All Questions
Tagged with special-relativity spinors
212
questions
4
votes
1
answer
266
views
Understanding spinors, double cover and professor's expanation
I'm following an introductory course in QFT, and we are facing the spin group part. I think that most of the details are left apart because it would take too much time to be developd, and my profesor ...
- 361
0
votes
0
answers
47
views
Question about spinor inner products
Let a 2D spinor be given by
$$\chi_2(p)=\pmatrix{\xi^1\\\xi^2}+i\pmatrix{\xi^3\\\xi^4}$$
with the $\xi^i$'s being real for $i=\{1,2,3,4\}$.
Assume, now, that I want to represent this spinor by a real-...
- 3,992
0
votes
0
answers
55
views
Questions on Lorentz generators in Spinor-Helicity formalism
I have read the following PSE posts on Lorentz generators in Spinor-Helicity formalism:
Total Angular Momentum Operator in Spinor-Helicity formalism
Derivation of conformal generators in spinor ...
- 3,992
0
votes
0
answers
112
views
Spin and Representation Theory
So for integer spin, the way I understand it mathematically (in a classical limit), is that under a Lorentz transformation (i.e. change of coordinates), spin $n$ particles transform like rank $n$ ...
- 269
-2
votes
1
answer
103
views
Wavefunction spinor in Dirac equation
Which is the physical interpretation that in Dirac's equation the wavefunction is a spinor?
1
vote
1
answer
101
views
Question on the spinor Indices, in non-relativistic quantum mechanics
I've caught by a loop of:
Standard texts of Non-Relativistic Quantum Mechanics $\to$ Representation theory of Lie groups and Lie algebras of $SO(3)$ and $SU(2)$ $\to$ Discussions of infinitesimal ...
- 315
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
5
votes
1
answer
156
views
How do projective representations act on the QFT vacuum?
Let $U:\mathcal{G}\to \mathcal{U}(\mathcal{H})$ be a unitary projective representation of a symmetry group $\mathcal{G}$ on a Hilbert space $\mathcal{H}$. It satisfies the composition rule:
$$U(g_1)U(...
- 1,455
6
votes
1
answer
236
views
Projective representations of the Lorentz group can't occur in QFT! What's wrong with my argument?
In flat-space QFT, consider a spinor operator $\phi_i$, taken to lie at the origin. Given a Lorentz transformation $g$, we have
$$\tag{1} U(g)^\dagger \phi_i U(g) = D_{ij}(g)\phi_j$$
where $D_{ij}$ is ...
- 1,455
0
votes
0
answers
47
views
$S$-operator for proper Lorentz transformation
By applying infinitesimal Lorentz transformatios successively (with rotation angle $\omega$ around the $\bf n$ axis) one would get
$$\Psi'(x') = \hat{S}\Psi(x) = e^{-(i/4)\omega\hat{\sigma}_{\mu\nu}(\...
- 45
0
votes
0
answers
561
views
Bilinear covariants of Dirac field
In the book "Advanced quantum mechanics" by Sakurai there is a section (3.5) about bilinear covariants, however i can't really find a definition of these objects, neither in the book nor ...
- 59
1
vote
2
answers
100
views
Rotation by 360°, spin-1/2 fermions and quaternions
Rotating a spin-1/2 fermion by 360° multiplies the quantum state by -1.
Representing a continuous 360° rotation as a quaternion is also a multiplication by -1.
Is there a relationship between these ...
- 190
8
votes
3
answers
2k
views
What are Dirac spinors and why did relativistic quantum mechanics need them?
I have a good grasp of the Schrödinger equation and the basics of special relativity But the Dirac equation is alien to me. What are Dirac spinors and why did Dirac use them?
user353451
0
votes
1
answer
97
views
What does quantization of spin have to do with spinors?
A fermion has half-integer spin. In the context of the theory, this means its wavefunction is made of spinors: geometric objects which, under Lorentz rotations, transform in such a way that they ...
- 2,475
0
votes
0
answers
75
views
Is there an analog of $\Lambda^T\eta\Lambda = \eta$ in any representation of the restricted Lorentz group?
The Lorentz group $O(1,3)$ is defined by
$$\Lambda^T \eta \Lambda = \eta \quad(1)$$
which we call the defining representation.
Given an irreducible representation of the restricted Lorentz group $SO^+...
user346886