We can embed the spinors of a Clifford algebra into the Clifford algebra itself by representing them as a minimal left ideal. I'm looking at the case of 3D space where a chosen basis satisfies $e_1^2=...

This question is about something from page 162 of Physics from Symmetry by Schwichtenberg (second edition). The doublet is an electroweak $SU(2)$, say a left-handed neutrino and left-handed electron. ...

I'm having this confusion because in my neutrino physics course, they kept speaking about left handed neutrinos. At the field level, it's obvious or just definition that a Dirac field $\Psi$ contains $...

In the book What is a Quantum Field Theory by Michel Talagrand, he introduces (in §10.15) a "massive Weyl spinor."* In physics, common wisdom says there is no such thing. A quick internet ...

I am very much confused about the spin projection operator of the Dirac field. I am not getting proper resources regarding this. From what I understood, in analogy with the non-relativistic case, we ...

I have currently been searching for the form of the Belinfante-Rosenfeld Stress-Energy tensor to calculate the stress energy of a Dirac field (because the tensor derived from Noether’s Theorem is not ...

I have currently inputted the full Dirac equation for a free electron in space in Desmos. However, I haven't been able to find a good way to represent it. Singular spinors can be represented by hopf ...

Consider the following current of a Grassmann spinor given by$$J^{\mu} = \bar{\theta}\sigma^{\mu}\theta$$ where $\theta$ is a Grassmann-valued spinor. Now, if I use$$\bar{\theta}_a\theta_{b} = -\...

I've realised that this question is a duplicate of Proof involving exponential of anticommuting operators, where one can find some answer.I'm struggling to show the equations mentionned in the title. ...

So, I'm reading about the spinor helicity formalism. In some references, I see angle brackets referring to left-handed (dotless) spinors. For example, Cheung writes (equation numbers in this post ...

On the text book I'm studying with there's this expression for the wave function of a particle with spin but it's not clear to me how the resolution of the identity it introduces makes each factor ...

Rather simple question that I'm sure has been asked before, but I haven't been able to figure out a way to phrase it that the search engine understands.As I understand, the group ${\rm Spin}(n)$ is ...

For the Dirac Equation:\begin{equation}\label{eq:DiracLibreMomentoDefinido}i\hbar \frac{\partial}{\partial t} \psi = \left(c\boldsymbol{\alpha} \cdot \mathbf{p} + \beta mc^2 \right)\psi,\end{...

Given a symmetry group in a quantum theory, it is well-known that we must work with its projective representations. For $\text{SO}^+ (1, 3)$, these representations are equivalent to standard ...

In the massless spinor helicity formalism,$$p_{\alpha\dot{\alpha}} = \lambda_\alpha\tilde{\lambda}_\dot{\alpha}$$one can show thatthe hermiticity of $p_{\alpha\dot{\alpha}}$ (i.e. real momenta) ...