# Tagged Questions

The tag has no usage guidance.

19 views

104 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 $\sigma^{\mu\nu} = \frac{1}{4}[\gamma^\mu, \gamma^\nu]$ ...
21 views

### What are possible ways to construct J-matrices (higher order Pauli matrices)?

I'm looking for possible ways to construct $J$-matrices. $J$-matrices are the higher-order version of Pauli matrices. Pauli matrices are suited for spin-1/2 systems, while J-matrices can be for any ...
55 views

### Real irreducible representation of $SU(2)$ [closed]

Consider a real irreducible representation of $SU(2)$ group in $d$-dimensional space-time. How many components do the spinors (eigenvectors) have? For instance, a real irreducible spinor in 10-dim has ...
156 views

### Why complexify in order to construct Dirac representation?

Suppose we have a theory is covariant under the Spin group Spin(2n-1; 1). We consider the real vector space $V = R^{2n-1,1}$, which naturally comes with a Lorentzian inner product. On this vector ...
38 views

### Acting for a covariant derivative on charged spinor [closed]

For field, theory what i know $i.e$,complex scalar QED \begin{align} D_\mu \phi = \partial_{\mu} \phi - i Q A_{\mu} \phi \end{align} and \begin{align} D_\mu \phi^{\dagger} = \partial_{\mu} \phi^{\...
33 views

72 views

### Coupling a spinor field to a preexisting scalar field?

So I'm not a physicist, but I'm thinking about a mathematical problem where I think physical insight might be useful. We're working on a Riemannian manifold $(M,g)$ (positive definite metric) with a ...
41 views

### Left-handed Majorana mass term forbidden by $SU(2)$?

I'm trying to figure out why a left-handed Majorana mass term is mathematically forbidden by the $SU(2)_L$ symmetry in the context of the seesaw model. As far as I get it, it is because the left ...
177 views

### How do simple two-component Fierz identities follow from a property of the Pauli matrices?

On page 51 Peskin and Schroeder are beginning to derive basic Fierz interchange relations using two-component right-handed spinors. They start by stating the trivial (but tedious) Pauli sigma identity ...
24 views

### How does a linearly polarized spin 1/2 wave look like?

Spin 1 waves are easy to illustrate and a linearly polarized spin 2 wave looks like this, but what is the counterpart for a spin 1/2 wave?
26 views

### Probability density for spinors

I am approaching Relativistic Quantum Mechanics seriously for the first time, going through Bjorken & Drell and doing all the excercises, but I am facing some problems with 3.1. Derive (3.11) ...
58 views

50 views

### Why are half integer and full integer spin properties of elementary particles, not of all points in space?

Tensors and spinors arise mathematically from the representation of the rotation group $SO(3)$ as a ball in 4D with all antipodal points on the surface identified. In this picture it is shown that ...
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 ...