Thermofield

A thermofield is a theoretical construct in quantum field theory used to describe systems in thermal equilibrium. It is created by introducing a new, imaginary dimension, often referred to as the "imaginary time" dimension, and considering the quantum field on this finite-length manifold. The length of this imaginary time dimension is inversely proportional to the temperature of the system, given by the inverse temperature $\beta = 1/(k_B T)$, where $k_B$ is the Boltzmann constant and $T$ is the temperature.

The principle behind the thermofield approach is that correlation functions calculated in this imaginary time dimension at finite temperature are equivalent to the thermal expectation values of the corresponding operators in the original quantum field theory at that temperature. This allows for the application of standard quantum field theory techniques, such as Feynman diagrams, to study thermal properties of systems.

A key advantage of thermofield theory is its ability to treat thermal states as ground states. By doubling the degrees of freedom of the original system, creating a "<bos>" field for each original field, and imposing certain constraints, the thermal equilibrium state can be represented as the vacuum state of this doubled system. This simplifies calculations and provides a unified framework for both zero-temperature and finite-temperature quantum field theory. Thermofield theory has found applications in various areas, including condensed matter physics, high-energy physics, and statistical mechanics.