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# Questions tagged [dirac-matrices]

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### Converting two component product to four component notation

Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry, \chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta \end{...
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### Time reversal operator symmetry of dirac lagrangian

I want to prove time reversal symmetry of Dirac Lagrangian, I have some problems with calculations. I start with \begin{eqnarray} T\psi T = U \psi \end{eqnarray} \begin{eqnarray} T\bar{\psi } T = ...
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### Motivation for spinors

After it was found that the gamma matrices couldn't be Pauli matrices and only had to be larger and even, why was their need to define a new algebraic object (i.e a Dirac spinor)? Why couldn't a ...
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### Parity on gamma matrices

I want to understand clearly why $P \gamma^{\mu} P = \gamma^{\mu}$, where $P$ is the parity operator. This result follow for example from pag. 66 of Peskin-Schroeder. The parity operator acts ...
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### Simplifying a seemingly simple gamma matrix identity

When studying from the book by Wise and Manohar, Heavy Quark Physics (pg 102), I came across a seemingly simple identity that I am not able to prove. It's likely an easy problem but I can't for the ...
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### $\gamma^5$ factor in Quantum Field Theory

I have a problem with interpretation of $\gamma^5$ factor in the interaction Hamiltonian. I know that $\frac{1\pm\gamma^5}{2}$ is a helicity projection and it requires helicity conservation in ...
644 views

### Proof of equivalence of different representations of the $\gamma$-matrices in the Dirac equation

This question concerns the Dirac equation and the $4\times4$ $\gamma$-matrices. The task is to prove that a similarity transformation of the standard $\gamma$-matrix conserves the commutation relation ...
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### Dimension of gamma matrices in higher dimensional Dirac equations

Reading about Dirac's equation in higher dimensional space-times I have read that the gamma matrices are $2^{[D/2]}\times{}2^{[D/2]}$. So, if we have $D=11$, for example, how is this formula supposed ...
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### What is $\langle G_{\mu\nu}\rangle\langle G_{\mu\nu}\rangle$ for the Dirac gamma matrices?

Given the following 16 matrix multiplications of the Dirac gamma matrices \begin{align} G_{\mu\nu} = \dfrac{1}{2} \begin{pmatrix} I && \gamma_{0} && i\gamma_{123} && i\gamma_{...
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### Do Dirac Gamma Matrices act like Tensors?

Do Dirac Gamma Matrices act like Tensors? Is it true that $$\gamma_\mu = \eta_{\mu\nu}\gamma^\nu~?$$ Also what about $\sigma_{\mu\nu}$, where $\sigma_{\mu\nu}$ is defined to be: \begin{align*} \...
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### Why in the relativistic quantum mechanics $\gamma_4$ name is not used instead of $\gamma_5$?

I have seen in the in the Dirac equation $$\gamma_0,\gamma_1,\gamma_2,\gamma_3.$$ Then I have seen the definition of a new matrix $$\gamma_5=i\gamma_0\gamma_1\gamma_2\gamma_3.$$ Now my question is why ...
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### What is unitarily similar matrices?

In one of tasks I met the concept of unitarily similar matrices: in particular, I need to prove that sets $\gamma_{\mu}, -\gamma_{\mu}$ (Dirac gamma matrices) are unitarily similar. I don't know what ...
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The trace of matrix is always sum of its eigen values , which can be seen if $\hat{U}$ transforms the matrix $\alpha_i$ into it's diagonal form . $$\begin{pmatrix} A_1 & 0 & \cdots & 0 \... 0answers 232 views ### Are Lifshitz and Berestetskii right in this case? In the Quantum electrodynamics book (look at the problem) its authors Lifshitz and Berestetskei claim that operator of charge conjugation \hat {C} = -\alpha_{2} in Majorana basis transforms as \hat ... 2answers 2k views ### Why the lowest order of matrices in Dirac equation are 4x4 matrices? [duplicate] Why the lowest order of matrices in Dirac equation (Relativistic Quantums) are 4x4 matrices (and can not be 2x2 matrices)? How to prove it? 1answer 1k views ### Closed formula for product of gamma matrices I was asking myself if there is a closed formula for the following product of gamma matrices:$$\gamma_\mu\gamma_\nu \gamma_5.$$I would like to express this matrix in terms of the basis$${\...
The spinor inner product in particle physics is given by $\overline{\psi} \psi = \psi^{\dagger} \gamma_0 \psi$, where I take the convention that the zeroth gamma matrix is hermitian while the rest ...