# Questions tagged [trace]

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### Taking derivatives of traces over matrix products

I started with evaluating the following derivative with respect to a general element of an $n\times n$ matrix, $$\frac{\partial}{\partial X_{ab}}\left(\mathrm{Tr}{(XX)}\right)$$ I wrote out the ...
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### Symmetrized Operators [closed]

Let $A$ be an operator on $H^{n} = H \otimes H \otimes ... \otimes H$ and $W$ be a statistical operator on $H^{n}$. A text books says, if $A$ is symmetric, thenfor any $W$ $Tr(AW) = Tr(AW_{sym})$ ...
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### Trace of the Operator

I want to ask a question about the fundamental knowledge of trace of the an operator. The operator $A$ is $$A = v (G_r-G_a)$$ where v is the velocity operator of the Hamiltonian ($v=dH/dk$); $G_r$ and ...
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### Trace class of the position autocorrelation function

Let us consider a quantum system of $N$ distinguishable particles, and let us tag the configuration $\hat q_j$ of one of those. I am interested in checking whether the position auto-correlation ...
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### Closed quark loops written as traces

I'm working out the quark loop diagram. I draw it as follows: where the greek letters are the lorentz and dirac indices for the gluon and quark respectively and the other letters are color indices. ...
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### Why is the stress-energy tensor for electromagnetic radiation traceless?

A photon gas obeys the equation of state $\rho=P/3$ and hence $T^{\mu}_{\quad\mu}=3P-\rho=0$. (Can also be seen by expressing the stress energy tensor in terms of of the electromagnetic tensor as ...
In Wald (Wald: General Relativity on page 218, equation 9.2.10) is stated that $$v^c∇_cB_{ab}=−B^c_bB_{ac}+R^d_{cba}v^cv_d$$ and to continue in order for the equation to be derived one needs to take ...