# Questions tagged [dirac-matrices]

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### Dirac conjugation of a 3x3 matrix

This question might be stupid, but when I compute $\bar{B}$ in the Lagrangian, I have to multiply 3x3 $B$ matrix with 4x4 $\gamma_0$ matrix (Dirac's conjugation) which are incompatible in size. What ...
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### Sign of pair of Dirac spinor bilinear

I don't understand the following statement: Any pair of Dirac spinors verifies $(\bar{\Psi}_1\Psi_2)^\dagger=\bar{\Psi}_2\Psi_1$ and it is valid for both commuting and anti-commuting (Grassmann-valued)...
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### Equivalence of the Dirac representation of the Lorentz algebra and its conjugate in even dimensions - Polchinski

In Polchinski's String Theory, Appendix B.1 we look at the smallest irreps of the Clifford algebra in even-dimensional spacetimes $d=2k+2$. In (B.1.16) he defines two operators from the gamma matrices ...
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### Hermitian Adjoint of Dirac Equation vs Dirac Lagrangian

I have a question about the self-adjointness of the gradient in spinor space. In the derivation of the Dirac adjoint equation, as in Hermitian adjoint of 4-gradient in Dirac equation , it has been ...
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### Why did Dirac choose a linear equation in momentum for formulating a relativistic wavefunction?

The Dirac equation arose out of the need for a quantum mechanical wave equation that treats position and time on an equal basis, just as relativity expects them to be. Now the Schrodinger equation is ...
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### Gamma matrices - Dirac [closed]

I tried to ask this question: Prove that $\{\gamma_\mu , \gamma_\nu\} = 0$, but I was unable to resolve it. Can someone help me?
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### Going from the Dirac Lagrangian to the adjoint Dirac equation

I am comfortable doing the following calculation, Derivation of the adjoint of Dirac equation, notably — going from the standard Dirac equation to the adjoint Dirac equation via using Dirac ...
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### Generalization of Dirac matrices

Is it possible to have a set of 16-dimensional matrices $\gamma_{\mu}^{a}$ such that $$\{\gamma_{\mu}^{a},\gamma_{\nu}^{b}\} = 2\delta^{ab}\eta_{\mu\nu}$$ where $\eta_{\mu\nu}$ is the Minkowski metric ...
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### Dirac matrix algebra from bosonic creation/anihilation operators?

Using some generic fermionic creation/anihilation operators $a_i$ and $a_i^{\dagger}$ ($i, j = 1, 2, 3, \dots, N$) such that \begin{align} \{ a_i, \, a_j^{\dagger} \} &= \delta_{ij}, \tag{1} \\[...
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### What transformation gives a Weyl-like representation by flipping $\gamma^0$ and $\gamma^5$?

The usual Weyl representation of the Dirac matrices is defined like this: $$\tag{1}\gamma_W^a = T_W \, \gamma^a \, T_W^{-1},$$ where \begin{align}\tag{2} T_W &= \frac{1}{\sqrt{2}} (1 + \gamma^5 \, ...
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### Fierz Identity problem in P&S

I have a few questions about the Fierz identity. First of all in general form it has terms as $(\bar u_1\Gamma^Au_2)(\bar u_3\Gamma^Bu_4)$ which is a product of Dirac field bilinears. The question is ...
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### For two majorana field $\psi$ and $\chi$, is it true that $\bar{\psi} \chi = - \bar{\chi} \psi$?

For two majorana field $\psi$ and $\chi$, which satisfy $\psi_{c}=\psi$ and $\chi_{c} = \chi$, where the charge-conjugation operation we define as $$\Psi_{c} = C \Psi^{\ast}$$ where we work in the ...
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Using the Dirac equation with or $p=$ zero and the $\gamma^0$ matrix defined as $$\gamma^0=\begin{pmatrix}0 & \sigma_0 \\ \sigma_0 & 0\end{pmatrix} = \begin{pmatrix}0 & \bf{I} \\ \bf{I} &... 1answer 77 views ### Fierz identities and anticommutation relations Let us consider the following term$$\bar\psi(p_1)M\psi(p_2) \bar\psi(p_3)N\psi(p_4)$$According to Ortin's book (equation (D.65)), from the Fierz identity we would have something like$$\bar\psi(...
I have the following doubt about the identity in this page: $${a\!\!\!/}{a\!\!\!/} \equiv a^\mu a_\mu \cdot I_4 = a^2 \cdot I_4$$ however: {a\!\!\!/}{a\!\!\!/}=a^{\mu}\gamma_{\mu}a_{\mu}\gamma^{...