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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I suppose this would be overkill... – Cosmas Zachos May 15 '21 at 16:20
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1You may be interested in this paper which computes the free energy for several different QFTs on the d-sphere: https://arxiv.org/abs/1105.4598 – Seth Whitsitt May 15 '21 at 20:26
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3Does this answer your question? Suggested reading for quantum field theory in curved spacetime – Níckolas Alves Jan 28 '22 at 07:28