All Questions
Tagged with quantum-electrodynamics spinors
30
questions
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
63
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Commutation behavior of spinors in Feynman diagrams
I am currently playing around with computing cross sections of several simple interactions in QED like Bhabha and Compton Scattering and I have stumbled upon a question which I havent yet managed to ...
- 101
0
votes
1
answer
114
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Question on Spinor choice in QED
In QED (see Peskin and Schoeder's book on QFT or Srednicki's book), to determine the fermion wave-function, we usually start with a spinor of a massive particle that is not moving, say
$$u_+(\vec{p}=\...
- 3,992
0
votes
1
answer
123
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A problematic equation for Dirac field:$[\psi,\hat{J_z}]=J_z\psi+i(x{\partial \psi\over\partial y}-y{\partial\psi\over\partial x})$ How is this true?
The Dirac field is quantized as:
$$\psi(x^\mu)=\int{d^3 p\over(2\pi)^3\sqrt{2\omega_p}}[a_s(p)u_s(p)e^{-ipx}+b_s^{\dagger}(p)v_s(p)e^{ipx}]$$
In the title:$$[\psi,\hat{J_z}]=J_z\psi+i(x{\partial \psi\...
- 619
1
vote
2
answers
87
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How to prove $-i\gamma_2u_{s}^*(p)=v_{s}(p)$ for Dirac spinors?
It should be true and it's obvious for $p^{\mu}=(m,0,0,0)$, but I'm having trouble with the gamma matrices Algebra and prove it for general momentum.
I'm using Weyl representation:
$$u_{\uparrow}=\...
- 619
3
votes
0
answers
102
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Total Angular Momentum operator in spinor-helicity formalism
I am reading Evidence for a new Soft Graviton theorem, by Cachazo and Strominger. At some point, they express the relation
$$J_{\mu\nu}\sigma^{\mu}_{\alpha\dot{\alpha}}\sigma^{\mu}_{\beta\dot{\beta}}
=...
- 3,992
1
vote
1
answer
85
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Basis vectors for quantum electrodynamics
The following unnormalized vectors are solutions to the Dirac equation.
\begin{align*}
u_1&=\begin{pmatrix}E+m\\0\\p_z\\p_x+ip_y\end{pmatrix}
\exp\left(\frac{i\phi}{\hbar}\right)
%
& v_1&=\...
- 23
1
vote
2
answers
191
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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
3
votes
0
answers
290
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Understanding the factorization of subleading soft contributions-massless QED
I am reading The SAGEX Review on Scattering Amplitudes Chapter 11: Soft Theorems and Celestial Amplitudes. In subsection 2.2, the subleading soft photon theorem is derived. The result is
$$A^{\mu}=\...
- 3,992
2
votes
1
answer
133
views
Frenkel or Tulczyjew-Dixon Condition and QED
What is the physical motivation behind imposing Frenkel's condition,
$$p_{\mu}S^{\mu\nu}=0$$
for an electron of momentum $p$ and spin given by some tensor $S^{\mu\nu}$?
In addition, a direct ...
- 3,992
1
vote
1
answer
121
views
Antiparticles of spinors
As far as I know, to couple scalar fields with photons, the fields must be complex, and have two degrees of freedom, which explains why the antiparticles exist. In the spinor cases, spinors themselves ...
- 11
2
votes
1
answer
118
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Peskin and Schroeder chapter 5 - going from gamma matrices to sigma [closed]
I am trying to recreate all steps from 5.97 to 5.103. Can someone explain how to go from 5.97 to 5.99 ? I understand the denominator part, my issue is with the transformation from gamma to sigma ...
0
votes
1
answer
191
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Where does the $i$ come from in the left helicity antimuon spinor?
Context: this appears in $e^{+}e^{-} \rightarrow \mu^{+}\mu^{-}$ scattering.
Page 247 of Larkoski particle physics says $$v_L(p) = \sqrt{2E}(e^{-i\frac{\phi}{2}}\cos(\frac{\theta}{2}), e^{i\frac{\phi}{...
user310742
1
vote
1
answer
257
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Spinor product in QED scattering
Equation 6.36 in Larkoski’s Introduction to Particle Physics says
$v^{\dagger}_{L}\sigma^{\mu}u_R$ =
$E_{cm}(0, -i)(1, \sigma_1, \sigma_2, \sigma_3)\begin{bmatrix}1 & 0\end{bmatrix}$
Which is one ...
user310742
1
vote
0
answers
75
views
Charge Conjugation at Spinors
In the schwartz book, Quantum Field Theory and the Standard Model, at the chapter 11 is define the charge conjugation operator
$C:\;\;\psi\rightarrow-i\gamma^2\psi^*$
$C:\;\;\psi^*\rightarrow-i\gamma^...
