The dirac-equation tag has no wiki summary.
9
votes
1answer
219 views
How is the Dirac adjoint generalized?
I am wondering how one can generalize the Dirac adjoint to flat "spacetimes" of arbitrary dimension and signature. To be more specific, a standard situation would be to consider 4 dimensional ...
3
votes
1answer
207 views
Energy spectrum of a Dirac electron
How do you explain easily "The spectrum of an electron in a repulsive potential " and hence "bound state of charge conjugation" in Dirac hole theory ?
3
votes
0answers
107 views
Dirac action and conventions
I have a (possibly) fundamental question, which is driving me crazy.
Notation
When considering the Dirac action (say reading Peskin's book), one have
$\int ...
2
votes
0answers
69 views
Relativistic genarization of Quantum Harmonic Oscillator
I am trying to find out relativistic description of a quantum harmonic oscillator.
For a classical relativistic oscillator mass is a function of co-ordinates(http://arxiv.org/abs/1209.2876).
...
1
vote
0answers
44 views
Lagrangians for non-local equations of motion
Say I have a multicomponent field $X_a(x,t)$ such that I know it Fourier modes satisfy the following equation of motion,
$(\delta_{ab} \partial_t + \Omega_{ab}(t))X_b(k,t) = e^t \int \frac{d^3p ...
1
vote
0answers
53 views
WKB expression for Dirac equation?
given the one dimensional Schroedinger equation
$$ - \frac{\hbar ^{2}}{2m} \frac{d^{2}}{dx^{2}}\Psi(x)+ V(x) \Psi(x) =E_{n}\Psi (x) $$
the WKB method for the energies is $$ (n+1)2\pi \hbar ...
1
vote
0answers
164 views
Matrix manipulation for Dirac matrices
From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix}
0 & \sigma^i \\
-\sigma^i & 0
\end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix}
I & 0 \\
0 & -I
...
1
vote
0answers
63 views
Translate a two dimensional classical Dirac theory to a (1+1)-dim quantum theory
Suppose I have a two dimensional classical Dirac Hamiltonian with $\Psi=(\psi_1,\psi_2)^T$:
$$
H=\int \mathrm{d}x \mathrm{d}y \Psi^\dagger(\sigma^x i\partial_x+\sigma^y i\partial_y+m\sigma^z)\Psi.
$$
...
0
votes
0answers
103 views
Gordon decomposition of Dirac current in spherical coordinates
Is there any meaningful analog of the Gordon decomposition of the Dirac current
$j^\mu = ...
0
votes
0answers
61 views
Is it necessary to use all solutions when calculating an expectation value in a spin state?
I'm given an spinor $\Psi$ which is solution of the Free Dirac equation, such that is an eigenfunction of $\hat{\vec{p}}$ and has positive energy. Then I'm asked to calculate the expectation value of ...
