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
◮ Expand fields in terms of their Fourier modes
◮
ϕ(τ, x) = T ∑ ∫
d 3 p
ei(p·x+ωnτ)
(2π) 3 ϕ n (p),
n
ω n = 2nπT , n ∈ Z
Fourier series in τ direction due to compactness of
temporal direction
◮ Now, a short exercise produces (up to T -indep. constant)
ln Z = − V ∑
∫
d 3 (
p
2 (2π) 3 ln n 2 + β2 (p 2 + m 2 )
)
(2π) 2 n
∫ [√
d 3 p p
= −V
2 + m 2
(2π) 3 + ln
(1 − e −β√ p 2 +m 2) ]
2T
◮ Reminiscent of point particle result for bosons!
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Aleksi Vuorinen, CERN
Finite-temperature Field Theory