Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2010-06-18
Physics
High Energy Physics
High Energy Physics - Phenomenology
13 pages, 1 figure
Scientific paper
10.1103/PhysRevD.82.065010
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field $\phi_c$, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schr\"{o}dinger field-representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle-point for fixed boundary fields, which is the classical field $\phi_c$, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally-reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
Bessa A.
Brandt Fernando T.
de Carvalho Carlos A. A.
Fraga Eduardo S.
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