The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡
In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Rieman...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-03-01
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| Series: | Universe |
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| Online Access: | http://www.mdpi.com/2218-1997/5/3/79 |
| _version_ | 1798043661041139712 |
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| author | Walter Dittrich |
| author_facet | Walter Dittrich |
| author_sort | Walter Dittrich |
| collection | DOAJ |
| description | In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Riemann’s zeta function to regularize the otherwise infinite results of the so-called Heisenberg–Euler Lagrangian. As a spin-off, we also calculate some integrals that are useful in mathematics and physics. |
| first_indexed | 2024-04-11T22:52:14Z |
| format | Article |
| id | doaj.art-dcbfaf08b8dd47f4839d31f8cd0d8dc2 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-04-11T22:52:14Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-dcbfaf08b8dd47f4839d31f8cd0d8dc22022-12-22T03:58:33ZengMDPI AGUniverse2218-19972019-03-01537910.3390/universe5030079universe5030079The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡Walter Dittrich0Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, GermanyIn particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Riemann’s zeta function to regularize the otherwise infinite results of the so-called Heisenberg–Euler Lagrangian. As a spin-off, we also calculate some integrals that are useful in mathematics and physics.http://www.mdpi.com/2218-1997/5/3/79Riemannzeta functionfunctional equationHeisenberg-Euler Lagrangian |
| spellingShingle | Walter Dittrich The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡ Universe Riemann zeta function functional equation Heisenberg-Euler Lagrangian |
| title | The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡ |
| title_full | The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡ |
| title_fullStr | The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡ |
| title_full_unstemmed | The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡ |
| title_short | The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡ |
| title_sort | role of riemann s zeta function in mathematics and physics † ‡ |
| topic | Riemann zeta function functional equation Heisenberg-Euler Lagrangian |
| url | http://www.mdpi.com/2218-1997/5/3/79 |
| work_keys_str_mv | AT walterdittrich theroleofriemannszetafunctioninmathematicsandphysics AT walterdittrich roleofriemannszetafunctioninmathematicsandphysics |