Spinors Definition and 119 Threads

Often I see QFT texts introduce dirac spinors by comparing them to the two component spin states (which I have come to accept are also spinors) in NRQM. And arguing that since the NRQM spinors transform via SU(2), our desired quantum fields for spin 1/2 particles should be some higher...

Consider the Spinor object for an electron. Are the non-relativistic and relativistic (Dirac equation) Spinor objects, from a mathematical point-of-view, identical? Thanks in advance.

Hello. I would like to ask something that will help me understand a little better how we work with Dirac spinors' inputs... I know that the dirac equation has 4 independent solutions, and for motionless particles, the (spinor) solutions are: u_{+}=(1,0,0,0)^{T} electron +1/2...

First, greetings from newbie to "staff" Now, let's start: Since some days I'm struggling a little bit with this paper: http://jmp.aip.org/resource/1/jmapaq/v5/i9/p1204_s1?isAuthorized=no , especially with two questions: 1) On page 1205, II, A (right column): What does \tilde v B...

SL(2,C) to Lorentz in Carmeli's "Theory of Spinors" On page 56 of "Theory of Spinors", Eq. (3.84a), Carmeli gives the formula for the Lorentz matrix in terms of Pauli matrices and an SL(2,C) matrix g: \Lambda^{\alpha\beta}=(1/2)Tr(\sigma^\alpha g \sigma^\beta g^*) His sigma matrices are the...

I am very confused by the treatment of Peskin on representations of Lorentz group and spinors. I am confronted with this stuff for the first time by the way. For now I just want to start by asking: If, as usual Lorentz transformations rotate and boost frames of reference in Minkowski...

LQG, strink theory and Penrose's spinor theory, or maybe it's twistor theory, I don't know, all I know is that all three theories achieve mathematical miracles in their attempts to go beyond the Standard Model - how can all three theories do this but be mutually exclusive at the same time. Or...

Hello! I´m currently taking a course in RQM and have some questions for which I didnt get any satisfactory answers on the lecture. All comments are appricieted! 1. Is the gamma zero tensor some kind of metric in the space for spinors? When normalizing our solution to the Dirac equation it...

I have to compute the square of the Dirac operator, D=γaeμaDμ , in curved space time (DμΨ=∂μΨ+AabμΣab is the covariant derivative of the spinor field and Σab the Lorentz generators involving gamma matrices). Dirac equation for the massless fermion is γaeμaDμΨ=0. In particular I have to show that...

I'm currently reading about parity and it's role in QFT and I am trying to understand an argument of why parity exchanges right-handed and left-handed spinors. At page 94 in http://www.damtp.cam.ac.uk/user/tong/qft/four.pdf David Tong states that "Under parity, the left and...

Hi all, I am troubled by the flag and flagpole analogy for two-spinors and would like some clarification. Please refer to the post by Hans de Vries. https://www.physicsforums.com/showthread.php?t=239191 Am I right to say that the usage of spin rotation operators (eg...

For spin-1/2, the eigenvalues of S_x, S_y and S_z are always \pm \frac{\hbar}{2} for spin-up and spin-down, correct? What is the difference between eigenvectors, eigenstates and eigenspinors? I believe eigenstates = eigenspinors and eigenvectors are something else? I'm just getting confused...

I've been watching Sidney Coleman's QFT lectures (http://www.physics.harvard.edu/about/Phys253.html, with notes at http://arxiv.org/pdf/1110.5013.pdf), and I'm now on to the spin 1/2 part of the course. We've gone through all the mechanics of constructing irreducible representations D^{(s1,s2)}...

I just started studying supersymmetry, but I am a little bit confused with the superspace and superfield formalism. When expanding the vector superfield in components, one obtains therms of the form \theta^{\alpha}\chi_{\alpha}, where \theta is a Grassmann number and \chi is a Weyl vector. I...

There's something I don't think I quite understand about spin and how it acts a generator of rotations. I'll start with quickly going over what I do understand. Suppose you want to do an infinitesimal rotation around the z-axis on some state: \def\ket#1{\left | #1 \right \rangle} \ket{\psi...

Homework Statement Hi, This question is about Lorentzgroups. In my course of Relativity, we've seen a very little about representations of complete Lorentz groups but there are two little exercises, which we can do, but I do not understand what should be checked, not even how to start this...

Are spinors needed in modern theoretical physics as opposed to tensors? I have come across Penrose's book "Spinors and space-time". Does anybody know what mathematical prerequisites are needed to actually understand it? (at least volume 1) Can I manage to go through it with a good knowledge of...

I need to show that u^{+}_{r}(p)u_{s}(p)=\frac{\omega_{p}}{m}\delta_{rs} where \omega_{p}=\sqrt{\vec{p}^2+m^{2}} [itex]u_{r}(p)=\frac{\gamma^{\mu}p_{\mu}+m}{\sqrt{2m(m+\omega_{p})}}u_{r}(m{,}\vec{0})[\itex] is the plane-wave spinor for the positive-energy solution of the Dirac equation...

Hi guys! I'm having some problems in understanding the direct products of representation in group theory. For example, take two right weyl spinors. We can then write\tau_{0\frac{1}{2}}\otimes\tau_{0\frac{1}{2}}=\tau_{00}\oplus\tau_{01} Now they make me see that...

Hi, I was pondering a bit about the mobius strips and I was wondering if there is a relationship between spinors and there transformation under rotations and that, in a manner of speaking, one must go around a mobius strip twice to return to the original position. To me it seems there would be...

HI! i have to face the problem of decomposition of the spinor representation of SO(6,6) into smaller subgroups of SO(6,6), in a generic way, as possible. Because I almost don't know too much about decomposition of representations of the classical groups, I wonder if someone knows where I can...

Hi guys, I'm currently struggling to show something my lecturer told us in class. We have that \Psi\left(x\right) \rightarrow S\left(L\right)\Psi\left(L^{-1}x\right) under a Lorentz transform defined L = exp\left(\frac{1}{2}\Omega_{ij}M^{ij}\right) with S\left(L\right) =...

Why is it not possible to have Weyl spinors in odd dimensions?

Hi there, i have a very simple question, but still, i don't know what the answer is, her it goes. I havew Dirac spinor \psi and its hermitian timex \gamma^0, \bar \psi. My question is the following: we can think of \psi as a vector and \bar \psi as a row vector, then, if i take...

How to obtain Kerr Metric via Spinors (Newman-Penrose Formalism)? I am a bit confused with Ray d'Inverno's Book. Why perform the coordinates transformation: 2r-1 -> r-1 + r*-1 I am bit confused of it. And I am a bit confused, too, of how to write out null tetrad...

Hi togehter. I encountered the following problem: The timeordering for fermionic fields (here Dirac field) is defined to be (Peskin; Maggiore, ...): T \Psi(x)\bar{\Psi}(y)= \Psi(x)\bar{\Psi}(y) \ldots x^0>y^0 = -\bar{\Psi}(y)\Psi(x) \ldots y^0>x^0 where \Psi(x) is a Dirac...

Hi, I'm new on this forum. I have a doubt regarding helicity and Weyl spinors: I can't understand when I have to use left or right-handed Weyl spinors in order to describe particles or antiparticles. What i have understood is that a charged current is described by left-handed Weyl fields...

Hey guys, something that puzzles me everytime I stumble across spinors is the following: I know that i can express Dirac spinors in terms of2-component Weyl spinors (dotted/undotted spinors). Now, if i do that, i can reexpress for instance the Lorentz or conformal algebra in terms of Weyl...

Hey guys, i'm stuck (yet again! :) ) I am somewhat confused by Dirac spinors u,\bar{u}. Take the product (where Einstein summation convention is assumed): u^r u^s\bar{u}^s Is this the same as u^s\bar{u}^s u^r? Probably not because u^r is a vector while the other thing is a matrix...

Homework Statement Using (\sigma^{\mu \nu})^{\beta}_{\alpha} (\sigma_{\mu \nu})^{\delta}_{\gamma} = \epsilon_{\alpha \gamma} \epsilon^{\beta \delta} + \delta^{\delta}_{\alpha} \delta^{\beta}_{\gamma} show that \Psi_{\alpha} X_{\beta} = \frac{1}{2} \epsilon_{\alpha \beta} (\Psi X) +...

Hi, I'm trying to understand spinors better, and I seem to be getting stuck on understanding the reason they're said to transform differently from vectors, and I'd appreciate any help with a justification for that. I'm sure I'm missing something pretty simple, but here goes; Here's what I've...

So since I learning QFT a while ago, I've always struggled to understand fermions. I can do computations, but I feel at some level, something fundamental is missing in my understanding. The spinors encountered in QFT develop a lot from "objects that transform under the fundamental representation...

What is the difference between left and right Weyl spinors? (probably they transform differently under boosts or rotations). Thanks for answer.

hi, can se say loosely that a spinor is a rank-1/2 tensor or the square root of a vector, since a scalar does not change under rotations, a vector changes one time, a rank 2-tensor two times, a rank 3 tensor 3 times, and a spinor 1/2 time. also a scalar in 4d has 1 component, a vector 4...

In http://relativity.livingreviews.org/Articles/lrr-2004-2/" (section 2.1.5.2) the following is the first sentence in the section reviewing spinors: "Spinors are representations of the Lorentz group only; as such they are related strictly to the tangent space of the space-time manifold."...

I think I get the difference between spinors and tensors in the context of algebraic topology and QM but I want someone to scrutinize my understanding before I move on to another topic. I've never had a class in topology so I might be using some math terms incorrectly. The 3D parameterized...

Hey guys, I have a question about said spinors. In supersymmetry introductions one finds (e.g. for two left-handed spinors \eta , \nu ) that \eta\nu=\nu\eta due to their Grassmannian character and the antisymmetry of the spinor product. If I look, however, at modern field theoretical...

I am interested in using hypercomplex numbers and not using tensors. Therefore a question about the difference between spinors and vectors. I read that they both can be written as quaternions. Vector: Vq = ix + jy + kz Spinor: Sq = ix + jy + kz So what is the difference between...

This is not an assignment problem, but I am studying for my quantum mechanics final exam and came across a derivation in the book which I can't seem to get my head around :( The example in the book is solving for the probabilities of getting +h(bar)/2 and -h(bar)/2 if we are to measure the...

Hi, I'm trying to teach myself a bit about spinors, mainly from reading about geometric algebra. There is something that I can't figure out though. According to GA, spinors are elements of the even graded subalgebra, so scalars, bivectors and so on. But the electromagnetic field is a bivector...

In e.g. Burgess and Moore - standard model a primer it is stated that for two spinors (majorana) \bar{\psi_1}\psi_2 = (\bar{\psi_1}\psi_2)^T = - \psi_2^T \bar{\psi_1}^T since the spinors are anticommuting objects, thus ordering reversion gives -1 but they also state that...

Homework Statement Show that \psi (\gamma^a\phi)=-(\gamma^a\phi)\psi Homework Equations Maybe \{\gamma^a, \gamma^b\}=\gamma^a\gamma^b+\gamma^b\gamma^a=2\eta^{ab}I Perhaps also: (\gamma^0)^{\dag}=\gamma^0 and (\gamma^i)^{\dag}=-(\gamma^i) The Attempt at a Solution The gammas are...

I guess the answer to this question actually should be pretty obvious, but I still have problems getting it right though. I wonder about the definition of the time ordered product for a pair of Dirac spinors. In all the books I've read it simply says: T\left\{\psi(x)\bar{\psi}(x')\right\} =...

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...

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}...