Correspondence between imaginary-time and real-time finite-temperature field theory

It is known that one-particle-irreducible graphs found using the imaginary-time formalism of finite-temperature field theory differ in general with those of the real-time formalism. Here it is shown that within the real-time formalism one can consider a sum of graphs, motivated by causality arguments, which at least in a number of simple examples agree with the corresponding analytically continued imaginary-time result. The occurrence of multiple statistical factors in this sum of graphs is discussed