Measures on Banach Manifolds and Supersymmetric Quantum Field Theory
| dc.creator | Weitsman, Jonathan | |
| dc.date | 2005-09-05 | |
| dc.date | 2005-11-25 | |
| dc.date.accessioned | 2026-07-07T12:46:23Z | |
| dc.date.available | 2026-07-07T12:46:23Z | |
| dc.description | We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum field theory. We give three concrete examples of our construction. The first example is a family $μ_P^{s,t}$ of measures on a space of functions on the two-torus, parametrized by a polynomial $P$ (the Wess-Zumino-Landau-Ginzburg model). The second is a family $μ_\cG^{s,t}$ of measures on a space $\cG$ of maps from $¶^1$ to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family $μ_{M,G}^{s,t}$ of measures on the product of a space of connection s on the trivial principal bundle with structure group $G$ on a three-dimensional manifold $M$ with a space of $\fg$-valued three-forms on $M.$ We show that these measures are positive, and that the measures $μ_\cG^{s,t}$ are Borel probability measures. As an application we show that formulas arising from expectations in the measures $μ_\cG^{s,1}$ reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar computation for the measures $μ_{M,SU(2)}^{s,t},$ where $M$ is a homology three-sphere, will yield the Casson invariant of $M.$ | |
| dc.description | Minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0509104 | |
| dc.identifier | http://arxiv.org/abs/math/0509104 | |
| dc.identifier | Commun.Math.Phys. 277:101-125,2008 | |
| dc.identifier | doi:10.1007/s00220-007-0359-3 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221362 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 81T60,57R56,58D20 | |
| dc.title | Measures on Banach Manifolds and Supersymmetric Quantum Field Theory | |
| dc.type | text |