Hi!
Is it possible to construct gamma matrices satisfying the Clifford algebra ##\{\gamma^\mu, \gamma^\nu \} = \eta^{\mu \nu}## that are *real*, for ##\eta = diag(-1,1,1)##?
I know that I can construct them in principle from sigma matrices, but I don't know how to construct real gamma...
I'm currently working out quantities that include the vector and axialvector currents ##j^\mu_B(x)=\bar{\psi}(x)\Gamma^\mu_{B,0}\psi(x)## where B stands for V (vector) or A (axialvector). The gamma in the middle is a product of gamma matrices and the psi's are dirac spinors. Therefore on the...
Hi all, I am working on a project at the moment, and I have to evaluate the trace by using the Casimir's trick.
The trace form is
$$Tr[(\displaystyle{\not} P +M_{0})\gamma^{\mu}(\displaystyle{\not} P^{'} +M^{'}_{0})(\displaystyle{\not} p^{'}_{1} +m^{'}_{1})\gamma^{\nu}(\displaystyle{\not} p_{1}...
Homework Statement
I define the gamma matrices in this following representation:
\begin{align*}
\gamma^{0}=\begin{pmatrix}
\,\,0 & \mathbb{1}_{2}\,\,\\
\,\,\mathbb{1}_{2} & 0\,\,
\end{pmatrix},\qquad \gamma^{i}=\begin{pmatrix}
\,\,0 &\sigma^{i}\,\,\\
\,\,-\sigma^{i}...
I would like to know where one may operate with tensor quantities in quantum field theory: Minkowski tensors, spinors, effective lagrangians (for example sigma models or models with four quark interaction), gamma matrices, Grassmann algebra, Lie algebra, fermion determinants and et cetera.
I...
Here it is a simple problem which is giving me an headache,
Recall from class that in order to build an invariant out of spinors we had to introduce a somewhat
unexpected form for the dual spinor, i.e. ߰ψ = ψ†⋅γ0
Then showing that ߰ is invariant depends on the result that (ei/4⋅σμν⋅ωμν)† ⋅γ0...
Hi,
I'm currently going through Griffith's Particle Physics gamma matrices proofs. There's one that puzzles me, it's very simple but I'm obviously missing something (I'm fairly new to tensor algebra).
1. Homework Statement
Prove that ##\text{Tr}(\gamma^\mu \gamma^\nu) = 4g^{\mu\nu}##...
Hi,
I've been studying Dirac's theory of fermions. A classic topic therein is the proof that the equation is covariant. Invariably authors state that the gamma-matrices have to be considered constants: they do not change under a Lorentz-transformation. I am looking for the reason behind this. It...
Consider a Majorana spinor
$$
\Phi=\left(\begin{array}{c}\phi\\\phi^\dagger\end{array}\right)
$$
and an pseudoscalar current ##\bar\Phi\gamma^5\Phi##. This term is invariant under hermitian conjugation:
$$
\bar\Phi\gamma^5\Phi\to\bar\Phi\gamma^5\Phi
$$
but if I exploit the two component...
Trace of six gamma matrices
I need to calculate this expression:
$$Tr(\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma^{\sigma}\gamma^{\alpha}\gamma^{\beta}\gamma^{5}) $$
I know that I can express this as:
$$...
I'm reading through some lecture notes and there is a proof that the gamma matrices are traceless that I've never seen before (I've seen the "identity 0" on wikipedia proof) and I can't work out some of the steps:
\begin{align*}
2\eta_{\mu\nu}Tr(\gamma_\lambda) &=...