# Questions tagged [dirac-matrices]

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### Derivation of the adjoint of Dirac equation

My goal is to deduce the adjoint of Dirac equation: $$\overline \psi (i\gamma^\mu \partial_\mu+m)=0 \tag{1}$$ My process: I started with Dirac equation $(i\gamma^\mu \partial_\mu-m)\psi=0$. ...
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### Could there be a pseudovector kinetic term for fermions?

Could there be a kinetic term of the form $\bar{\Psi} \gamma_5 \gamma^\mu \partial_\mu \Psi$ in addition to the usual one? Or is this forbidden by a symmetry?
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### A question about the decoupling of Dirac equation in 1+1 dimension

It is said that in 1+1 dimension, if we take $\gamma^0=i\sigma^2$ and $\gamma^1=\sigma^1$, then the two components of dirac spinor $\psi_L$(upper component) and $\psi_R$(lower component) decouple in ...
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### Mapping from spinor to tetrad

I am reading the journel by Patrick l. Nash: mapping from tetrad to Dirac spinor. While reading this ,I came across the term concrete real 4*4 irreducible representation of SO(3,3). I know SO(3) is ...
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### Gamma matrices invariant under lorentz transformation

I know this has been asked before but I just can't seem to get my head around it based on the answers I've read. So the idea is that we have the gamma matrices $\gamma^{\mu}$. Now from my ...
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### weak interaction are not parity invariant

I'm having some hard time trying to see why the left-handed lagrangian for fermions $\psi$, $$\mathcal{L} := G\overline{\psi}_{1L}\gamma^\mu\psi_{2L}\overline{\psi}_{3L}\gamma_\mu\psi_{4L}$$ is not ...
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### How to prove $\{\gamma^{\mu}, \gamma^{\nu}\}$ ? (notation problem)

I want to prove that $\{\gamma^{\mu}, \gamma^{\nu} \}=2g^{\mu \nu}$ what are the indices $\mu$ and $\nu$ here? because I know the gamma matrices from 0 to 5 and I need to verify the anti ...
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### Question about $\gamma^{0}$ matrix

I see different definitions in different places so here is my question. why is $\gamma^{0}$ sometimes defined as a 2 by 2 matrix and sometimes as a 4 by 4 matrix? shouldn't a definition be something ...
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### About the central charge of 4D extended supersymmetry algebra

The 4D SUSY algebra can be written as $$\{ Q_{\alpha}^{A} , Q_{\beta}^{B \dagger} \} = 2 m \delta^{AB} \delta_{\alpha \beta} + 2 i Z^{AB} \Gamma^0_{\alpha \beta}, \tag{B.2.37}$$ in a particular ...
I am a bit confused about something. $\gamma^\mu$ is a (Lorentz) vector (c.f. Pesking & Schroeder chapter 3), and so is $p^\mu$, therefore I’d expect their product $\displaystyle{\not}p \triangleq ... 0answers 123 views ### Proving a General Result for a Trace of$n$Gamma Matrices I am attempting to prove a set of results for the products of gamma matrices and traces of products of gamma matrices, but got stuck on this particular one. $$Tr(\gamma^{\mu_1}...\gamma^{\mu_n})=g^{... 1answer 98 views ### How is \gamma^{\mu} defined in the anti commutation relation \{{\gamma_{5},\gamma^{\mu}}\}? how is \gamma^{\mu} defined in the anti commutation relation \{\gamma_{5},\gamma^{\mu}\}? does it make a difference if you write the index {^\mu} lower? what does usually change if the index is ... 1answer 105 views ### Signature of trace of Dirac Matrices I came across this question in my problem set: Let \gamma^\mu, \mu=0,1,2,3 be the Dirac matrices, satisfying: \begin{eqnarray} \gamma^\mu\gamma^\nu+\gamma^\nu\gamma^\mu=2\eta^{\mu\nu}I, \:\:\:... 1answer 158 views ### Gamma matrices in Gaiotto-Witten analysis of N=4 Super Yang-Mills boundary conditions In the paper Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory by Gaiotto and Witten, an in-depth analysis of supersymmetric boundary conditions in N=4 Super Yang-Mills in four ... 1answer 167 views ### The photon propagator term in Peskin & Schroeder Eq. 6.38 In Peskin and Shcroeder, when calculating the one-loop vertex correction, the line above Eq. (6.38) reads$$ \rightarrow \int \frac{d^4 k}{(2\pi)^4} \frac{-ig_{\nu\rho}}{(k-p)^2 + iϵ} \bar{u}(p') (-... 0answers 149 views ### QED parity invariance and gamma 5 [closed] Why does the invariance of parity of QED indicate that gamma-5 can not appear in Feynman diagrams? 1answer 290 views ### Spin Operator in terms of Gamma-5 The QM spin operator can be expressed in terms of gamma matrices and I am trying to do an exercise where I prove an identity which uses$\gamma^5$and${\mathbf{\alpha}}: $$\mathbf{S}=\frac{1}{2}\... 4answers 2k views ### Proof of the Anti-Commutation Relation for Gamma Matrices from Dirac Equation My textbook on QFT says that the Dirac equation can be used to show the following relation:$$\{\gamma^{\mu},\gamma^{\nu}\}=2g^{\mu\nu}I have searched around and unable to find how to prove this ... 2answers 133 views ### \mu \rightarrow e\gamma in the R_\xi gauge: trouble with momenta and Dirac matrices My first ever question on stackexchange! Sorry if it is clumsy... I am trying to follow the computation of \mu \rightarrow e \gamma in Cheng and Li and am confused about the second and third ligns ... 0answers 223 views ### 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{... 2answers 434 views ### 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 ... 1answer 180 views ### 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 ... 2answers 631 views ### 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 ... 1answer 35 views ### 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 $$However, the dimensions don't seem to make ... 1answer 82 views ### Weak isospin current I cannot understand the product of a Dirac gamma matrix and a Pauli matrix in this formula of the weak isospin current:$$J_α^i(x)=\frac12\bar \psi_L(x)\gamma_\alpha\tau^i\psi_L(x),$$where γ_α is ... 0answers 361 views ### Spin covariant derivative of gamma matrices? Where can I find a general expression (on curved manifolds) in local coordinates, for the following:$$\nabla^S_{\mu}\gamma^{\nu} = ?$$\nabla^S_{\mu} = \partial_{\mu} + \omega^S_{\mu} is the spin ... 2answers 109 views ### What is the meaning of \not{p} in physics? I am reading Srednicki's QFT book in physics. On page 286, the formula (45.16) has a notation \not{p}. What is the meaning of \not{p} in physics? Thank you very much. 1answer 205 views ### Trace of 2n gamma matrices To proof$$\mathrm{Tr}(\gamma_{\mu_1}\cdots\gamma_{\mu_{2n}}) =\mathrm{Tr}(\gamma_{\mu_{2n}}\cdots\gamma_{\mu_1}),$$I use \gamma_\mu^\dagger=\gamma^0\gamma_\mu\gamma^0 and get$$\cdots=\mathrm{Tr}... 1answer 130 views ### How to prove\gamma^0=(\gamma^0)^T$? The Dirac gamma matrix$\gamma^0$is symmetric in Dirac, Weyl and Majorana representation. Is it in general true that$\gamma^0=(\gamma^0)^T$? Can it be proved that$\gamma^0=(\gamma^0)^T$in a ... 1answer 88 views ### Dirac operator identity separating out gamma matrices I am trying to show that $$(i\gamma^\mu\partial_\mu -e\gamma^\mu A_\mu)^2 = (i\partial_\mu -eA_\mu)^2 -\frac{e}{2} \sigma^{\mu\nu}F_{\mu\nu},$$ where$\sigma^{\mu\nu} = \frac{i}{2}[\gamma^\mu,\gamma^\...
I recently come across a paper in which the notation of some equation confuses me a lot. Let's say, if I have an expression represented by delta $\delta_{jk},\delta_{jl}$, infinitesimal strain tensor \$...