Three approaches to classical thermal field theory

Research highlights: → Classical thermal field theory admits three equivalent path integral formulations. → Classical Feynman rules can be derived for all three formulations. → Quantum Feynman rules reduce to classical ones at high temperatures. → Classical Feynman rules become much simpler when superfields are introduced. - Abstract: In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.