Functional Determinants for Radially Separable Partial Differential Operators

• Main Author: G. V. Dunne
• Format: Article
• Language: English
• Published: CTU Central Library 2007-01-01
• Series: Acta Polytechnica
• Subjects: quantum field theory; functional determinants; zeta functions; spectral theory; partial differential operators
• Online Access: https://ojs.cvut.cz/ojs/index.php/ap/article/view/916

Functional determinants of differential operators play a prominent role in many fields of theoretical and mathematical physics, ranging from condensed matter physics, to atomic, molecular and particle physics. They are, however, difficult to compute reliably in non-trivial cases. In one dimensional problems (i.e. functional determinants of ordinary differential operators), a classic result of Gel’fand and Yaglom greatly simplifies the computation of functional determinants. Here I report some recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators), with applications in quantum field theory.