# Questions tagged [trace]

Use this tag when having questions concerning expressions with the trace of a matrix/operator.

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### How is the Ricci scalar the trace of the Ricci tensor?

The Ricci scalar is the uncontracted version of the Ricci tensor $R=R^{\mu}_{\mu}=g^{\mu\nu}R_{\mu\nu}$. Carrol describes the Ricci scalar as being the trace of the Ricci tensor, but I do not ...
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### The covariance matrix $\mathbf{C}$: Why does $\ln \text{det} \mathbf{C}=\text{Tr}\ln \mathbf{C}$ hold? [migrated]

Prof. Max Tegmark first introduced the Fisher information matrix into cosmology in his paper titled Karhunen-Loeve eigenvalue problems in cosmology: How should we tackle large data sets? As I read the ...
1 vote
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### (Anti-)Fundamental Representation of $SU(5)$ GUT

In many places, it has been mentioned that the sum of electrical charges of the particles present in $\overline{5}$ of $SU(5)$ is zero since the trace of $SU(5)$ generators is zero. I do not ...
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### Trace of stress tensor in 2D average null energy condition

I was looking through Zamolodchikov's derivation of the $c$-theorem and stumbled across an equation which says the following - $$\Theta = T^\mu_\mu = 4T_{z\bar{z}}.$$ As far as I understand, for two ...
310 views

### Generators of ${\rm SU}(n)$ are traceless. Why?

A general element of the Lie group ${\rm SU}(n)$ is written as $$g({\vec{\theta}})=e^{-i\sum_a\theta_a T_a}$$ where $\theta_a$ for $(a=1,2,\ldots,n^2-1)$ denotes $n^2-1$ real parameters. The ...
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### Physical interpretation of unbounded trace class linear maps

Quite generally, quantum states are defined to be positive, trace-class linear maps with trace equal to one on a complex separable Hilbert space $\mathcal{H}$. If we require that these trace-class ...
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### A limit of a particular Quantum Fidelity

I have the following problem. Let $\mathbf{\hat{\rho}}(t)$ and $\mathbf{\hat{\sigma}}(t)$ be two trace class positive operators acting on a Hilbert space of infinite dimension for all $t > 0$. More ...
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### Why does the trace of the pion operator vanish?

I am working my way through Srednicki's QFT book. Currently I'm in chapter 94. Between equations 94.20 and 94.21, Srednicki says that the following expression vanishes in the case of two light ...
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### Why is the trace of the outer product of two states equal to the inner product of the two states?

Why is it that, given two quantum states $|\psi_1\rangle$, $|\psi_2\rangle$, $$\mathrm{Tr}(|\psi_1\rangle\langle\psi_2|) = \langle\psi_2|\psi_1\rangle \quad$$ I went through the equation with the ...
285 views

1 vote
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### Lorentz generators trace

I am reading Peskin's and Schroeder's book "An introduction to Quantum Field Theory". At some point in Chapter 3.1, they write down a particular representation for the Lorentz generator of a ...
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### Notation of trace in QCD

I have been reading about QCD, and I have found a notation about the trace at Schwinger Dyson equation like $Tr_D[exp]$ and I don not know whats does means. Thank you. Update reference: equation 27 ...
1 vote
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### Linearity of partial trace

In Quantum Processes Systems, and Information by Schumacher and Westmoreland we are given this property of the partial trace  Tr_R G^{RQ} = Tr_R \left( |\alpha^R,\phi^Q \rangle\langle\beta^R,\psi^Q| ...
1 vote
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### The significance of trace of a matrix [duplicate]

Since the determinant and trace of a matrix give information about the solution of the 1D propagation system, i.e. the solution is propagating, scattering or tunneling, etc. How do we extract ...
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### Trace and determinants in QFT's

I'm trying to understand this paper: https://doi.org/10.1103/PhysRevA.46.6490. It's about path integration with defects (theories on submanifolds). Let me here try to explain what in particular I'm ... I learned that if you have a density matrix $\rho$ then $\mathrm{Tr}(\rho^2)=1 \Rightarrow$ pure state $\mathrm{Tr}\rho^2<1 \Rightarrow$ mixed state Can one have $\mathrm{Tr}(\rho^2)>1$? For ...