0
$\begingroup$

We can construct the unitary transformation for change of basis from $x$ to number operator $n$ in harmonic oscillator by using $a|0\rangle=0$ and then multiply $\langle x|$ to the both side and calculating $\langle x | 0 \rangle$ and then find $\langle x | p \rangle$ and finally use the completeness relation to find the transformation.

Now I would like to somehow find the transformation for a free, real Klein-Gordon Lagrangian with $[\phi(x)]$ being the field operator. How can we construct a unitary transformation from occupation number $|n \rangle$ basis to $|\phi \rangle$ basis?

Improve this question
$\endgroup$
13
  • $\begingroup$ Related, and also. $\endgroup$
    – Cosmas Zachos
    May 30, 2019 at 16:45
  • $\begingroup$ Linked. $\endgroup$
    – Cosmas Zachos
    May 30, 2019 at 16:48
  • $\begingroup$ yes it does relate but those are not unitary operators so i cant make a unitary transformation out of them $\endgroup$
    – Jason
    May 31, 2019 at 8:13
  • $\begingroup$ @CosmasZachos I studied all of those you've mentioned, however specifically talking i couldn't follow the generalization you've mentioned at the end of this to find the QFT version of it. could you please be more specific about how to achieve such formula? $\endgroup$
    – Jason
    May 31, 2019 at 13:14
  • $\begingroup$ First, you must appreciate that the standard transition from the Fock vacuum to $|x\rangle$ is not and cannot be made unitary. Do you understand why? As indicated here, you are solving problem 14.4.a in Schwartz's QFT standard book. $\endgroup$
    – Cosmas Zachos
    May 31, 2019 at 15:02

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.