Finite-temperature Field Theory - Theoretical Physics (TIFR)

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Basics of Statistical Physics and Thermodynamics Scalar fields at finite temperature Interacting scalar fields Statistical QM Simple examples One degree of freedom ◮ Consider one state system with E = ω, and ignore zero point energy Ĥ | n〉 = ω ˆN | n〉 = n ω | n〉 ◮ For bosons/fermions with chemical potential µ, obtain ∞∑ Z b = Tr e −β(ω−µ) ˆN = 〈n | e −β(ω−µ) ˆN 1 | n〉 = 1 − e , −β(ω−µ) Z f = Tr e −β(ω−µ) ˆN = n=1 1∑ 〈n | e −β(ω−µ) ˆN | n〉 = 1 + e −β(ω−µ) n=1 ◮ Taking derivatives... N b = 1 e β(ω−µ) − 1 , E b = ωN b N f = 1 e β(ω−µ) + 1 , E f = ωN f logo Aleksi Vuorinen, CERN Finite-temperature Field Theory
Basics of Statistical Physics and Thermodynamics Scalar fields at finite temperature Interacting scalar fields Statistical QM Simple examples One degree of freedom ◮ Consider one state system with E = ω, and ignore zero point energy Ĥ | n〉 = ω ˆN | n〉 = n ω | n〉 ◮ For bosons/fermions with chemical potential µ, obtain ∞∑ Z b = Tr e −β(ω−µ) ˆN = 〈n | e −β(ω−µ) ˆN 1 | n〉 = 1 − e , −β(ω−µ) Z f = Tr e −β(ω−µ) ˆN = n=1 1∑ 〈n | e −β(ω−µ) ˆN | n〉 = 1 + e −β(ω−µ) n=1 ◮ Taking derivatives... N b = 1 e β(ω−µ) − 1 , E b = ωN b N f = 1 e β(ω−µ) + 1 , E f = ωN f logo Aleksi Vuorinen, CERN Finite-temperature Field Theory
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