All Questions
4 questions
0
votes
0
answers
117
views
Are eigenvalues of slashed covariant derivative real?
I am trying to demonstrate that the slashed covariant derivative
$$
\gamma^\mu D_\mu = \gamma^\mu(\partial_\mu -iA_\mu)
$$
has real eigenvalues:
$$
\gamma^\mu D_\mu \varphi_m(x)=\lambda_m \varphi_m(x)...
- 161
3
votes
1
answer
113
views
How does the $\not{\partial}$ work in the Dirac Lagrangian?
The Dirac Lagrangian (Density) is defined in the text "Quantum Field Theory, An Integrated Approach" by Fradkin as:
$$\mathcal{L}=\bar{\Psi}\left(i\not{\partial}-m\right)\Psi\equiv \frac{1}{...
- 179
-2
votes
1
answer
73
views
How do I keep track of what to differentiate in a Dirac Hamiltonian/Lagrangian?
Suppose we have the dirac Hamiltonian:
$$
H = \int d^3y\bar\psi(y)_b(-i\gamma^k\partial_k+m)_{bc}\psi(y)_c.
$$
My question is should I think the derivative operator $\partial_k$ is acting on the ...
- 1,853
5
votes
1
answer
536
views
What is the definition of $\overleftrightarrow{\partial}$ in Dirac Lagrangian?
In my course, the teacher wrote the Dirac Lagrangian as :
$$ \mathcal{L}=\frac{i}{2} \bar{\psi}\gamma^{\mu}\overleftrightarrow{\partial_\mu} \psi -m \bar{\psi} \psi $$
I just would like to ...
- 1,560