All Questions
25
questions
1
vote
1
answer
57
views
What happens to the fermion spin when I move around it in a full circle
I would like to understand the actual meaning of the description of a fermion as a spinor. I have a background in QFT and understand the calculations, but there is a leap to the actual experiment ...
- 1,734
0
votes
1
answer
73
views
$2\pi$-rotation of fermionic states vs. fermionic operators
Given a fermionic state $|\Psi\rangle$, a $2\pi$ rotation should transform it as
\begin{equation}
|\Psi\rangle \quad\to\quad -|\Psi\rangle \,,
\end{equation}
On the other hand, given a fermionic ...
- 426
3
votes
0
answers
50
views
Field strength renormalization for fermions
Following section 7.1 and 7.2 in Peskin and Schroeder (P&S), I've tried to consider what the derivation of the LSZ formula looks like for (spin $1/2$) fermions (in the text, they explicitly ...
- 863
0
votes
0
answers
31
views
How to derive Fermion Propagator for Special Kinetic Term?
I am currently working through chapter 75 of the book on QFT by Srednicki. There, he considers the example of a single left-handed Weyl field $\psi$ in a $U(1)$ gauge theory. The Lagrangian, written ...
2
votes
1
answer
74
views
Product of spinors in Dirac field anticommutators
I am reading a "A modern introduction to quantum field theory" by Maggiore and on page 88 it shows the anticommutators of the Dirac field:
$$
\{\psi_a(\vec{x},t),\psi_{b}^{\dagger}(\vec{y},t)...
- 613
3
votes
1
answer
155
views
Mean field and interacting Dirac QFT: channels and spinors
I am dealing with a QFT of Dirac fermions with an interaction term
$$L_I=\bar\psi\psi\bar\psi\psi=\psi^\dagger\gamma^0\psi\psi^\dagger\gamma^0\psi,$$
with $\gamma^0$ a Dirac matrix and $\psi$, $\psi^\...
- 503
1
vote
2
answers
188
views
Massless QED modified Lagrangian
Consider a massless theory of QED, with Lagrangian
$$\mathcal{L}_{QED}=
-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\bar{\Psi}i\gamma^{\mu}\partial_{\mu}\Psi+
e\bar{\Psi}\gamma^{\mu}A_{\mu}\Psi$$
Is there any ...
- 3,992
1
vote
1
answer
108
views
When does the spinor need to be in a Grassmann variable?
Follow the closed question When does the spinor need to be in a grassmann variable?
--
Does the spinor in the spinor representation of the space-time symmetry
Lorentz space-time symmetry, like $so(1,...
- 593
3
votes
2
answers
239
views
Connection between column matrix and Grassmann numbers in Dirac field
In canonical quantization the Dirac equation is a complex column matrix, while in path integral formulation it's Grassmann numbers.
Is there a formula to convert from complex matrix to Grassmann ...
- 925
2
votes
1
answer
138
views
Spinor index, dirac field equation
Sometimes I read anticommute
$$\{\psi(x),\psi^\dagger(y)\}=\delta^{(3)}(x-y)$$
Sometimes,
$$\{\psi_a(x),\psi_b^\dagger(y)\}=\delta^{(3)}(x-y)\delta_{ab}$$
Are they the same, second one just emphasis ...
- 326
0
votes
0
answers
88
views
Scattering right handed fermions
Assume we have a QED like vector exchange, and I scatter only right handed electron-positron pair- ${e}_ R^+ e_R^-\to e_R^+ e_R^-$. Am I correct that
There is no s-channel amplitude-they cannot ...
- 2,758
4
votes
0
answers
102
views
Are there non-lagrangian field theories for massive Weyl spinors?
It is a well-known fact that a chiral fermion is massless, since the mass term involves both a right-handed and a left-handed field. If you have one chirality only there are no mass terms one can ...
-2
votes
2
answers
874
views
Fermion Determinant [closed]
When we calculate fermion determinant for either Majorana or Weyl spinors, why do we get an extra factor of half in the coefficient of the determinant as compared to the Ghost determinant?
5
votes
1
answer
114
views
Internal flavor symmetry of the $N$ left-handed complex Weyl spinors v.s. $N$ real Majorana spinors: ${\rm U}(N)$ vs. ${\rm O}(2N)$ or ${\rm O}(N)$
Consider 4d spacetime, it seems that for massless particles, we can easily change
the left-handed complex Weyl spinor basis (2 component in complex $\mathbb{C}$ for Euclidean spacetime Spin(4))
to
...
- 4,336
2
votes
2
answers
543
views
Can we derive free field expansion formula for the spin-1/2 Dirac field?
The Dirac field has the expansion $$\Psi(x)=\int\frac{d^3p}{\sqrt{(2\pi)^32E_p}}\sum\limits_{s=1,2}\Big(b_s(p)u^s(p)e^{-ip\cdot x}+d^\dagger_s(p)v^s(p)e^{+ip\cdot x}\Big)$$ where $b_s$ and $d_s$ are ...
- 11.8k