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One loop boundary effects: techniques and applications

A pedagogical introduction to the heat kernel technique, zeta function and Casimir effect is presented. Several 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. Then we rederive the Casimir energies for perfectly conducting rectangular cavities using a new technique. The new results for the attractive Casimir force acting on each of the two perfectly conducting plates inside an infinite perfectly conducting waveguide of the same cross section as the plates are presented at zero and finite temperatures.