Finite-temperature Field Theory - Theoretical Physics (TIFR)

Basics of Statistical Physics and Thermodynamics
Scalar fields at finite temperature
Interacting scalar fields
Partition function for scalar field theory
Non-interacting examples
◮ Define again thermal Green’s function
[ ]
G F (x, y; τ, 0) = Tr
{ˆρT τ ˆψ(x, τ) ˆψ(y, }
0)
◮
This time field operators anticommute!
◮ Using cyclic property of the trace...
{
G F (x, y; τ, 0) = Z −1 Tr e −βĤe }
βĤ ˆψ(y, 0)e −βĤ ˆψ(x, τ)
}
= Z −1 Tr
{e −βĤ ˆψ(y, β) ˆψ(x, τ)
= −Z −1 Tr
{e −βĤT [
τ ˆψ(x, τ) ˆψ(y, β) ]}
= −G F (x, y; τ, β)
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Aleksi Vuorinen, CERN
Finite-temperature Field Theory