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 />
Side remark: Direct proof of periodicity<br />
◮ Define thermal (time-ordered) Green’s function<br />
[<br />
G B (x, y; τ, 0) = Tr<br />
{ˆρT τ ˆφ(x, τ) ˆφ(y, 0) ]}<br />
◮ Using cyclic property of the trace...<br />
{<br />
G B (x, y; τ, 0) = Z −1 Tr e −βĤe }<br />
βĤ ˆφ(y, 0)e −βĤ ˆφ(x, τ)<br />
{<br />
}<br />
= Z −1 Tr e −βĤ ˆφ(y, β) ˆφ(x, τ)<br />
= Z −1 Tr<br />
{e −βĤT [ ]<br />
τ ˆφ(x, τ) ˆφ(y, }<br />
β)<br />
= G B (x, y; τ, β)<br />
logo<br />
Aleksi Vuorinen, CERN<br />
<strong>Finite</strong>-<strong>temperature</strong> <strong>Field</strong> <strong>Theory</strong>