FANTOMAS said:SORRY FOR MY BAD ENGLISH.
Matsubara Formalism is a mathematical framework used in statistical physics to describe the behavior of systems at finite temperature. It is used to calculate thermodynamic properties and correlation functions of a system in equilibrium.
Matsubara Formalism was developed by the Japanese physicist Tomonaga Shin'ichirō in the 1950s.
Matsubara Formalism is unique in that it uses imaginary time, or Euclidean time, instead of real time. This simplifies the calculations and allows for a direct connection to quantum mechanics. It also incorporates the concept of Matsubara frequencies, which are used to describe oscillatory behavior in the system.
Matsubara Formalism is limited to systems in thermal equilibrium and cannot be applied to systems out of equilibrium. It also assumes that the system is in a macroscopic state and does not consider microscopic fluctuations. Additionally, it is not applicable to systems with long-range interactions or non-equilibrium phase transitions.
Matsubara Formalism is commonly used in condensed matter physics, quantum field theory, and nuclear physics. It has also been applied to problems in statistical mechanics, such as calculating the critical temperature of a system undergoing a phase transition. It has also been used to study the properties of materials at high temperatures and in extreme conditions, such as in astrophysics.