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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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Simple QFT simulation - how to do it
Defining commutation relation $[\hat{\phi}(x,t),\hat{\Pi}(x',t')] = i \delta(x-x',t-t')$, I should somehow make contact with the ladder operators $a$ and $a^{\dagger}$. … Secondly, once I make contact with ladder operators, I can then express any state of the system as a concatenation of ladder operators on the vacuum state $|0\rangle$ such as $a^{\dagger}_{p_2} a^{\dagger …