The tag has no wiki summary.

learn more… | top users | synonyms (1)

3
votes
1answer
303 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
1answer
309 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 ...
3
votes
2answers
444 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
1answer
125 views

The relationship between spin and spinor curvature

The identity, $$ -\gamma^b{\mathcal{R}}_{ab} = {\mathcal{R}}_{ab}\gamma^b = \frac{1}{2}\gamma^b R_{ab}$$ is presented in the answer to the question Dirac Equation in General Relativity. How does ...
3
votes
2answers
116 views

Electromagnetic current for interaction with Dirac spinors

The covariant form of the Dirac equation is given by $$(i\gamma^{\mu}\partial_{\mu} - M) \Psi(x) = 0 $$ Einstein's summation is implied here, $x=(x^0,x^1,x^2,x^3)^T$. I am simply looking for the ...
3
votes
1answer
215 views

Why do we use spinors for describing fermions?

I.e., what properties of the spinors gives us a reason for using them for describing of wavefunctions of fermions?
3
votes
1answer
205 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 ...
3
votes
1answer
255 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
39 views

Dirac operator partial integration

When you have an action with bosonic $X$ and fermionic $\psi$ (Majorana) fields and perform a SUSY transformation $\epsilon$ (the constant, infinitesimal parameter of transformation, a real, ...
3
votes
2answers
77 views

Some questions about Dirac spinor transformation law

I have perhaps meaningless question about Dirac spinors, but I'm at a loss. The transformation laws for for left-handed and right-handed 2-spinors are $$ \tag 1 \psi_{a} \to \psi_{a}' = N_{a}^{\quad ...
3
votes
1answer
209 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 ...
3
votes
0answers
60 views

Diffeomorphisms and the Dirac action

I have a question concerning fermions in curved space-time. Please read it to the end before suggesting the spin-connection and vierbein-based approach. I heard that there is a special way of ...
3
votes
1answer
128 views

Fierz identity for Weyl spinors in tensor currents

Using Fierz identity I found that certain four-fermion operator with left $l_i$ and right-chiral $r_i$ Weyl spinors vanish $\bar{l}_1\sigma_{\mu\nu} r_2 \bar{r}_3 \sigma^{\mu\nu} l_4 =$ $ ...
3
votes
0answers
74 views

Transformation law for spinor functions multiplication

Let's have Dirac spinor $\Psi (x)$, which formally corresponds to $$ \left( 0, \frac{1}{2} \right) \oplus \left( \frac{1}{2}, 0 \right) $$ representation of the Lorentz group. What representation is ...
3
votes
0answers
79 views

Transformations of gamma-matrices through Pauli matrices transformations

I have the transformation law of the Lorentz group for Pauli matrices: $$ \tag 0 (\sigma^{\mu})_{a \dot {a}}{'} = \Lambda^{\mu}_{\quad \nu} N_{a}^{\quad c}(\sigma^{\nu})_{c \dot {c}}(N^{-1})^{\dot ...
3
votes
0answers
120 views

Parity violating Dirac particle

We normally write down the Dirac Lagrangian as \begin{equation} {\cal L} _D = \bar{\psi} ( i \partial _\mu \gamma ^\mu - m ) \psi \end{equation} but are the Lagrangian's, \begin{equation} ...
3
votes
0answers
93 views

What is the point of path integral for boson and fermion?

I am a beginner to study QFT and confused about path integral for boson or fermion. I have read about the path integral for single particle, and finished some problems. But I cannot understand the ...
3
votes
0answers
44 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, ...
3
votes
0answers
166 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 $S$ ...
2
votes
2answers
427 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 ...
2
votes
2answers
165 views

A whole lot of doubts on Lorentz representation

Can someone tell me in layman's language how the $(1/2,1/2)$ represents a vector field and $(0,1/2)$ or $(1/2,0)$ represents spinors and $(0,0)$ represents scalar field. Please don't be pedantic on ...
2
votes
1answer
281 views

Non-linear Dirac equation in Einstein Cartan theory

Can someone explain this Wikipedia article, specifically the section on Einstein-Cartan theory? I have no idea how the equation ...
2
votes
1answer
63 views

Question on spinor brackets

I have been given the Lorentz generator $$J_{ab}=\lambda_a \frac{\partial}{\partial \lambda^b}+a\leftrightarrow b$$ I know $\frac{\partial}{\partial \lambda^b}\lambda_a=\epsilon_{ba}$ and ...
2
votes
1answer
242 views

Can one prove the full spin-statistics theorem from the spin 0, 1/2 and 1 cases?

Using second quantization for scalar field, spinor field and vector fields, we can get commutation and anticommutation relations for the birth and destruction operators of the fields, which leads us ...
2
votes
1answer
61 views

How does interpreting negative energy electrons as positrons solve the negative energy problem?

How does interpreting negative energy electrons as positive energy positrons solve the negative energy problem? How does change of “interpretation” without fixing the mathematics have such a profound ...
2
votes
1answer
99 views

Confusion about Dirac mass term

In chiral basis, $\psi=\begin{pmatrix} \psi_L\\ \psi_R \end{pmatrix}$ and therefore, $\overline\psi=\psi^\dagger\gamma^0=\begin{pmatrix} \psi^\dagger_L & \psi^\dagger_R ...
2
votes
2answers
177 views

Recovering 4-vector Lorentz transformation from spinor formalism

I'm trying to recover the 4-vector transformation laws using spinors. I have defined $$v^{\dot{a}b} = v^{\nu} \sigma_{\nu}^{\dot{a}b}$$ as usual, with $\sigma_0=1$. Now with the rules for dotted ...
2
votes
1answer
616 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
68 views

An identity for spinor helicity formalism

I have a question about the spinor helicity formalism from arXiv:1308.1697 Denote the massless spin-1/2 fermions as Eqs. (2.10)-(2.11) in that paper $$v_+(p)= \begin{pmatrix} |p]_a \\ 0 ...
2
votes
1answer
84 views

A simple question about matrix product with spinor indices

I have a big problem with dotted and undotted spinor indices. For example, suppose we have two convolutions: $$ \sigma^{\dot {a} a}F_{ab}, \quad \sigma^{\dot {a} a}F_{\dot {a} \dot {b}}, \quad F_{ab} ...
2
votes
1answer
65 views

Compatibility conditions of spinors and Riemannian Metrics

I came across an interesting article by Montesinos (J. Geom. Phys. 2 (1985), no. 2, 145–153.). In it, he finds that spin structures (as lifts of $SO(4)$) are not compatible with all Riemannian metrics ...
2
votes
1answer
240 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 ...
2
votes
0answers
74 views

What are Killing spinors?

What are Killing spinors? How can they be motivated? Are they directly related to Killing vectors and Killing tensors and is there an overarching motivation for all three objects? Any answer is ...
2
votes
0answers
75 views

Does anybody know of a source that explains Wick rotation for fermions in 3-dimensional spacetime?

I've been looking for a long time and I've not had a lot of luck. I've found sources that use fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space. ...
2
votes
0answers
49 views

Irreducible representation for the massless particle with helicity 2 and the Weyl tensor

As it can be shown, the equations for the irrep with zero mass and helicity 2, -2 respectively can be given in a form $$ \tag 1 \partial^{\dot {b}a}C_{abcd} = 0, \quad ...
2
votes
0answers
132 views

How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum?

How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum? I used the Gordon Decomposition to split the Probability Current of the Dirac Field into its orbital current and ...
2
votes
0answers
65 views

One question about Weinberg's derivation of arbitrary spin fields expressions

In his book "QFT" (vol. 1) Weinberg writes the expression for an arbitrary spin massive field: $$ \hat {\Psi}_{a}(x) = \sum_{\sigma = -s}^{s} \int \frac{d^{3}\mathbf p}{\sqrt{(2 \pi)^{3}2 ...
2
votes
0answers
77 views

One more relation with spherical spinors

Let's have the spherical spinors: $$ \mathbf {Y}_{j, m, l = j \pm \frac{1}{2}} = \frac{1}{\sqrt{2l + 1}}\begin{pmatrix} \pm \sqrt{l \pm m +\frac{1}{2}}Y_{l, m - \frac{1}{2}} \\ \sqrt{l \mp m ...
2
votes
0answers
111 views

Pauli matrices product identity

How to prove the identity $$ \tilde {\sigma}_{\alpha}\sigma_{\beta}\tilde {\sigma}_{\gamma} = g_{\alpha \beta}\tilde {\sigma}_{\gamma} + g_{\alpha \gamma}\tilde {\sigma}_{\beta} - g_{\beta \gamma} ...
2
votes
1answer
273 views

Parity transformation for spinors (pinors) in odd spacetime dimensions

What is the transformation law for spinors (pinors) under parity in an odd number of spacetime dimensions? I know how to derive the transformation properties of spinors (pinors) under parity in an ...
2
votes
0answers
59 views

Why does the object $\epsilon_L Q_L + \epsilon_R Q_R$ correspond to a 16-component conserved supercharge when we have a Dp-brane?

I understand that when a 10-dimensional superstring theory has a Dp-brane (say, extending in the $x_0, ... , x_p$ directions) we have the total conserved supercharge given by: \begin{equation} ...
2
votes
0answers
100 views

Two spinor tensors and Maxwell's equations

Let's have two symmetric (by the indices) spinor tensors $F_{ab}, F_{\dot {a}\dot {b}}$ and conditions $$ F_{ab}, \partial^{\dot {a} a}F_{ab} = 0, \quad F_{\dot {a}\dot {b}}, \partial^{\dot ...
2
votes
0answers
91 views

Questions on the elementary excitations in the resonating-valence-bond(RVB) states?

It is known that the RVB states can support spin-charge separations and its elementary excitations are spinons and holons. But it seems that there are some different possibilities for the nature of ...
2
votes
0answers
251 views

Unitary Lorentz transformation on quantized Dirac spinor

I am stuck again on page 59 of Peskin and Schroeder. In particular, I do not know how they get equation (3.110). Let me first give some background in the way that I understand it (but I might be ...
2
votes
0answers
115 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 ...
1
vote
4answers
185 views

Nature of Fields in QFT

I'm not exactly an expert in quantum physics, but this seems to be a simple question, and I can't find an answer anywhere! There are specific types of fields used in physics: scalar fields (i.e. as ...
1
vote
1answer
130 views

Massless neutrinos and Chirality

The massless neutrinos can be represented by two component Weyl spinors. Then how does one say that it is an eigenstate of the chirality operator $\gamma^5$, which is a $4\times 4$ matrix and can act ...
1
vote
1answer
210 views

Spinor formalism in QFT

We can describe fields by two formalisms: vector and spinor. This is the result of possibility of representation of the Lorentz's group irreducible rep as straight cross product of two $SU(2)$ or two ...
1
vote
3answers
1k views

Energy Spectrum of pair of spin-1/2 particles with general Hamiltonian

I found this problem, and so far I am stumped. I was wondering if anyone wanted to solve it with me, or help me calculate eigenvectors, or just give insight on my questions. Consider a system of ...
1
vote
2answers
79 views

Converting two component product to four component notation

Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry, \begin{equation} \chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta ...