I am considering canonical quantiziation of a free scalar field $\chi$ in a spherical background, which can be spacetime or another scalar background $\varphi$ that couples with $\chi$. In this case, the spatial translation symmetries are lost and one should do the quantization using the spherical polar coordinates. One particular example is the scalar fields in Schwarzschild spacetime. However, I did not find a good textbook which introduce details about how to do the quantization of a scalar field in such a background. Anybody knows of a good material?
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