Positronium {bold {ital S}}-state spectrum: Analytic results at O(mα⁶)

We present an analytic calculation of the O(m alpha^6) recoil and radiative recoil corrections to energy levels of positronium nS states and their hyperfine splitting. A complete analytic formula valid to O(m alpha^6) is given for the spectrum of S states. Technical aspects of the calculation are discussed in detail. Theoretical predictions are given for various energy intervals and compared with experimental results.