One-loop corrections in the O(5) Skyrme model

The calculation of one-loop corrections in the Skyrme model in a curved space is considered. It is shown that the reduced system leads to the calculation of the determinant of a nondiagonal operator that acts on a space of world vector functions. A procedure is developed for calculating the Minakshisundaram–Seetey coefficients for such operators using the Balian–Bloch expansion for the Green's function in the curved space. The results show that the equivalence which holds between the Skyrme model and the Yang–Mills field at the classical level is not true at the quantum level.