Ten Physical Applications of Spectral Zeta Functions

Zeta-function regularization is a powerful method in perturbation theory. This text is meant as a guide for the student of this subject. It gives explanations and several applications to show how the procedure works in practice: for example, Casimir effect, and gravity and string theory.

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Zeta-function regularization is a powerful method in perturbation theory. This text is meant as a guide for the student of this subject. It gives explanations, in particular on the mathematical difficulties and tricky points, and several applications are given to show how the procedure works in practice (for example, Casimir effect, gravity and string theory, high-temperature phase trasition, topological symmetry breaking). The formulas can be used for accurate numerical calculations.