# Questions tagged [dirac-matrices]

The tag has no usage guidance.

306 questions
Filter by
Sorted by
Tagged with
134 views

### How to calculate the trace below?

I am currently reading Peskin's QFT book on my own. Though it introduces the Trace Technology in Section 5.1, the trace calculations in the following sections are still far from clear to me. Here is ...
398 views

### Solution of the Dirac equation by Pauli four-vector

Reading through David Tong lecture notes on QFT. On page 100, he solves the Dirac equation by Pauli four-vector. See below link: QFT notes by Tong, Chapter 4 In (4.107) he gives the solution in ...
341 views

### What is the Hermitian conjugate of the 4-vector momentum in Dirac equation?

I am quite confused about the Hermitian conjugate of the 4-vector momentum $p=(p^0, p^1, p^2, p3)$. The confusion mainly arises when deriving the Dirac adjoint and the charge current probability. (1)....
1k views

### Hermitian properties of the gamma matrices

The gamma matrices $\gamma^{\mu}$ are defined by $$\{\gamma^{\mu},\gamma^{\nu}\}=2g^{\mu\nu}.$$ There exist representations of the gamma matrices such as the Dirac basis and the Weyl basis. Is it ...
821 views

709 views

82 views

### From $\gamma$ to $\sigma$, finding proper basis

For $d$ dimensional case, usual gamma matrices have basis $\Gamma^A = \{1, \gamma^a, \cdots \gamma^{a_1 \cdots a_d}\}$ (Let's think about even case only for simplicity, I know for odd case only up to ...
717 views

### Some general formula with trace of gamma matrices relating $\gamma^{(d+1)}$

I want to figure out the trace of gamma matrices relating with $\gamma^{(d+1)}$ for even $d$ dimensional case. First define $\gamma^{(d+1)}$ as \begin{align} \gamma^{(d+1)} = \gamma^1 \gamma^2 \...
84 views

526 views

### Can we make the Dirac representation a gauge theory?

I'm looking for comments and references about an idea : gauging the Dirac representation of the Dirac matrices. What kind of field interaction would it give ? Specifically, the Dirac equation is ...
65 views

### Sign choice for sigma-matrices

I'm trying to figure out the consequences of the sign choice $$\sigma^\mu = (\mathbf{1},\vec\sigma)\qquad\text{vs.}\qquad \sigma^\mu = (-\mathbf{1},\vec\sigma) \,.$$ This choice does not affect the ...
266 views

### Proof of two Lorentz-algebra identities

I am currently working through the QFT introduction text by Peskin and Schroeder and try to fill in two identities that I wasn't able to prove (it should be fairly simple, but my experience with this ...
1k views

629 views

### Symmetry properties of gamma matrices

While reading a paper on supersymmetry i faced the following problem. Its about the symmetry property of charge conjugation matrix in different space time dimension. The charge conjugation matrix is ...
244 views

4k views

### Deriving the Spinor Completeness Relation without using a Representation

Reference: DAMTP problem set 3, question 5 but ignore the spinor solutions given. To preface, this has taken up 1 entire day and a further 2 afternoons of work so I will just list the most promising ...
780 views

135 views

149 views

### Pseudoscalar current of Majorana fields

Consider a Majorana spinor $$\Phi=\left(\begin{array}{c}\phi\\\phi^\dagger\end{array}\right)$$ and an pseudoscalar current $\bar\Phi\gamma^5\Phi$. This term is invariant under hermitian conjugation:...
873 views

### How to show that $\bar\psi\gamma^\mu\psi$ of a Dirac spinor $\psi$ transforms as a vector?

This is part 2 of exercise II.1.1 of Zee's QFT in a Nutshell (here's part 1). This is what I have got: \begin{align} \bar\psi\gamma^\lambda\psi \mapsto \bar\psi^{\,\prime}\gamma^\lambda\psi^{\,\...
737 views

### How to show that $\bar\psi\psi$ of a Dirac spinor $\psi$ transforms as a scalar?

I would like to show that for a Dirac spinor $\psi$, the scalar product $\bar\psi\psi$ transforms as a scalar under a Lorentz transformation $\Lambda$, where $\bar\psi = \psi^\dagger\gamma^0$. This is ...
63 views

In the discussion of external bremsstrahlung, the following amplitude is used: $$M=i\bar{u}_e(k')e \left(\gamma^\nu\epsilon_\nu \left[ \frac{i \gamma^\nu(k'_\nu+\omega_\nu) + m}{(k'+\omega)^2-m^2}\... 2answers 404 views ### Local Lorentz transformations If \gamma^m denotes a tangent space gamma matrix, and \gamma^\mu denotes a curved space gamma matrix, then they are related by$$\gamma^\mu(x) = \gamma^m e_{m}^{\mu}(x)$$where e_{m}^{\mu}(x) ... 2answers 3k views ### Gamma matrices and trace operator I'm trying to show that the trace of the product of the following three Gamma (Dirac) matrices is zero, i.e.$$\text{tr}(\gamma_{\mu} \gamma_{\nu} \gamma_{5})=0 \text{.} I attempted to use the fact ...
In this document, after equation 62 on page 9, the author says that we can rewrite $\alpha^i \alpha^j \partial_i \partial_j$ as \$\frac{1}{2} (\alpha^i \alpha^j + \alpha^j \alpha^i)\partial_i\...