Definition of Thermal State of Scalar Field in QFT

[paweld]

What is the definition of thermal state of scalar field in QFT.
Is it possible to express the condition in algebraic way
(without referring to palticluar choice of representation).

 

[xepma]

Yes, this condition is introduced in a very neat way. First, you allow for the time variable to take on complex values. Then, to evaluate the expectation value of any operator with respect to a thermal state at temperature T, you integrate over the complex time variable from 0 to 1/T along the imaginary axis. In some sense you 'propagate' the operator for an amount of 1/T in the direction of imaginary time. The final condition you have to impose is that the 'in' state at t=0 and the 'out' state at t=i/T are the same states -- this is done by demanding that the correlators are periodic with respect to the translation t --> t +i/T (for fermions we need antiperiodicity).

It's a bit a technical, so you probably want to consult a proper book on this stuff!

 

[paweld]

I really like this definition!
What are correlators?