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 />
Feynman rules at finite <strong>temperature</strong><br />
Thermodynamics of ϕ 4 theory<br />
Feynman rules for φ 4 theory<br />
◮ Assume massive scalar theory with L I = ϕ 4<br />
◮<br />
Graphs composed of four-ϕ vertices and propagators<br />
1<br />
D 0 (ω n , p) =<br />
ωn 2 + p 2 + m 2<br />
◮ Feynman rules almost the same as at T = 0:<br />
◮ As usual, only need to compute connected diagrams<br />
◮ Same symmetry factors, vertex functions, etc.<br />
◮ Only changes due to discrete values of p 0 :<br />
◮ In integration measure: ∫ d 4 p<br />
→ T ∑ ∫ d 3 p<br />
(2π) 4<br />
n (2π) 3<br />
◮ In vertices: δ (4) (P 1 − P 2 ) → δ n1 ,n 2<br />
δ (3) (p 1 − p 2 )<br />
◮ Question: How to evaluate the necessary sum-integrals?<br />
◮ Will be covered in more detail later...<br />
logo<br />
Aleksi Vuorinen, CERN<br />
<strong>Finite</strong>-<strong>temperature</strong> <strong>Field</strong> <strong>Theory</strong>
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