# Questions tagged [dirac-matrices]

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### Commutator of Dirac gamma matrices

Quick question...For some reason I'm having trouble finding an identity or discussion for the commutator of the gamma matrices at the moment...i.e $$\gamma^u\gamma^v-\gamma^v \gamma^u$$ but I am not ...
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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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Is it possible to show that ${\gamma^5}^\dagger = \gamma^5$, where $$\gamma^5 := i\gamma^0 \gamma^1 \gamma^2 \gamma^3,$$ using only the anticommutation relations between the $\gamma$ matrices, \... 2answers 521 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 ... 2answers 2k views ### How to find a particular representation for the gamma matrices? I asked this question as a subquestion in another thread, but got the answer below and thought it deserved a thread of its own. Two well-known representation of the gamma matrices are the Weyl and ... 1answer 866 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^{\,\... 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? 2answers 1k views ### How does Schur's Lemma mean that the Dirac representation is reducible? In chapter 3 of Peskin and Schroeder, when they're talking about "Dirac Matrices and Dirac Field Bilinears," they introduce \gamma^{5} and give some properties of it. One of the properties is [\... 1answer 3k views ### 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 ... 2answers 497 views ### Zee's use of Kronecker Product in “QFT in a Nutshell” to represent Dirac matrices In his book Quantum Theory in a Nutshell (2nd edition, p. 94), Zee describes the Dirac gamma matrices and lists a representation using Pauli matrices and the identity matrix. For example he writes ...
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I'm having issues deriving the Dirac adjoint equation, $$\overline{\psi}(i\gamma^{\mu}\partial_{\mu}+m)=0.\tag{1}$$ I started by taking the Hermitian adjoint of all components of the original Dirac ...
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### Spinors, Spacetime and Clifford algebra

I'm looking to understand the intrinsic connection that Clifford algebra allows one to make between spin space and spacetime. For a while now I've trying to wrap my head around how the Clifford ...
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I can't solve this apparent paradox; I have the free lagrangian for massive fermions $\mathscr L = i\bar\Psi\gamma^\mu\partial_\mu\Psi - m\bar\Psi\Psi$ which is invariant under the global phase ...
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### Physical interpretation of gamma matrices

Just out of plain curiosity, I want to ask: What are/is the physical interpretation(s) of the gamma matrices? If there is none, is it right to assume that it is just a mathematical fudge-factor?
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### Why do we need matrices in the Dirac equation?

Consider the following equation: \begin{equation} \nabla^2 - \frac{1}{c^2}\frac{\partial^2}{\partial t^2} = \left(A \partial_x + B \partial_y + C \partial_z + \frac{i}{c}D \partial_t\right)\left(A \...
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### Proof of the Anti-Commutation Relation for Gamma Matrices from Dirac Equation

My textbook on QFT says that the Dirac equation can be used to show the following relation: $$\{\gamma^{\mu},\gamma^{\nu}\}=2g^{\mu\nu}$$ I have searched around and unable to find how to prove this ...
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### What is the relationship between the Lorentz group and the $CL(1,3)$ algebra?

In my classes the dirac equation is always presented as the "square root" of the Klein Gordon equation, then from this you can demand certain properties from the Matrices (anticommutation relations, ...
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### Missing identity element in the Clifford relation

While studying the Dirac equation, $$\left(i\gamma^{\mu} \partial_{\mu} - m\right)\psi = 0.$$ I have been finding difficulty understanding the following summarisation of the algebra that the $\gamma$-...
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I know there are many questions about this topic and also various answers, but it's never stated explicitly, why there is a certain sign before the mass term in the Dirac Lagrangian. I'm also confused,...
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### How can pseudospin be a vector? (Graphene)

In graphene science, I don't understand how one interprets pseudospin as a vector. I thought 'pseudospin' was the vector of Pauli matrices. So how can it be a vector that one can plot for example in ...
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### A more general completeness relation for Dirac spinors

Assume that we have two 1/2-spin particles with four-momenta $p$ and $p'$. Particle Dirac spinors satisfy the completeness relation $$\sum_{s=1}^2u_s(p)\overline{u}_s(p)=\not p+m$$ My goal now is to ...