Spinor Definition and 114 Threads

I found a paper that derives the Dirac equation in 1 + 1 dimensional space-time. It is equation 8, here, http://academic.reed.edu/physics/faculty/wheeler/documents/Classical%20Field%20Theory/Miscellaneous%20Essays/A.%202D%20Dirac%20Equation.pdf and here...

I was reading in this book: Supergravity for Daniel Freedman and was checking the part that has to do with Extremal Reissner Nordstrom Black Hole. He was using killing spinors (that I am very new to). I was understanding the theory until he stated with the calculations: He said that the...

I would like to take the trace over spinorial indices of the following expression: (\gamma_{\mu}\gamma^{0})_{\alpha}^{\beta}=(\gamma_{\mu})_{\alpha}^{\gamma}(\gamma^{0})_{\gamma}^{\beta}. How do I go about doing this? I reckon I could expand the trace out (let's say I want to do this in 4D)...

Can you give me an intuitive understanding of the following: "The spin states of massive and massless Majorana spinors transform in representations of SO(D-1) and SO(D-2), respectively". I see the similarity with vectors bosons, where massive vectors have d-1 degrees of freedom and massless...

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.

I got this while I was reading spinor indices manipulating in Sredinicki's qft in case of spinor representation we get a relation like the following one: ##[(ψ_a^{'}(0))^{\dagger},M^{\mu \nu},]= [(S^{\mu \nu}{}_R)_{a^{'}}{}^{~b^{'}}](ψ_{b {'}}(0))^{\dagger}## where ##a^{'}## and ##b^{'}##...

Hello everyone, this has been on my mind for a while and I finally realized I could just ask on here for some input :) I think in general, when most people start learning quantum mechanics, they are under the impression that the wave function \Psi represents everything you could possibly know...

In the Dirac equation, the only thing about the gamma matrices that is "fixed" is the anticommutation rule: \gamma^\mu \gamma^\nu + \gamma^\nu \gamma^\mu = 2 \eta^{\mu \nu} We can get an equivalent equation by taking a unitary matrix U and defining new spinors and gamma-matrices via...

Homework Statement This complies when I type it in my Latex editor, but not on here. If you could either let me know how to fix that or copy and paste what I have into your own editor to help, that'd be great. Thanks! While Ryder is setting up to derive a transformation rule for Dirac...

First of all note that 8-dinensional Finsler space (t,x,y,z,t^*,x^*,y^*,z^*) preserving the metric form \begin{equation} S^2 = tt^*-xx^*-yy^*-zz^*, \end{equation} actually presents doubled of the Minkowski space. Then the solution with one-dimensional feature localized on the world line...

THREAD CHANGE *SPINOR IDENTITY*...although it's connected with SuSy in general, it's more basic... I am trying to prove for two spinors the identity: θ^{α}θ^{β}=\frac{1}{2}ε^{αβ}(θθ) I thought that a nice way would be to use the antisymmetry in the exchange of α and β, and propose that...

Homework Statement I am reading Srednicki's QFT up to CPT symmetries of Spinors In eq. 40.42 of http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf I attempted to get the 2nd equation: C^{-1}\bar{\Psi}C=\Psi^{T}C from the first one: C^{-1}\Psi C=\bar{\Psi}^{T}C Homework Equations...

The question is about the spinor representation decomposed under subgroups. It's a common technique in string theory when parts of dimensions are compactified and ignored, and we are only interested in the remaining sub-symmetry. I'm learning it from the appendix B in Polchinski's big book...

Dear Sir, I am currently doing an advanced course in Quantum Mechanics. This current doubt of mine, I am unable to clarify it properly. It follows as: Spin 1/2 particles reside in 2dim-Hilbert space( Spinor Space)...However, we talk about rotations of states in this space where the angle...

Is there a connection between the Dirac four spinor and "spin up", i.e one of the four spinor states is spin up or are these two separate unconected things.

An electron field is a superposition of two four-component Dirac spinors, one of them multiplied with a creation operator and an exponential with negative energy, the other multiplied with an annihilation operator and an exponential with positive energy. So I assume one Dirac spinor creates a...

Homework Statement Hi All, this problem is related to spin-1/2 in an arbitrary direction, in particular building off of, but going beyond, Griffiths QM 4.30. I am given an unnormalized general spin state, \chi in the z basis, and then asked "in what direction is the spin state pointing?"...

Hi, from Srednickis QFT textbook, we know the following coupling of Lorentz group representations: (2,1)\otimes (2,1) = (1,1)_A \oplus (3,1)_S, which yields \epsilon_{a b} as an invariant symbol. Generalising, we can look at (2,1)\otimes (2,1) \otimes (2,1) \otimes (2,1) = (1,1) \oplus...

Homework Statement Show the spinor representation corresponding to the rotation through an angle θ about an axis with direction vector n = (n_x, n_y, n_z) has the form: g=exp{-i\frac{θ}{2}(n_x σ_x+n_yσ_y+n_zσ_z)}, σ_{x, y, z} are respectively Pauli matrixHomework Equations h=gxg^{-1}The...

Hello all I am working on a model in D=5 N=2 supergravity where the metric background is described by a time-dependent three brane, with one extra spatial dimension (a brane-world with bulk sort of set up). The vanishing of fermionic variations gives me the following weird projections...

I'm working through some spinor calculations in the following book...

Generally, Gamma matrices with one lower and one upper indices 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 construct gamma matrices with two lower indices. There...

Hello, sorry for my english.. I have a problem with weyl's spinors notation. I'm confused, becouse i read more books (like Landau, Srednicki and Peskin) and it's seems to me that all of them use different and incompatible notations.. If i define...

I was told the space S^3 is isomorphic to the set of all 2 component spinors with norm 1 (see https://www.physicsforums.com/showthread.php?t=603404 ). Can I infer that the space of all 4 component spinors with norm 1 is isomorphic to S^7? If so is a Dirac spinor isomorphic to S^7? Thanks for...

Can a point in S^3 be uniquely labeled by a 2 component Spinor? Thanks for any help!

Hi guys, i'm looking at one-loop calculations in terms of helicity spinor (basically a paper by Brandhuber, Travglini and others) language but i have no idea how to integrate them :) For instance \int FeynParam\int d^D L \frac{\langle a|L|b]^2}{(L^2-\Delta^2)^3} How would I do...

Spinor notation exercise with grassman numbers I'm checking a term when squaring a vector superfield in Wess-Zumino gauge, but its really just an excercise in index/spinor notation: I need to square the term...

how spinor vector envolves in describing the atom

Hi there, I'm having a problem calculating the energy momentum tensor for the dirac spinor \psi (x) =\left(\begin{align}\psi_{L1}\\ \psi_{L2}\\\psi_{R1}\\ \psi_{R2}\end{align}\right)(free theory). So, with the dirac lagrangian \mathcal{L}=i\bar{\psi}\gamma^\mu\partial_\mu\psi-m\bar{\psi}\psiin...

Hi guys! I still have problem clearing once and for all my doubt on the spinor representation. Sorry, but i just cannot catch it. 1) ----- Take a left handed spinor, \chi_L. Now, i know it transforms according to the Lorentz group, but why do i have to take the \Lambda_L matrices belonging...

In Qed they replace the current vector J^{\alpha} by ie\overline{\Psi}\gamma^{\alpha}\Psi. I don't understand how this is done. I understand that J^{A\dot{A}}=J^{\alpha}{\sigma^{A\dot{A}}_\alpha} but if J^{A\dot{A}} is a rank two matrix then...

Homework Statement The task is to show the invariance of a given Lagrangian (http://www.fysast.uu.se/~leupold/qft-2011/tasks.pdf" ), but my problem is just in one step (which i got from Peskin & Schröder, page 70) which i can not reproduce due to my lack of knowledge regarding spinors. The...

http://arxiv.org/abs/1106.3548 Emergence of Superstring from Pure Spinor Ichiro Oda (Submitted on 17 Jun 2011) Starting with a classical action where a pure spinor $\lambda^\alpha$ is only a fundamental and dynamical variable, the pure spinor formalism for superparticle and superstring is...

I believe Dirac spinors are not in any Hilbert space since it has no positive definite norm. However one QM axiom I learned told me any quantum state is represented by a state vector in Hilbert space, so what is happening to Dirac spinor?Or is it just that the axiom is not for relativistic QM?

I am currently trying to find how to derive the decomposition for two particles via the tensor notation, for instance for the product of two particles of spin 1/2 : \frac{1}{2} \otimes \frac{1}{2} = 1 \oplus 0 Giving the components of spin 1 and 0. So to do it, I write down the product...

Hi, In a calculation I am doing, I encounter terms of the form \bar{u}^{s_1}(\boldsymbol{\vec{p}})\gamma^{\mu}{v}^{s_2}(\boldsymbol{\vec{q}}) where u and v are the electron and positron spinors. Is there any recipe for simplifying this expression, using the spin sums or other identities? I am...

Hi, I totally understand why \chi\psi=\chi^{a}\psi_{a}=-\psi_{a}\chi^{a}=\psi^{a}\chi_{a}=\psi\chi. Where the first equality is just convention, the second is anticommutation of the fields, the third is due to \chi^{a}\psi_{a}=-\chi_{a}\psi^{a} because of the \epsilon^{ab} . But now if...

Hi, I'm just looking at the stuff on left and right handed spinor fields in Srednicki. Srednciki distinguishes fields in the left rep from those in the right rep by putting a dot over them. Since hermitian conjugation swaps the two SU(2) algebras, the hermitian conj of a left spinor is a right...

Homework Statement I want to compute the transpose of the adjoint of a Dirac spinor.Homework Equations My reasoning, based on learning Griffiths notation in “Intro to Elementary Particles”, p. 236, [7.58]: {\bar u^T} = {({u^\dag }{\gamma _0})^T} = {\gamma _0}^T{u^\dag }^T<mathop> =...

Hi there, I have a question, something that is confusing me. If a particle of spin 1 is measured to have m=1 along the x direction, would the spinor state just be a column vector with (1,0,0), which would also be the spinor if x was infact z. OR would the spinor be determined by multiplying...

The question is the following: At one instant, the electron in a hydrogen atom is in the state: |phi>=sqrt(2/7) |E_2,1,-1,+> + 1/sqrt(7) |E_1,0,0,-> - sqrt(2/7) |E_1,0,0,+> Express the state |phi> in the position representation, as a spinor wavefunction How am I supposed to do this...

Homework Statement Consider the spinor \frac{1}{\sqrt{5}}\left(\begin{array}{cc}2\\1\end{array}\right) . What is the probability that a measurement of \frac{3S_{x}+4S_{y}}{5} yields the value -\frac{\hbar}{2}? Homework Equations...

Hi, one labels the Weyl- and Vector-representations of the Poincare group by (0,1/2), (1/2,0), (1/2,1/2) etc., where does the Majorana spinor fit into this? Or can you say it belongs somehow to the real part of the (0,1/2)+(1/2,0) rep, although this sounds pretty unfamiliar. Thanks for...

I'm having a memory blank on this particular area of field theory. Is the product of two spinors a scalar or scalar type entity and if so, can I treat it like a scalar? (i.e. move it around without worrying about order etc) i.e. is \Phi_1^{\dagger} \Phi_1 a scalar? and if so does...

Consider a compressible fluid such as air. Assume we can neglect viscosity. We might describe such a fluid at some small region with a set of numbers. Three numbers would give the components of the velocity vector of the air at that small region and two more numbers would give the density and...

I'm differentiating with respect to Grassman variables, and I'm getting something very inconsistent: Suppose \xi and \chi are two-component, left-handed, grassman-valued spinors. Now, I take derivatives with of the product, \xi^a \chi_a, respect to \xi two different ways, and denote their...

The Dirac field is an anticommutating field. But what part of it is anticommutating? Is it the spinors, or the coefficient in front of the spinors? In quantum field theory I think it's the coefficients that anticommute, so that the spinors should commute, but not their coefficients. In classical...

Actually, the original motivation is to check the closure of SUSY \delta X^\mu = \bar{\epsilon}\psi^\mu \delta \psi^\mu = -i\rho^\alpha\partial_\alpha X^\mu\epsilon where \rho^\alpha is a two dimensional gamma matrix, and \psi^\mu ia s two dimensional Majorana spinor, the index \mu in the...

Hi, I doubted whether to post this in the homework section, but decided not to because a) it's only a very small part and b) I think my question is important in general. Looking at page 107 of Zee's Introduction to QFT I am trying to get from (16) to (17). For this I need to evaluate several...

can someone explain to me that is a spinor and how do I calculate the spin operators from it? for ex. (from homeword) the spinor is (|a|*e^(i*alpha), |b|*e^(i*beta))