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We give an introduction to the heat kernel technique and zeta function. Two applications are considered. First we derive the high temperature asymptotics of the free energy for boson fields in terms of the heat kernel expansion and zeta function. Another application is chiral anomaly for local (MIT bag) boundary conditions.doi:10.1063/1.1800737 fatcat:cq4i3kzqgfbi5cmsnh7wwlwdfa