All Questions
Tagged with conventions dirac-matrices
40
questions
2
votes
1
answer
51
views
$CP$-transformation for fermionic bilinears
I am trying to derive the transformation of the fermionic bilinear $\bar{\psi}\psi$ under $CP$ transformation.
I know that $P$ acts as:
$$\psi(t, \vec{x}) \xrightarrow{P} \gamma^0 \psi(t, -\vec{x})$$
...
0
votes
1
answer
35
views
Question about meaning of "bar"-ing in the context of Dirac fields
Following chapter 38 of Srednicki, "bar"-ing means (based on eq. 38.15)
$$\bar{A} = \beta A^\dagger\beta$$
One can show for instance that $$\bar{\gamma^\mu} = \gamma^\mu$$ My question is, ...
- 1,713
1
vote
1
answer
70
views
Why does Dirac bilinear $\bar{\psi}\sigma^{\mu\nu}\psi$ is frequently written with a factor of $i$?
The tensor Dirac bilinear $\bar{\psi}\sigma^{\mu\nu}\psi$ has the matrix tensor $\sigma^{\mu\nu}=\frac{i}{2}\left[\gamma^\mu,\gamma^\nu\right]$.
I can understand that the factor of $\frac{1}{2}$ is a ...
- 925
1
vote
0
answers
49
views
Is the sign of the mass in the Dirac action irrelevant? [duplicate]
In even dimensions all the representations of the gamma matrices are equivalent, in particular $\gamma^\mu$ and $-\gamma^\mu$ are equivalent. Usually the Dirac Lagrangian is
\begin{equation}
\psi^\...
- 106
1
vote
0
answers
137
views
About Einstein's sum rule and Dirac equation
I am studying the Dirac equation and I'm having some trouble about something that I think should be trivial. I'm working in a (1+1)-dimensional Minkowski spacetime with signature $(+, -)$, i.e., $ds^2=...
- 503
0
votes
1
answer
480
views
Pauli matrices: lower index vs upper index
I have read some identities about the Pauli matrices in 4-vector notation and I am a little confused. as $$\sigma ^\mu=(I,\sigma ^i);\qquad \overline{\sigma}^\mu=(I,-\sigma ^i).$$
But what exactly is $...
- 326
0
votes
1
answer
125
views
$\displaystyle{\not}{a}\displaystyle{\not}{a} = a^2$ or $-a^2$ in Srednicki
I'm confused: In Srednickis Book (Equation 37.26), he has:
$$\displaystyle{\not}{a}\displaystyle{\not}{a} = -a^2$$
However, every other source I found (for example this SE question says that it's:
$$\...
- 6,763
2
votes
0
answers
119
views
(Non-)Hermiticity of Dirac operator
I have a Dirac operator given by
\begin{equation}
D\!\!\!/[A, A^{5}]=\gamma^\mu D_\mu=\gamma^\mu (\partial_{\mu} - {\rm i} A_{\mu} - {\rm i} \gamma_{5} A_{\mu}^{5}),
\end{equation}
where $A_{\mu}$ ...
- 374
0
votes
1
answer
230
views
Does $\{\gamma^\mu,\gamma^\nu\}=2g^{\mu\nu}\mathbb1$ determine the hermiticity of the gamma matrices?
If I remember correctly, the derivation of the Dirac equation requires that $\gamma^0$ is Hermitian while $\gamma^i$ for $i=1,2,3$ is anti-Hermitian. This is clearly true for the standard Dirac ...
- 1,215
0
votes
1
answer
53
views
Expression of $\not{p}$ in Dirac equation
In scattering amplitudes, page 9, equation (2.6), (2.7), $\not{p}$ (in the Dirac equation (2.4)) is as follows:
\begin{align}
\not{p} = \left( \begin{matrix} 0 & p_{a\dot{b}} \\ p^{\dot{a}b} & ...
- 257
3
votes
1
answer
237
views
Sign error when deriving Weyl spinor transformation laws (3.37) in Peskin Schroesder
I am having some trouble deriving the transormation laws for the weyl spinors, equation (3.37) in the Peskin Schroesder book on quantum field theory.
Beginning with the relation $\psi\to(1-\frac{i}{2}\...
- 173
1
vote
2
answers
176
views
Missing sign in Dirac equation
This is very trivial, but it's really bugging me. The ansatz for the Dirac equation in terms of $\boldsymbol\alpha$ and $\beta$ matrices is
$$
[i(\partial_t+\boldsymbol\alpha\cdot\boldsymbol\nabla)-\...
2
votes
1
answer
289
views
$\gamma^5$ rotation of chiral fermion in (1) Peskin&Schroeder, (2) Weinberg, or (3) Srednicki
The theta angle due to the chiral gamma^5 rotation of chiral fermion results in the phase alpha(x) that has different + or - sign for
(1) Peskin&Schroeder, (2) Weinberg or (3) Srednicki.
Here
...
- 4,336
1
vote
1
answer
217
views
Sign of pair of Dirac spinor bilinear
I don't understand the following statement: Any pair of Dirac spinors verifies $(\bar{\Psi}_1\Psi_2)^\dagger=\bar{\Psi}_2\Psi_1$ and it is valid for both commuting and anti-commuting (Grassmann-valued)...
- 129
1
vote
1
answer
202
views
Is this a typo in Peskin's QFT?
In ''An intro to QFT (2018)'' chapter 3, Peskin does the following:
Let me introduce some notation first, let $v^s_k=\begin{pmatrix}\;\;\,\sqrt{k\cdot\sigma}\,\xi^{-s}\\-\sqrt{k\cdot\bar{\sigma}}\,\...
- 266