2005/12/18 by Valery N. Marachevsky, Marachevsky, Valery N.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Numerical methods in inverse problems #Quantum Electrodynamics and Casimir Effect #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.hep-th/0512221
openalex publication_date 2005/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.