Perturbation theory of rotating scalar fields and vacuum insensitivity to rotation

We formulate the finite-temperature perturbation theory of interacting scalar fields under external rotation. Because of the translational non-invariance in the radial direction, Green’s functions are described using the Fourier-Bessel basis, instead of the conventional Fourier basis. We derive the leading-order correction to the partition function and the one-loop self-energy. The Feynman rules obtained in our perturbation theory shows that due to the finite-size effect required by the causality constraint, the zero-temperature thermodynamics in the perturbation theory is unaffected by rotation, similarly to that in the noninteracting theory.