Spinors Definition and 130 Threads

I'm working on a realisation of an exceptional group. I'm having some troubles with spinors. Here goes: Given a Weyl-spinor of so(6,6) (let's say the chiral one). Under the decomposition of so(6,6) into so(5,5) + u(1), what does the spinor split into? Two different Weyl-spinors (of so(5,5))...

Suppose we have a real field, S(x,y,z,t), that satisfies E^2 = P^2 + m^2. Here the tangent space could be R^1? Say we can expand the tangent space and let it be R^3 but make the restriction that "movement" of the field in the tangent space was restricted to some orbit about the origin of the...

Dear guys, I want to understand the spinors in various dimensions and Clifford algebra. I tried to read the appendix B of Polchinski's volume II of his string theory book. But it's hard for me to follow and I stuck in the very beginning. I will try to figure out the outline and post my...

Hey! I have a problem with problem 5.6 (b) from Peskin + Schroeder. Maybe I just don't see how it works, but I hope somebody can help me! Homework Statement We are asked to calculate the amplitude for the annihilation of a positron electron pair into two photons in the high-energy limit. The...

Ryder in chapter two of his book says that if we consider parity then it is no longer enough to talk about two spinors and so he introduces 4 spinors. Is there some postulate of Quantum physics that has to do with state trasformation under parity??

Let x1, x2, x3 be the components of a complex vector. If x1^2 + x2^2 + x3^2 = 0 Cartan calls this a isotropic vector. So if, x1 = a*exp(i*theta) then x1^2 = a^2*exp(2*i*theta) ? I think I'm being confused with what I read here, http://www.sjsu.edu/faculty/watkins/spinor.htm in...

Can we make a connection? Consider the phase space of a point particle in R^3. Six numbers are required, three for position and three for velocity. Now consider an isotropic vector, X, in C^3 with X*X = 0. X = (x1,x2,x3), X*X = (x1*x1 + x2*x2 + x3*x3), x1 = c1 + i*c2, x1*x1 = (c1*c1 +...

Weyl spinors are not eigenstates of the helicity operator when the mass is not zero. But they have well-defined chiralities no matter what the mass is. Yet, it seems to me that references keep talking of Weyl spinors as if they have well-defined helicities, regardless of the mass...

I've been searching online and in my qft books (im an early phd student) and I can't find a clear explanation. If you have one, or can simply direct me to a page that does please do so. For a generic scattering/decay matrix : \sum _{polarization} \left|M|^2\right.=\sum _{polarization}...

I was reading a web page (http://electron6.phys.utk.edu/qm1/modules/m12/spinor.htm) that claims that the state vector of a spin-1/2 particle is completely specified by a two-component spinor, just as the state vector of a spinless particle is completely specified by its components in position...

This could have gone in about 4 different forums, so I apologize if I picked the wrong one. I'm wondering if anyone can explain what (conformal) killing spinors are all about. All I can find is that they are sections of the spinor bundle of a spin manifold satisfying: \nabla_\mu \epsilon =...

As suggested by Marcus, I have read the whole paper and decided to start a discussion of Kober's paper by asking a few questions. The paper certaintly presents a very interesting view. Part of it is an extension of Heisenberg's work on unified QFT, that the mass originates from self-interaction...

I think that anyone who has done a course in QFT has had their progress hampered by AT LEAST a month by Dirac Spinors. Why is it that the only sensible way to write the Standard Model down is to use Weyl Spinors, but the only sensible way to do calculations is to use Dirac spinors and...

Hi. I'm looking at Berkovits' pure spinor formulism of string theory. I am a PhD student studying mathematics and so am having trouble with some of the physics behind the mathematics. Say we have V a 10 dimensional vector space and we pick an irreducible representation of Spin(V) - which is...

Hi all! I am currently preparing a talk about Clifford algebras and pin/spin-groups. Since half the audience will consist of physicians (as I am myself) I also want to get more into the connection of the mathematical definitions and derivations (as one may find in Baker, "Matrix groups" or...

I bought a book on susy and there is a chapter on spinors in d-dimensions. Now, maybe I am extremely dumb but I just can't understand the first few lines! EDIT: I was being very dumb except that I think there is a typo...See below... BEGINNING OF QUOTE Consider a d-dimensional...

Does anybody know a simple proof of the fact that there are no finite-dimensional extensions of the \textsl{so(n)}-spinor representation to the group of general linear transformations. The proof seems can be based on the well-known fact that when rotated 2\pi a spinor transforms...

Why in every single text about GUT theories only the left spinors are used? Why use the conjugate of the spinor instead of the spinor itself? Is it just a another historic definition? Thanks

I am not sure where to post this question since it involves GR and particle physics but here it goes. I am reading in a book that when coupling a spinor to gravity, one replaces \partial_\mu \psi [/tex] by a covariant derivative D_\mu \psi [/tex] which must transform like a spinor under...

I'm wondering how in Peskin & Schroeder they go from i\mathcal{M} = {\overline{v}^s^'} (p^{'}) (-ie\gamma^\mu)u^s(p) \left( \frac{-ig_{\mu\nu}}{q^2} \right) \overline{u}^r (k) (-ie\gamma^\nu) v^{r^{'}} (k) at the bottom of page 131 to (5.1) at the top of 132 which reads i\mathcal{M}...

are spinors just wavefunctions in the dirac field?

Are spinor wave functions describing e.g. electrons, necessarily describing them as massless? Spinors representing physical entities are often described as corresponding to null vectors in space-time, which suggests that they can only describe massless entities. Nevertheless, the Dirac...

Weinberg shows in his book on QFT that the effect of a rotation on a massive particle's spin is the same as applying exp(-i \theta J.n) on the state, regardless of particle's momentum. In other words just rotate the spinor in its own representation. This makes calculations very simple. But what...

Hi, I have a question about spinors If \Lambda is a Lorentz Transformation what is (and how do you show that it is) the spinor representation of the Lorentz group ? I think it has somnething to do with the equivalence transformation S\dagger{\gamma}S=\Lambda\gamma But that is just a...

I've been looking into Geometric Algebra approaches to linear transformations and have found it to be MUCH nicer than the conventional matrix approaches for certain kinds of transformations. Moreover, I find it much more intuitive, particularly in its way of dealing with complex numbers. For...

When solving Dirac equation (for free massive particles) we usually impose normalisation conditions upon the eigenfunction in a single stroke. I am wondering, Is it possible/useful to impose separate normalisation conditions upon the left and right spinors? Should we still have a resolution...

Be kind with me I am just a dentist; nevertheless I am trying to understand the GR and the Theory of Spinors. In this sense I tried to explore the fundations of the GR and made use of a Taylorisation of the variations of the basis vectors de (with subscript 0, 1, 2 or 3) until the second order...

Can anyone give me some hints? I need to prove that all spinors to a spin-1/2 particle are eigenvectors to \hat S^2! /Daniel

What mathematically speaking is a spinor? Why isn't it a tensor? I didn't find the mathworld defintion very useful at all as it describes it as a complex column vector which really tells me nothing especially as we usually think of such an object as a tensor!

Self Adjoint very nicely gave me an example when QM doesn't work with GR using something called Spinors which define quantum mechanical particles. i was wondering how exactly is spinors pronounced Is it like spinners umm like the rims lol :) ? Sorry for the odd question, I just don't...