A common statement is that post-SSB electroweak gauge bosons are linear combinations of pre-SSB gauge bosons.

It is also usually stated that pre-SSB bosons can also be thought of as linear combinations of post-SSB bosons - it's just a choice of basis, after all.

However, with a choice of basis, there usually comes an operator corresponding to an observable which allows us to measure the eigenstates corresponding to the chosen basis . The eigenvectors of such operator will correspond to the basis states.

If there was a quantum operator / observable whose eigenvectors correpond to the 'pure' pre-SSB boson states (B, W1, W2, W3), we would be able to 'detect' pre-SSB bosons in post-SSB environment - i.e. measure whether the photon 'chooses' to be a 'B' or a 'W' at any given interaction.

So: does such an operator / observable exist? Can it be constructed? Or does it even make sense?


I'm thinking in terms of the following analogy:

  1. A photon is usually emitted in a superposition of spin left / spin right states. Upon 'arrival' however we can always measure it to be either one or the other.
  2. A photon is emitted in superposition of B / W states. Upon 'arrival' we should somehow be able to measure if it is one or the other.

1 Answer 1


It's linear algebra. In terms of the mass eigenstates, $\gamma , Z^0$, $$\begin{pmatrix} B^0 \\ W^3 \end{pmatrix} = \begin{pmatrix} \cos \theta_\text{W} & -\sin \theta_\text{W} \\ \sin \theta_\text{W} & \cos \theta_\text{W} \end{pmatrix} \begin{pmatrix} \gamma \\ Z^0 \end{pmatrix} , $$ so the operators destroying the corresponding states, usable in projectors, are $$ B^0= \cos\theta_W ~~ \gamma -\sin\theta_W ~~ Z^0, \\ W^3= \cos\theta_W ~~ Z^0 +\sin\theta_W ~~\gamma, $$ but I am not sure what you expect to learn from them.

So the photon is 0.22 B and 0.78 W, if you could measure that.

  • $\begingroup$ Yes, these are exactly the eigenstates I am talking about. I'm wondering if there theoretically exists a physical observable to measure them. $\endgroup$ Commented Apr 21, 2023 at 21:40
  • $\begingroup$ Perhaps in an early universe simulation comparing multiplicities. But in each energy regime, one of the two bases are promising to be dysfunctional/meaningless... $\endgroup$ Commented Apr 21, 2023 at 21:44
  • $\begingroup$ Perhaps, but I feel the observable should still exist. Could you elaborate on 'comparing multiplicities' a bit, please? $\endgroup$ Commented Apr 21, 2023 at 22:00

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