DeWitt–Seeley–Gilkey coefficients for nonminimal differential operators in curved space

Asymptotic heat kernel expansion for nonminimal differential operators on curved manifolds in the presence of a gauge field is considered. The complete expressions for the fourth coefficient ($E_4$) in the heat kernel expansion for such operators are presented for the first time. The expressions were computed for general case of manifolds of arbitrary dimension $n$ and also for the most important case $n=4$. The calculations have been carried out on PC with the help of a program written in C.