# Can spherical harmonics be used in relativity equations?

I have a neutral pion of mass $$m_{\pi}$$, and it decays into two photons. In it's reference frame the decay is isotropic. One of the photons has a helicity of $$+\hbar$$ and the other $$-\hbar$$. In another frame the pion has relatavistic momentum $$\vec p=p \hat z$$, and the probability to find the + helicity photon at angular position $$(\theta,\phi)$$ is:

$$dP_+=f(\theta,\phi)\sin\theta d\theta d\phi$$

and then we have (because it's a probability)

$$P=\int_0^{\pi}\sin\theta d\theta \int_0^{2\pi} d\phi \ f(\theta,\phi)=1$$

The goal is to find $$f(\theta,\phi)$$. I'm looking at this and it reminds me a lot of spherical harmonics. Mostly because spherical harmonics are denoted by

$$\big<\theta,\phi\big|l,m\big>=Y_{l,m}(\theta,\phi)$$

Which are functions of the angles $$\theta$$ and $$\phi$$. And $$f(\theta,\phi)$$ is also a function of the same angles. And another connection I see is that the probability to find a particle in a certain state, within the solid angle $$d\Omega$$ at the angles $$\theta$$ and $$\phi$$ is $$\big|Y_{l,m}(\theta,\phi)\big|^2d\Omega$$ and

$$P=\int_0^{\pi}\sin\theta d\theta \int_0^{2\pi} d\phi \ \big|Y_{l,m}(\theta,\phi)\big|^2=1$$

These last two things are from my quantum mechanics textbook, and they look very similar to the first equations I wrote because $$\sin\theta d\theta d\phi$$ is an infinitesimal solid angle, just like $$d\Omega$$. Is $$f(\theta,\phi)$$ the magnitude of a spherical harmonic? Or is it not because we are dealing with a different reference frame than the decay and we need to take relativity into account?