Thermal quantum field theory

In theoretical physics, thermal quantum field theory (thermal field theory for short) or finite temperature field theory is a set of methods to calculate expectation values of physical observables of a quantum field theory at finite temperature.

There are three main formalisms used to describe finite-temperature states:

  • Matsubara formalism, based on evolving the system in imaginary time.
  • Schwinger–Keldysh formalism, based on the real-time evolution, allowing the treatment of non-equilibrium processes.
  • Umezawa formalism (thermo field dynamics), which is based on real-time evolution, and introduces a doubled Hilbert space to represent thermal states.
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