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In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!

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Can Hadamard's formula be used for fermionic operators?

[B, [B,A]] + \dots$$ for fermionic operators? Suppose I have fermionic operators that obey anticommutation relations $\{a,a^{\dagger}\}=1$ and $\{a,a\}=\{a^{\dagger},a^{\dagger}\}=0$. … [a, (1-2a^{\dagger}a)]+\dots$ Is this formula universal for fermionic and bosonic operators? …
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