Three approaches to classical thermal field theory

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.

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.