# Questions tagged [dirac-matrices]

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### How can I prove this relation involving gamma matrices?

Let $$l^{\mu} = l^{\mu}_{\parallel} + l^{\mu}_{\bot}$$ be a D-dimensional vector living in a Minkowskian space; the only non-zero components of $l^{\mu}_{\parallel}$ are the first four, while the only ...
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### How is $\gamma^{\mu}$ defined in the anti commutation relation $\{{\gamma_{5},\gamma^{\mu}}\}$?

how is $\gamma^{\mu}$ defined in the anti commutation relation $\{\gamma_{5},\gamma^{\mu}\}$? does it make a difference if you write the index ${^\mu}$ lower? what does usually change if the index is ...
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### Signature of trace of Dirac Matrices

I came across this question in my problem set: Let $\gamma^\mu$, $\mu=0,1,2,3$ be the Dirac matrices, satisfying: \begin{eqnarray} \gamma^\mu\gamma^\nu+\gamma^\nu\gamma^\mu=2\eta^{\mu\nu}I, \:\:\:...
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### Gamma matrices in higher (even) spacetime dimensions

Suppose we write the gamma matrices in this following representation: \begin{align*} \gamma^{0}=\begin{pmatrix} \,\,0 & \mathbb{1}_{2}\,\,\\ \,\,\mathbb{1}_{2} & 0\,\, \end{...
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### Choice of Dirac gamma matrix representation and definition of adjoint spinor

Is the definition of the adjoint spinor $\bar{\psi}=\psi^\dagger \gamma^0$ forcing a particular choice of representation of the Dirac matrices (or a subset of the possible choices)? More precisely, I ...
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### spinor vs vector indices of Dirac gamma matrices

I am struggling to understand the nature of the components of the Dirac matrices. If we view the four components of a Dirac spinor as $\psi^a$ with $a$ being a 'spinor' index, then if a gamma matrix ...
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### When can the Minkowski metric be treated as a “number”?

I am starting to study QED at the moment. I can not wrap my head around why the metric ($g_{\mu\nu}$) is used as a number sometimes. In this case it is pretty obvious that it has to be the number ...
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### Dirac Equation Dimensionality

In Griffith's Introduction to Elementary Particles, the Dirac equation is given during its derivation as (Equation 7.19): $$\gamma ^ \mu p_\mu - mc = 0$$ However, the dimensions don't seem to make ...
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### Spin covariant derivative of gamma matrices?

Where can I find a general expression (on curved manifolds) in local coordinates, for the following: $$\nabla^S_{\mu}\gamma^{\nu} = ?$$ $\nabla^S_{\mu} = \partial_{\mu} + \omega^S_{\mu}$ is the spin ...
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### Weak isospin current

I cannot understand the product of a Dirac gamma matrix and a Pauli matrix in this formula of the weak isospin current: $$J_α^i(x)=\frac12\bar \psi_L(x)\gamma_\alpha\tau^i\psi_L(x),$$ where $γ_α$ is ...
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### What is the meaning of $\not{p}$ in physics?

I am reading Srednicki's QFT book in physics. On page 286, the formula $(45.16)$ has a notation $\not{p}$. What is the meaning of $\not{p}$ in physics? Thank you very much.
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### 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 \...
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### Transformation between Weyl and Dirac representation of Gamma matrices

I want to find a similarity transformation $T$ between the Weyl representation and the Dirac representation of the gamma matrices: $\gamma_W^\mu=T \gamma_D^\mu T^{-1}$. It turns out that I can look at ...
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### Dirac Fields and Derivatives (Am I gaining extra minus signs?)

I've given myself a severe headache jumping between East/West Coast sign conventions; I have picked up an extra minus sign and could do with a hand. I am currently using $\eta=\textrm{Diag}[-,+,+,+]$ ...
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### Charge conjugation in chiral representation

I'm reading Maggiore's book and I got to the part of charge conjugation symmetry for Dirac spinor. I get that the definition of charge conjugation is representation-dependent, however I couldn't find ...
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### Property of Charge Conjugation Operator

In class, we have defined the Charge Conjugation Operator ($C$) such that: \begin{equation} C \left(\gamma^\mu\right)^T C^{-1} = - \gamma ^\mu , \end{equation} \begin{equation} \psi^C \equiv C\,\...
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### How are the covariant Pauli matrices defined?

When doing calculations with Weyl spinors, terms like $\theta\sigma^\mu\theta^\dagger$ appear. I know that for 3+1 spacetime dimensions, $\sigma^\mu = (\textbf{1}, \sigma^i)$ with $i=1,2,3$ the usual ...
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### The fifth gamma matrix and fermion fields

I am aware of the various relations with Dirac spinors and chirality but how does the fifth gamma matrix $\gamma^5$ behave with fermion fields, $\psi$? Does the fifth gamma matrix have any particular ...
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I am unable to prove exactly one trace identity that appears in the appendix of Peskin and Schroeder's QFT book. Can someone help me? The theorem [Appendix A.4 eqn (A.28)] says that the order of $\... 1answer 774 views ### Trace of Gamma Matrices [closed] If I have:$Tr(\gamma^{\mu}\gamma^{\alpha}\gamma^{\nu}\gamma^{\beta}\gamma^{\rho}\gamma^{\gamma}\gamma^{\sigma}\gamma^{\delta})$and I want to get it re-ordered like$Tr(\gamma^{\alpha}\gamma^{\...
Consider $d$-dimensional gamma matrix structures. I have an expression like $$\sum_{h_2=\pm}\text{Tr}(\not{\xi}_2\not{p}_3\bar{\not{\xi}}_2\not{p}_1),$$ where $\not p=p^\mu \eta_{\mu\nu}\gamma^\nu$ ...
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  ...