# Thermal state in QFT

1. May 19, 2010

### paweld

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

2. May 19, 2010

### 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!

Last edited: May 19, 2010
3. May 19, 2010

### paweld

I really like this definition!
What are correlators?