# Questions tagged [dirac-matrices]

The tag has no usage guidance.

321 questions
Filter by
Sorted by
Tagged with
30 views

### Why $(\vec{\sigma}\cdot\vec{p}) (\vec{\sigma}\cdot\vec{p}) = (\vec{\sigma}\cdot\vec{p}) p^0$ for Pauli matrices?

I am trying to verify that the following equation is true: $$(\vec{\sigma}\cdot\vec{p}) (\vec{\sigma}\cdot\vec{p}) = (\vec{\sigma}\cdot\vec{p}) p^0$$ where $p^\mu=(p^0,\vec{p})$ is the four momentum ...
41 views

### Spinor matrix representation of a spacetime vector in 2+1D

Let $a^\mu$ be a spacetime vector in 2+1D: $(t,x,y)$. What would be the spinor-matrix representation ${A^\alpha}_\beta$ of the spacetime vector $a^\mu$? I have not been able to even find examples or ...
26 views

### Calculation of Parity in Quantum Field Theory

In the book "Relativistic Quantum Mechanics An Introduction To Relativistic Quantum Fields" by Luciano Maiani Omar Benhar, page 174, the picture of that page is provided below. I don't ...
40 views

### Show $[\gamma^\mu,\eta^{\nu\lambda}I]=0$ for Dirac matrices

I am trying to show the following commutation relation for the Dirac matrices $\gamma^\mu$ and the metric $\eta^{\nu\lambda}$: $$2[\gamma^\mu,\eta^{\nu\lambda}I]=0$$ where $I$ is the 4x4 identity ...
45 views

### Interchanging positions of Gell-Mann matrices with Dirac matrices, Pauli matrices

The anti-commutation relations for Gamma matrices $\big\{\gamma ^\mu , \gamma ^\nu \big\} = 2g ^{\mu \nu}$ can be used for interchanging positions of the respective matrices in a given expression, ...
43 views

### What is $D$ or $D$-with-a-slash-through-it in the Standard Model equation(s)?

In the mathematical formulation of the Standard Model, which I do not understand yet, there is a capital letter $D$ or $D$-with-a-slash-through-it that I can't find an explanation for. Flip Tanedo (a ...
21 views

35 views

### Time-reversal symmetry and the generalized special axes (eg: $y$) in any $D$ space dimension

In 3D space, it is common to choose the time-reversal symmetry acting on spin-1/2 doublet fermions as $$T = i \sigma_y K = \begin{pmatrix} 0 & 1\\ -1& 0\end{pmatrix}$$ where $K$ is complex ...
105 views

### Prove $\displaystyle{\not}{\nabla}^2=\nabla_{\mu} \nabla^{\mu}-R/4$ [closed]

I am trying to show $\displaystyle{\not}{\nabla}^2=\nabla_{\mu} \nabla^{\mu}+R/4$ where $R$ is Ricci scalar. $\nabla_{\mu}$ is covariant derivative for spinor: \begin{equation} \nabla_{\mu}=\partial_{...
45 views

### Dirac Bilinear Transformation Laws (vector)

The question is to verify that the following Dirac Bilinears obey the following transformation law: $$\bar\psi'(x') \gamma^\mu \psi'(x') = \Lambda^\mu_\nu \bar\psi(x) \gamma^\nu \psi(x)$$ What I know ...
61 views

29 views

### How does following relation generates Lorentz generator?

In Schwartz book sec 10.3, Schwartz says following: The Lorentz generators when acting on Dirac spinors can be written as $$S^{\mu \nu}=\frac{i}{4}[\gamma^{\mu},\gamma^{\nu}]$$ But what I am able to ...
104 views

### Matrix “dimensional analysis” of Lagrangians in QFT

Since the important things in the QFT Lagrangian are vectors and matrices, I wanted to do a "matrix dimensional analysis" of each term. The electromagnetic Lagrangian (ignoring all constants ...
61 views

81 views

41 views

65 views

### Is there a bosonic representation of Clifford algebra in (1,3) spacetime?

By a suitable combination of Dirac's $\gamma_\mu$ matrices one can define creation and destruction operators satisfying fermionic anticommutators. Is there a similar result for bosons in the context ...
61 views

66 views

78 views

### Is this an alternative Dirac Equation in curved space?

The usual covariant derivative for the Dirac equation in curved space is: $$D_\mu \psi = (\partial_\mu - {i \over 4} {\omega_\mu}^{ab} \sigma_{ab}) \psi$$ However, I think I found another ...