The tag has no wiki summary.

learn more… | top users | synonyms (1)

12
votes
1answer
747 views

Could this model have soliton solutions?

We consider a theory described by the Lagrangian, $$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$ The corresponding field equations are, ...
6
votes
1answer
172 views

Invariance of supersymmetric Yang-Mills theory under supersymmetry

I was following Brink, Scherk and Schwartz, "Supersymmetric Yang-Mills theories". The variation of the Lagrangian w.r.t a supersymmetry transformation can be reduced to $$ \delta L = -igf_{a b c} ...
4
votes
1answer
279 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 $\bar{l}_1\sigma_{\mu\nu} r_2 \bar{r}_3 \sigma^{\mu\nu} l_4 =$ $ ...
1
vote
1answer
68 views

How to derive the form of the invariant spinor inner product?

So we have gamma matrices that satisfy the spacetime algebra relations, $\{\gamma^\mu, \gamma^\nu\} = 2 \eta^{\mu\nu}$. We know that if we set $\sigma^{\mu\nu} = \frac{1}{4}[\gamma^\mu, \gamma^\nu]$ ...
0
votes
1answer
40 views

Do the eigenstates of the Pauli operators correspond to the six directions of the 3D world?

I understand that the six eigenstates of the three Pauli operators $X, Y, Z$ correspond to the six poles of the Bloch sphere. By fixing an orthonormal basis of our physical word, does "measuring Pauli ...
5
votes
0answers
122 views

Lorentz transformation of Gamma matrices $\gamma^{\mu}$

From my understanding, gamma matrices transforms under Lorentz transformation $\Lambda$ as \begin{equation} \gamma^{\mu} \rightarrow S[\Lambda]\gamma^{\mu}S[\Lambda]^{-1} = ...
5
votes
0answers
129 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 = ...
4
votes
0answers
56 views

How many Killing spinors exist on $S^5$?

So, I know that on $S^n$, a spinor of the form $$ \Sigma^\pm = \frac{1 \pm i\gamma^\alpha z_\alpha}{\sqrt{1+z^2}}\Sigma_0$$ where $\Sigma_0$ is a constant spinor, is a Killing spinor on $S^n$ ...
4
votes
0answers
144 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
68 views

How one can write $\bar{\psi}$ in odd dimension?

I know that the Dirac equation in general dimensions has a form of $$ (i\gamma_{\mu} \nabla_\mu - m ) \psi =0 $$ and the action for that is written as $$ S = \int d^d x \bar{\psi} (i\gamma_{\mu} ...
3
votes
0answers
72 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
0answers
88 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 ...
3
votes
0answers
95 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
153 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
150 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
49 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
174 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
0answers
33 views

Parker-Taylor formula in the $n=4$ simple case

I am trying to do ex. 2.23 of http://arxiv.org/pdf/1308.1697v2.pdf. I have chosen as reference spinors $q_1,q_2 = p_3$ and $q_3,q_4 = p_1$. Therefore if I compute $A^4[1^- 2^- 3^+ 4^+]$ the ...
2
votes
0answers
93 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
62 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
81 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
83 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
132 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
0answers
73 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
111 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
325 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
116 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
0answers
38 views

Some questions about Weyl spinor algebra

I am following a review on supersymmetry and I am having trouble with Weyl spinor algebra. These are equations (4.2.1) ...
1
vote
0answers
71 views

Spinor helicity formalism, exact form of the spinors

I am trying to understand how to perform computations with the spinor helicity formalism, I am studying on this review http://arxiv.org/abs/1308.1697. I have stumbled upon a problem though, in pag. ...
1
vote
0answers
37 views

How can a spinor represent an “epistemic” state?

I have read a lot of stuff on the seemingly endless debate on ontology/epistemology of the quantum state $\psi$. But I always wonder: how can a spinor be considered epistemic when $\psi$ really ...
1
vote
0answers
20 views

Proof of Pauli-Kofink relation

In an article "Effect of the self-induced torsion of the Dirac sources on gravitational singularities" written by Akira Inomata he proves the Pauli-Fierz relation: $$ \bar{\psi}P\gamma_{\mu}\psi ...
1
vote
0answers
157 views

Interpretation of Dirac Spinor components in Chiral Representation?

I failed to find any book or pdf that explains clearly how we can interpret the different components of a Dirac spinor in the chiral representation and I'm starting to get somewhat desperate. This is ...
1
vote
0answers
64 views

Polarization sum rule for Rarita-Schwinger field

There are Rarita-Schwinger equations: $$ \tag 1 (p\!\!\!/ - m)\psi_{\mu} = 0, \quad \gamma_{\mu}\psi^{\mu} = 0, \quad i\partial_{\mu}\psi^{\mu} = 0. $$ So the polarization sum $D_{\mu \nu}(p) = ...
1
vote
0answers
69 views

Spinor representation of $SO(d+1,1)$

I have been looking over the internet for a resource that tells me the number of dimensions of a spin $s-1$ spinor representation of $SO(d+1,1)$, but unfortunately have yet to be able to find it. In ...
1
vote
0answers
96 views

Two pairs of projection operators of the Dirac equation

The Dirac equation may be interpreted as the action of projection operator $\frac{1 - \Delta}{2}\Psi = 0$, where $$ \Delta = \begin{pmatrix} 0 & \Delta_{b \dot {a}} \\ \Delta^{\dot {b}a} & 0 ...
1
vote
0answers
90 views

Direct sum of the spinors and EM field tensor

EM field tensor refer to the direct sum of $(1, 0), (0, 1)$ spinor representation of the Lorentz group. How to show it? Each of these spinor representations corresponds to the symmetrical spinor ...
1
vote
0answers
63 views

Can we build spinorial eigenstates of Time reversal symmetry?

In the SM, and general theories with spinors, we can build the Parity left/right eigenspinors. Indeed, there are also ELKO fields, eigenstates of Charge operator (non-standard Wigner classes). Can we ...
0
votes
0answers
32 views

dagger operator in spinor representation

I just have trouble understanding how hermitian conjugation is acting like this in the following example (dot represents right-handed Weyl field, undot represents left-handed Weyl field). For ...
0
votes
0answers
32 views

Spinors and asymmetry of wave function

A spinor is a mathematical entity which changes sign if it is rotated by $2\pi$. Is this connected to the asymmetry of the spinor wave function?
0
votes
0answers
32 views

What are the conditions of wave function continuity when solving for Dirac Spinors as done in “Klein paradox” paper by Novoselov?

In the paper "Chiral tunneling and Klein paradox" paper by Katsnelson, Novoselov, and Geim, they use the wave function for Dirac spinors. What are the conditions for continuity of the wave function ...
0
votes
0answers
34 views

Euclidean Continuation of spinor

I would like a clear and useful answer or explanation about these following argument or question that I'll place in logical order for my purpose that deal the Euclidean continuation of spinors in 5 ...
0
votes
0answers
35 views

Explanation for orientation entanglement

I have to write a summary for "orientation-entanglement": the state of an object/subsystem depends in general not only (locally) on its configuration in space, but also (nonlocally) on its topological ...
0
votes
0answers
61 views

The Covariant Spinor Derivative in the Locally Supersymmetric Generalisation of the Polyakov Action and Potential Mistakes in the Literature

Questions) I recently came upon the thesis The Landscape of Free Fermionic Gauge Models by D. G. Moore and G.B. Cleaver. On pages 20 and 21 they explain that the locally supersymmetric action, ...
0
votes
0answers
37 views

representation of spinors

I am trying to get from the abstract representation of Spinors, as wave functions $|\Psi \rangle$ in the base of tensors products $| S_z \rangle \otimes | x \rangle$ of eigenvectors of the spin ...
0
votes
0answers
73 views

Lorentz transformations of spinors in $SL(2,\mathbb{C})$

I was wondering what the matrix representations of all the coordinate rotations and Lorentz boosts of the $SL(2,\mathbb{C})$ were along with a general method of solving for them. I've been able to do ...
0
votes
0answers
38 views

Real representations of chiral fields

Why we can´t have real representations of chiral fields, i.e. why does a multiplet of chiral field (Weyl spinors) under a real representaiton of a Lie Group transforms as a "vector". It is easy to see ...
0
votes
0answers
78 views

Angular momentum operator for 2 dimensions?

Recently I get the task to build (2 + 1)-Dirac theory. I wrote corresponding Dirac equation in a form $$ (i\sigma_{0}\partial_{0} + i\sigma_{1}\partial_{1} + i\sigma_{2}\partial_{2} - m)\Psi = 0, $$ ...
0
votes
0answers
49 views

How to find an action of $(\hat {\sigma} \cdot \hat {\mathbf L} )$ on spherical spinors?

Let's have the spherical spinors $\psi_{j, m, l = j \pm \frac{1}{2}}$, $$ 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}} ...
0
votes
0answers
132 views

Infinitesimal transformations and Poisson bracket for Dirac spinors

I apologize for the cumbersome calculations. Let's have $\Psi$, $i\Psi^{\dagger}$, which are canonical coordinate and impulse in space of solutions of Dirac equation. It can be showed that they have ...
0
votes
0answers
95 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} ...