The generalized Lichnerowicz formula and analysis of Dirac operators
| dc.creator | Ackermann, T. | |
| dc.creator | Tolksdorf, J. | |
| dc.date | 1995-03-23 | |
| dc.date.accessioned | 2026-07-07T04:21:02Z | |
| dc.date.available | 2026-07-07T04:21:02Z | |
| dc.description | We study Dirac operators acting on sections of a Clifford module ${\cal E}$\ over a Riemannian manifold $M$. We prove the intrinsic decomposition formula for their square, which is the generalisation of the well-known formula due to Lichnerowicz [L]. This formula enables us to distinguish Dirac operators of simple type. For each Dirac operator of this natural class the local Atiyah-Singer index theorem holds. Furthermore, if $M$\ is compact and ${{\petit \rm dim}\;M=2n\ge 4}$, we derive an expression for the Wodzicki function $W_{\cal E}$, which is defined via the non-commutative residue on the space of all Dirac operators ${\cal D}({\cal E})$. We calculate this function for certain Dirac operators explicitly. From a physical point of view this provides a method to derive gravity, resp. combined gravity/Yang-Mills actions from the Dirac operators in question. | |
| dc.description | 25 pages, plain tex | |
| dc.identifier | https://arxiv.org/abs/hep-th/9503153 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9503153 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/54162 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | The generalized Lichnerowicz formula and analysis of Dirac operators | |
| dc.type | text |