# How to relate classical field and quantum operator?

Recently I listened to a lecture from perimeter institute. There was an idea which I found interesting. That is, roughly, for a field $\phi(x)$ we can assume the relation with the creation operator like:

$$\phi(x)=\sum_\sigma\int d^3p \{u(x,p,\sigma)a^\dagger(p,\sigma)\}$$

Then from the fact that $\phi(x)$ transforms under a representation of Lorentz group and $a^\dagger|0\rangle$ transforms under a unitary group (it is a one-particle state), we can determine $u$ uniquely.

• Comment to the equation (v1): There seems to be a mismatch in the $x$-dependence on the left- and right-hand sides. – Qmechanic Jan 10 '16 at 19:56