Functional Determinants for Radially Separable Partial Differential Operators
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...
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| Format: | Article |
| Language: | English |
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CTU Central Library
2007-01-01
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| Series: | Acta Polytechnica |
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| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/916 |
| _version_ | 1811331208862236672 |
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| author | G. V. Dunne |
| author_facet | G. V. Dunne |
| author_sort | G. V. Dunne |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T16:17:02Z |
| format | Article |
| id | doaj.art-4057013d2e0943eda4420efa3dae7b5f |
| institution | Directory Open Access Journal |
| issn | 1210-2709 1805-2363 |
| language | English |
| last_indexed | 2024-04-13T16:17:02Z |
| publishDate | 2007-01-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica |
| spelling | doaj.art-4057013d2e0943eda4420efa3dae7b5f2022-12-22T02:40:02ZengCTU Central LibraryActa Polytechnica1210-27091805-23632007-01-01472-3916Functional Determinants for Radially Separable Partial Differential OperatorsG. V. DunneFunctional 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.https://ojs.cvut.cz/ojs/index.php/ap/article/view/916quantum field theoryfunctional determinantszeta functionsspectral theorypartial differential operators |
| spellingShingle | G. V. Dunne Functional Determinants for Radially Separable Partial Differential Operators Acta Polytechnica quantum field theory functional determinants zeta functions spectral theory partial differential operators |
| title | Functional Determinants for Radially Separable Partial Differential Operators |
| title_full | Functional Determinants for Radially Separable Partial Differential Operators |
| title_fullStr | Functional Determinants for Radially Separable Partial Differential Operators |
| title_full_unstemmed | Functional Determinants for Radially Separable Partial Differential Operators |
| title_short | Functional Determinants for Radially Separable Partial Differential Operators |
| title_sort | functional determinants for radially separable partial differential operators |
| topic | quantum field theory functional determinants zeta functions spectral theory partial differential operators |
| url | https://ojs.cvut.cz/ojs/index.php/ap/article/view/916 |
| work_keys_str_mv | AT gvdunne functionaldeterminantsforradiallyseparablepartialdifferentialoperators |