Overview and Warmup Example for Perturbation Theory with Instantons
| dc.creator | Axelrod, Scott | |
| dc.date | 1995-11-27 | |
| dc.date | 1996-03-08 | |
| dc.date.accessioned | 2026-07-07T09:04:11Z | |
| dc.date.available | 2026-07-07T09:04:11Z | |
| dc.description | The large $k$ asymptotics (perturbation series) for integrals of the form $\int_{\cal F}μe^{i k S}$, where $μ$ is a smooth top form and $S$ is a smooth function on a manifold ${\cal F}$, both of which are invariant under the action of a symmetry group ${\cal G}$, may be computed using the stationary phase approximation. This perturbation series can be expressed as the integral of a top form on the space $\cM$ of critical points of $S$ mod the action of ${\cal G}$. In this paper we overview a formulation of the ``Feynman rules'' computing this top form and a proof that the perturbation series one obtains is independent of the choice of metric on ${\cal F}$ needed to define it. We also overview how this definition can be adapted to the context of $3$-dimensional Chern--Simons quantum field theory where ${\cal F}$ is infinite dimensional. This results in a construction of new differential invariants depending on a closed, oriented $3$-manifold $M$ together with a choice of smooth component of the moduli space of flat connections on $M$ with compact structure group $G$. To make this paper more accessible we warm up with a trivial example and only give an outline of the proof that one obtains invariants in the Chern--Simons case. Full details will appear elsewhere. | |
| dc.description | 25 pages, latex, amssymb, epsfig(11 figures), epic & eepic(1 figure), uuencoded gz-compressed tar-file. Minor modifications, 1 figure, and notation index added. This is final version to appear in "Proceedings on Geometry & Physics" (proceedings are from workshop in Aarhus, Denmark 1995) | |
| dc.identifier | https://arxiv.org/abs/hep-th/9511196 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9511196 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149286 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Differential Geometry | |
| dc.title | Overview and Warmup Example for Perturbation Theory with Instantons | |
| dc.type | text |