1/2?

The derivation of both Klein-Gordon equation and Dirac equation is due the need of quantum mechanics (or to say more correctly, quantum field theory) to adhere to special relativity. However, excpet ...
2
votes
1answer
316 views

Magnetic moment derivation from Dirac equation

I am reading a text book where they show the electron has spin 1/2 using Dirac's equation. At one point in the derivation they define $\pi=P-qA/c$ where $P$ is the momentum operator and A is the ...
4
votes
4answers
1k views

Where is spin in the Schroedinger equation of an electron in the hydrogen atom?

In my current quantum mechanics, course, we have derived in full (I believe?) the wave equations for the time-independent stationary states of the hydrogen atom. We are told that the Pauli Exclusion ...
5
votes
4answers
1k views

Why are four-vectors needed in the Dirac equation, when there are 4 linearly independent 2D matrices?

I was taught that for the Dirac-equation to "work", you need matrices of the following form: $Tr(\alpha^i) = 0$. Eigenvalues +1 or -1 2 previous points together: equal number of negative and ...