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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.

Where can I find more information about this approach?

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    $\begingroup$ This is very nicely discussed in Weinberg I. A must-read indeed. $\endgroup$ – AccidentalFourierTransform Jan 10 '16 at 19:38
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    $\begingroup$ Comment to the equation (v1): There seems to be a mismatch in the $x$-dependence on the left- and right-hand sides. $\endgroup$ – Qmechanic Jan 10 '16 at 19:56
  • $\begingroup$ Search for quantization or field quantization in quantum field theory. $\endgroup$ – Mikey Mike Jan 10 '16 at 20:18
  • $\begingroup$ @AccidentalFourierTransform Thanks! I found the part! $\endgroup$ – Leaning Jan 10 '16 at 21:28

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