All Questions
10
questions
2
votes
1
answer
120
views
Columns, rows, dotted, undotted, $SL(2, \mathbb{C})$ reps, and building Dirac spinors from Weyl spinors
I'm looking through Introduction to Supersymmetry by Muller-Kirsten and Wiedemann, along with any other resource I can find. I'm specifically trying to understand the concepts and notations for ...
- 213
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
1
answer
88
views
Lorentz transformation of Weyl fields
In the Srednicki's textbook, Chapter 35, the author states (Equation 35.28):
$$
U(\Lambda)^{-1}[\psi^\dagger \bar\sigma^\mu \chi ] U(\Lambda) = \Lambda^\mu_{\,\,\nu} [\psi^\dagger \bar\sigma^\nu \chi ]...
- 86
3
votes
1
answer
352
views
Correct transformation of left-handed Weyl spinor
In the book "Matthew D. Schwartz, Quantum Field Theory and the Standard Model", page 164, it says that a left-handed spinor transforms as
$$\psi_L \rightarrow e^{\frac{1}{2}(i\vec{\theta} - \vec{\...
- 513
1
vote
1
answer
142
views
Sign-Conventions for Spinor Transformations
In the literature one encounters a lot of different conventions for how left-handed spinor transforms (rotation angle $\phi$, rapidity $\beta$), among them
$M_L = M_{(\frac{1}{2}, 0)} = e^{-i \frac{1}...
- 513
0
votes
1
answer
666
views
Transformation of the spinor indices of Hermitian $2\times 2$ matrices under the Lorentz group
The left-handed Weyl operator is defined by the $2\times 2$ matrix
$$p_{\mu}\bar{\sigma}_{\dot{\beta}\alpha}^{\mu} = \begin{pmatrix} p^0 +p^3 & p^1 - i p^2\\ p^1 + ip^2 & p^0 - p^3 \end{...
- 3,203
3
votes
1
answer
402
views
Different definitions of the parity transformation for the Dirac spinors
There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & ...
- 41
3
votes
2
answers
2k
views
Complex conjugation of Weyl Spinors
Let $\chi$ be a left-handed Weyl spinor transforming as $$\delta\chi=\frac{1}{2}\omega_{\mu\nu}\sigma^{\mu\nu}\chi.$$ In my lecture notes it is explicitly stated that complex conjugation interchanges ...
- 1,654
0
votes
0
answers
53
views
Index Placement for Spinors in Relativity
This may ultimately be a silly question, but a pedantic mind like mine gets tied into knots over differing notation. (Disclaimer: I'm a mathematician.)
Let $\mathbb{W}$ be a complex two-dimensional ...
- 913
2
votes
1
answer
378
views
Scalar products in the spinor helicity formalism
In A. Zee's book Quantum Field Theory in a Nutshell (2nd edition), Chapter N.2, page 486, the momentum $p$ is written as a $2\times 2$ matrix:
$$
p_{\alpha\dot{\alpha}} = p_{\mu} (\sigma^{\mu})_{\...
- 1,701