Finite-temperature Field Theory - Theoretical Physics (TIFR)
Finite-temperature Field Theory - Theoretical Physics (TIFR)
Finite-temperature Field Theory - Theoretical Physics (TIFR)
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Basics of Statistical <strong>Physics</strong> and Thermodynamics<br />
Scalar fields at finite <strong>temperature</strong><br />
Interacting scalar fields<br />
Partition function for scalar field theory<br />
Non-interacting examples<br />
◮ Recall path integral for transition amplitudes in QFT:<br />
〈φ b (x) | e −iĤ(t 1−t 0 ) | φ a (x)〉<br />
∫ [ ∫ t1<br />
∫ ]<br />
= N Dϕ exp i dt d 3 x L<br />
t 0<br />
ϕ(t 0 ,x)=φa(x)<br />
ϕ(t 1 ,x)=φ b (x)<br />
◮ For thermodynamic purposes, set t 0 = t 1 , t → −iτ:<br />
∫ β−it0 ∫<br />
iS → − dτ d d xL E ,<br />
L E = 1 2<br />
−it 0<br />
{<br />
(∂ t ϕ) 2 + (∂ i ϕ) 2 } + V (ϕ)<br />
◮ Finally, taking the trace...<br />
∫<br />
[<br />
Z = N Dϕ exp<br />
periodic<br />
∫ β−it0 ∫<br />
− dτ<br />
−it 0<br />
d d xL E<br />
]<br />
logo<br />
Aleksi Vuorinen, CERN<br />
<strong>Finite</strong>-<strong>temperature</strong> <strong>Field</strong> <strong>Theory</strong>