Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 301 / 4 / a / Solution

For ordinary bosonic operators at distinct times, time ordering places the later operator to the left:Equivalently, multiply these two products by the corresponding Heaviside step functions. For two odd fermionic operators the second product receives a minus sign; more generally a graded interchange has sign $(-1{)}^{F_1{F}_2}$. This sign is the fermionic sign convention for time-ordered field products, not a minus sign for arbitrary bosonic operators. No equal-time convention is needed for the two distinct times in this clause.