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Results tagged with trace
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user 342609
Use this tag when having questions concerning expressions with the trace of a matrix/operator.
3
votes
Can the Dirac trace of two gamma matrices always be made positive?
Quite generally, you have ${\rm Tr}(-A B)=-{\rm Tr}(A B)=-{\rm Tr}(BA)$ for arbitrary square matrices $A$, $B$.
- 7,298
2
votes
Accepted
What is the physically significance of having trace less than 1 in squared mixed state densi...
The trace of $\rho^2$ is thus given by ${\rm Tr} \rho^2 =\sum_n p_n^2 \le 1$, where the equality sign holds if and only if $p_m=1$ for some index $m$ and $p_n=0$ for $n\ne m$. …
- 7,298
0
votes
How to prove $\mathrm{Tr}[(\partial_\mu U)U^\dagger]=0$?
Even in the absence of an additional relation, a term of the form ${\rm Tr} (\partial_\mu A \,\, \partial^\mu B)$ in the Lagrangian would be (physically) equivalent to $- {\rm Tr} [ (\partial_\mu \ …
- 7,298
7
votes
Unitary equivalence between Hermitian operators
The time evolution of the position operator of a free particle in quantum mechanics (Hamiltonian $H=P^2/2m$) is a nice counterexample:
$ e^{iHt/\hbar} X e^{-iHt/\hbar} = X + P t/m$,
with $A=X$ (positi …
- 7,298