Tagged Questions
6
votes
3answers
207 views
Why is the Dirac equation not used for calculations?
From what I understand the Dirac equation is supposed to be an improvement on the Schrödinger equation in that it is consistent with relativity theory. Yet all methods I have encountered for doing ...
2
votes
2answers
85 views
Sign convention for basic Dirac equation
The dirac equation;$$(i\gamma^\mu\partial_{\mu} - m)\psi=0 $$ is just; $$(i\gamma^{0}\partial_{0} - i\gamma^{i}\partial_{i} - m)\psi=0 $$ in a (+,---) metric right?
1
vote
0answers
158 views
Matrix manipulation for Dirac matrices
From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix}
0 & \sigma^i \\
-\sigma^i & 0
\end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix}
I & 0 \\
0 & -I
...
6
votes
2answers
370 views
Charge conjugation in Dirac equation
According to Dirac equation we can write,
\begin{equation}
\left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0
\end{equation}
We seek an equation where $e\rightarrow -e $ and which ...
3
votes
2answers
195 views
Matrix operation in dirac matrices
If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ?
...
3
votes
2answers
352 views
Lorentz transformations in Dirac equation
Let's denote a spinor $\xi$. If $(\theta ,\phi)$ are the parameters of a rotation and pure Lorentz transformation, then how $\xi$ could be written as
$$\xi ~\rightarrow~ \exp\left(\ i ...
2
votes
1answer
219 views
Explanation of equation that shows a failed approach to relativize Schrodinger equation
I'm reading the Wikipedia page for the Dirac equation:
$\rho=\phi^*\phi\,$
......
$J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$
with the conservation of probability ...
1
vote
2answers
325 views
Spin matrices in Dirac equation
Why in every textbook when deriving Dirac's equation the smallest possible matrices ($2 \times 2$) are used?
I wonder why one couldn't use spin 1 matrices ($3 \times 3$) and get relativistic equation ...
2
votes
1answer
397 views
What is the exponential form gamma matrix for a general rotation and boost?
It would be nice to have a cute method that uses Lorentz transformations of basis vectors by exponential transformation using gamma matrices. To avoid confusion, let's assume -+++ signature. Given ...
