The spinors tag has no wiki summary.
9
votes
1answer
213 views
How is the Dirac adjoint generalized?
I am wondering how one can generalize the Dirac adjoint to flat "spacetimes" of arbitrary dimension and signature. To be more specific, a standard situation would be to consider 4 dimensional ...
8
votes
1answer
118 views
What're the relations and differences between slave-fermion and slave-boson formalism?
As we know, in condensed matter theory, especially in dealing with strongly correlated systems, physicists have constructed various "peculiar" slave-fermion and slave-boson theories. For example,
For ...
6
votes
3answers
563 views
What is the difference between a spinor and a vector or a tensor?
Why do we call a 1/2 spin particle satisfying the Dirac equation a spinor, and not a vector or a tensor?
0
votes
0answers
47 views
Finding the coefficients of a spinor
From the Schrödinger equation of a system I'm investigating, where the wave function is a 4-component spinor of coefficients $C_1, C_2, C_3, C_4$, I am able to obtain the expression
$\begin{pmatrix} ...
5
votes
1answer
106 views
Vector and Spinor Representation in Ramond-Neveu-Schwarz Superstring Theory
I am learning Ramnond-Neveu-Schwarz Superstring theory (RNS theory). I often find the following notation, especially in the closed string spectrum etc.:
$$\mathbf{8}_s,\mathbf{8}_v $$
And it is ...
3
votes
0answers
39 views
Spinors on algebraic plane curves
I'm interested in parameterizing spinors on Riemann surfaces. For my purposes, it's best to represent the Riemann surfaces as immersed in $\mathbb{C}P^2$, i.e. as algebraic plane curves. Apparently, ...
5
votes
0answers
101 views
Has hep-th/0312070 forgotten to fix $s_{0} = 1/2$ for the fermionic states in the second table on page 52?
Link to the original paper: The Gauge/String Correspondence Towards Realistic Gauge Theories (arXiv paper)
On page 52 we see that, for a theory of Dp-branes placed at an orbifold (orbifold = ...
2
votes
2answers
134 views
Two ways to form SU(2) singlets?
I am trying to reconcile the two ways of forming SU(2) singlets out of a pair of doublets.
Method (1):
If $v=\begin{pmatrix}v^1\\ v^2\end{pmatrix}$ and $w=\begin{pmatrix}w^1\\ w^2\end{pmatrix}$ are ...
4
votes
3answers
231 views
Difference between spinor and vector field [duplicate]
How do we distinguish spinors and vector fields? I want to know it in terms of physics with mathematical argument.
0
votes
4answers
365 views
Could one argue that h (Planck constant) and $\hbar$/2 (Dirac constant) are in fact independant constants?
My question is very naive and could sound strange but it seems to me natural in so far as the Planck constant is related to the first quantization (of newtonian particle mechanics/galilean relativity) ...
5
votes
1answer
100 views
Do Killing spinors know global information?
The conformal Killing spinor equations on $R\times S^3$ in Minkowski signature are
\begin{equation}
\nabla_\mu \epsilon=\pm \frac{i}{2}\gamma_\mu\gamma^0\gamma^5\epsilon
\end{equation}
whose solution ...
19
votes
2answers
63 views
Kerr Geometry, Separability and Twistors
One of the remarkable properties of the Kerr black hole geometry is that scalar field equations separate and are exactly solvable (reducible to quadrature), even though naively it does not have enough ...
4
votes
2answers
239 views
Number of Components of a Spinor
I'm trying to develop my understanding of spinors. In quantum field theory I've learned that a spinor is a 4 component complex vector field on Minkowski space which transforms under the chiral ...
3
votes
1answer
106 views
Inner product of particle-anti-particle spinor components
Suppose I have four-component spinors $\Psi$ and $\bar \Psi$ satisfying the Dirac equation with
$$\Psi(\vec x) = \int \frac{\textrm{d}^3 p}{(2\pi)^3} \frac{1}{\sqrt{2 E_{\vec p}}} \sum_{s = \pm ...
2
votes
1answer
140 views
How quantum field transforms in case of some particular spin
Except when a particle is spin-0, field of all particles transforms when frame of reference is changed, and this defines what spin is. The question is, specifically how does the quantum field ...
2
votes
1answer
246 views
How to construct the charge conjugation matrix for any given dimension?
Generally, Gamma matrices could be constructed based on the Clifford algebra.
\begin{equation}
\gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij},
\end{equation}
My question is how to generally ...
2
votes
1answer
214 views
Is Thirring model a particular case of Gross model?
Look at this: http://en.wikipedia.org/wiki/Gross-Neveu_model
Wikipedia sais "When N=1 it reduces to the integrable Thirring model". but the aditional term in thirring model is ...
4
votes
2answers
224 views
Relation for Dirac-spinors of different helicities
Assume that we have massless spin-1/2 particles. The Dirac-spinor is the solution of the Dirac equation:
$$ p^\mu \gamma_\mu u_\pm(p) = 0, \quad p^2 = 0$$
The subscripts $\pm$ denote two different ...
3
votes
1answer
164 views
Symmetrical Spinors and Symmetrical Tensors
In Quantum Electrodynamics by Landau and Lifshiz there is the following:
The correspondence between the spinor $\zeta^{\alpha \dot{\beta}}$ and
the 4-vector is a particular case of a general ...
3
votes
1answer
179 views
Twistor notation in space-time (Part 1)
This is sort of a continuation of this and this previous discussions.
In the first of my links one sees the surjective isometry between real or complex $(1,3)$ signature Minkowski space and the real ...
3
votes
0answers
146 views
Some more questions on conformal spinors of $SO(n,2)$
This is somewhat of a continuation of my previous question.
I had stated there that a conformal spinor ($V$) of $SO(n,2)$ can be created by taking a direct sum of two $SO(n-1,1)$ spinors $Q$ and $S$ ...
3
votes
1answer
164 views
Lorentz spinors of $SO(n,1)$ and conformal spinors of $SO(n,2)$
It would be great if someone can give me a reference (short enough!) which explains the (spinor) representation theory of the groups $SO(n,1)$ and $SO(n,2)$.
I have searched through a few standard ...
5
votes
1answer
93 views
Is there a review article that discusses the various suggestions for approaches to the Dirac spinor field?
I've come across many approaches to the Dirac spinor field over the years. A few have held more than passing interest but most of them are rather forgettable, so that I'd like to know of any reviews ...
3
votes
1answer
205 views
Spinor integration
I am learning on-shell methods for one loop integrals from this paper: Loop amplitudes in gauge theory: modern analytic approaches by Britto. Starting with formula (18) spinor integration is ...
4
votes
1answer
125 views
What is the definition of precession (in the context of Spinors)?
What is the definition of "precession"? How is it applicable to abstract objects such as Spinors? I understand the mathematics, but don't understand what one means by "precession angle" etc when it ...
8
votes
0answers
437 views
Could this model have soliton solutions?
$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$
Field equation $(i\gamma^\mu\partial_\mu-m+g\bar{\Psi}\Psi)\Psi=0$
Could this model have soliton ...
2
votes
0answers
112 views
Spin 1/2 finite-difference field simulator?
Is there a finite-difference field simulator for spin 1/2 fields, something like meep for electromagnetism (spin 1)? Looking for something free (GNU, MIT or other open/free style license) and easy ...
3
votes
2answers
281 views
Four vectors from spinors
In Exercise 2.3 of A modern introduction to Quantum Field Theory by Michele Maggiore I am asked to show that, if $\xi_R$ and $\psi_R$ are right-handed spinors, then
$$ V^\mu = \xi_R^\dagger \sigma^\mu ...
3
votes
2answers
650 views
parallel/anti-parallel vs. triplet/singlet description of two spins
If we consider two spins, we can think of the spins as being either parallel (up|up or down|down)or anti-parallel (up|down or down|up).
Or we can think of them as being in the triplet or singlet ...
0
votes
1answer
144 views
How to apply Andreev reflection formalism to ferromagnet ,normal metal interface?
The traditional formalism for andreev reflection deals with what happens at normal metal, super conductor interface.http://en.wikipedia.org/wiki/Andreev_reflection
(i.e when an electron from normal ...
6
votes
4answers
946 views
covariant derivative for spinor fields
scalars (spin-0) derivatives is expressed as:
$$\nabla_{i} \phi = \frac{\partial \phi}{ \partial x_{i}}$$
vector (spin-1) derivatives are expressed as:
$$\nabla_{i} V^{k} = \frac{\partial V^{k}}{ ...
