All Questions
Tagged with special-relativity spinors
60
questions with no upvoted or accepted answers
5
votes
0
answers
666
views
Why parity exchanges right handed and left handed spinors
Reading through David Tong lecture notes on QFT.
On pages 94, he shows the action of parity on spinors. See below link:
QFT notes by Tong
In (4.75) he confirms that parity exchanges right handed ...
user56963
4
votes
0
answers
149
views
Lorentz Invariance of kinetic terms for Weyl Spinors
Just to preface things, this exact question has been asked before here, but I don't feel like the answer really clarifies things for me.
The core issue is that we want to construct a 4-vector that we ...
- 328
3
votes
0
answers
147
views
Is the real spinor representation of the Lorentz group irreducible?
Specifically the $(\frac{1}{2},0)\oplus(0,\frac{1}{2})$ representation. Given that we label representations by the corresponding representations of the complexified Lie group, the direct sum can be ...
- 1,117
3
votes
0
answers
91
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Both formalisms of a chiral multiplet in Supersymmetry
For the description of a chiral multiplet in Supersymmetry there are 2 formalisms, the one I am used to presented for instance in the Supersymmetry Primer of SP Martin which is based on 2-component (...
- 9,778
3
votes
0
answers
330
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Transformations of gamma-matrices through Pauli matrices transformations
I have the transformation law of the Lorentz group for Pauli matrices:
$$
\tag 0 (\sigma^{\mu})_{a \dot {a}}{'} = \Lambda^{\mu}_{\quad \nu} N_{a}^{\quad c}(\sigma^{\nu})_{c \dot {c}}(N^{-1})^{\dot {c}}...
- 6,564
2
votes
0
answers
72
views
Interpretation of "spin-1/2" in classical Dirac field
I emphasize that the proceeding is purely classical physics. Consider the Grassmann-valued field (where $\mathcal{N}$ is a Grassmann number), which is a solution to the Dirac equation, given by
$$\psi(...
- 2,676
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
2
votes
0
answers
43
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Representation theoretic constraints in SUSY algebra
Let's try to build from scratch the SUSY commutator $[Q_\alpha^I, P_\mu]$. We know that the result of this commutator must be a fermonic generator belonging to $(1/2, 0)\otimes(1/2,1/2) \simeq (1, 1/2)...
- 81
2
votes
0
answers
146
views
Angular-momentum of the Dirac spinor theory
The standard Dirac action
$$
S = \int d^4 x \bar \psi (i \gamma^\mu \partial_\mu - m) \psi
$$
is invariant under Lorentz transformation.
In David Tong's lecture note, eq (4.96) lists that the ...
- 669
2
votes
1
answer
472
views
Transformation between left-handed spinors and right-handed spinors
I am learning (Weyl) spinor formalism from Müller-Kirsten and Wiedemann's Introduction to Supersymmetry (2nd Ed., WS, 2010, here). I am quite confused about the transformation between left-handed ...
- 81
2
votes
0
answers
339
views
Observables of Dirac equation
So I learned about the Dirac equation which describes a relativistic free particle with spin $\frac{1}{2}$. I get the mathematics but what i can't find nowhere:
What are the observables of this ...
- 1,012
2
votes
0
answers
377
views
An $SL(2,C)$ representation and Dirac Spinor
In PCT, spin and statistics, and all that book, the following example is given:
Let $S(A)$ be a representation of $SL(2,C)$ given as :
$$S(A)=\frac{1}{2}\left(a^{0} \mathbf{1}+\mathbf{a} \cdot \...
- 305
2
votes
1
answer
805
views
Lorentz Invariance of Weyl Lagrangian
I have been reading 'Quantum Field Theory and the Standard Model' by Schwartz and have gotten stuck on a line of reasoning in Section 10.2.2.
I understand that we can construct a (right-handed) four-...
- 574
2
votes
0
answers
78
views
Four-brackets (Hodges, Momentum Twistors)
I use the reference from Andrew Hodges, available at https://arxiv.org/abs/0905.1473. I am having trouble understanding his use of the four-bracket. I refer to equation 6 and equation 9, where he ...
- 65
2
votes
0
answers
754
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A few doubts with showing Lorentz invariance of Dirac equation and probability current
Trying to understand some about Lorentz invariance and representation theory, I thought that the best way is with an example of application: Show the Lorentz invariance of the Dirac Equation
$$(i \...
- 742