  We present a quantum many-body description of the excitation spectrum of
Rydberg polarons in a Bose gas. The many-body Hamiltonian is solved with
functional determinant theory, and we extend this technique to describe Rydberg
polarons of finite mass. Mean-field and classical descriptions of the spectrum
are derived as approximations of the many-body theory. The various approaches
are applied to experimental observations of polarons created by excitation of
Rydberg atoms in a strontium Bose-Einstein condensate.
