# Z and $\gamma$ bosons as mixtures of W and B: Part I

When it is said that the photon is "a mixture of W and B" ($$B$$ being a gauge field associated with the $$U(1)$$ hypercharge)

I have a question on this:

• When speaking of "mixtures", this is meant as analogous to the quantum mechanics terminology as the linear combination of two density matrices multiplied by classical probabilities? or this is meant in some more esoteric sense?

The photon being a “mixture” of the $$B$$ and the $$W$$ means that the photon’s quantum field is a linear combination of the $$B$$ quantum field and one of the components of the $$W$$ quantum field:
$$A_\mu=B_\mu\cos{\theta_W}+W^3_\mu\sin{\theta_W}$$
The mixing parameter $$\theta_W$$ is known as the “Weinberg angle”.
• For sake of completeness I would like to add that spontaneous symmetry breaking is essential to this "mixing", and that the Weinberg angle is assigned later due to the fact that the coefficients (coupling constants) are manipulated to give expressions like $\frac{g}{\sqrt{g^2+g'^2}}$ – Quantumness May 2 at 21:05