Feynman–Kac formula for perturbations of order $$\le 1$$, and noncommutative geometry

@article{Boldt2020FeynmanKacFF,
title={Feynman–Kac formula for perturbations of order \$\$\le 1\$\$, and noncommutative geometry},
author={Sebastian Boldt and Batu G{\"u}neysu},
journal={Stochastics and Partial Differential Equations: Analysis and Computations},
year={2020}
}
• Published 31 December 2020
• Art
• Stochastics and Partial Differential Equations: Analysis and Computations
<jats:p>Let <jats:italic>Q</jats:italic> be a differential operator of order <jats:inline-formula><jats:alternatives><jats:tex-math>$$\le 1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> on a complex metric vector bundle <jats:inline-formula><jats:alternatives><jats:tex…
7 Citations

A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold

• Mathematics
Communications in Mathematical Physics
• 2022
We give a rigorous construction of the path integral in N=1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}

Heat flow regularity, Bismut–Elworthy–Li’s derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature

• Mathematics
Electronic Journal of Probability
• 2021
We prove that if the Ricci tensor Ric of a geodesically complete Riemannian manifold M , endowed with the Riemannian distance ρ and the Riemannian measure m , is bounded from below by a continuous

A Chern-Simons transgression formula for supersymmetric path integrals on spin manifolds

• Mathematics
• 2021
Earlier results show that the N = 1 / 2 supersymmetric path integral J g on a closed even dimensional Riemannian spin manifold ( X,g ) can be constructed in a mathematically rigorous way via Chen

A differential topological invariant on spin manifolds from supersymmetric path integrals

• Mathematics
• 2021
We show that the N = 1/2 supersymmetric path integral on a closed even dimensional Riemannian spin manifold, realized via Chen forms and recent results from noncommutative geometry, induces a

A functional-analytic construction of the stochastic parallel transport in Hermitian bundles over Riemannian manifolds

This article presents a purely functional-analytic construction of the concept of stochastic parallel transport in Hermitian bundles over Riemannian manifolds. As a byproduct, we also obtain a form

References

SHOWING 1-10 OF 31 REFERENCES

Schrödinger Semigroups

Let H = \L + V be a general Schrödinger operator on R" (v~> 1), where A is the Laplace differential operator and V is a potential function on which we assume minimal hypotheses of growth and

Heat flow regularity, Bismut–Elworthy–Li’s derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature

• Mathematics
Electronic Journal of Probability
• 2021
We prove that if the Ricci tensor Ric of a geodesically complete Riemannian manifold M , endowed with the Riemannian distance ρ and the Riemannian measure m , is bounded from below by a continuous

Perturbation of Dirichlet forms by measures

• Mathematics
• 1996
AbstractPerturbations of a Dirichlet form $$\mathfrak{h}$$ by measures μ are studied. The perturbed form $$\mathfrak{h}$$ −μ−+μ+ is defined for μ− in a suitable Kato class and μ+ absolutely

Heat Kernels and Dirac Operators

• Mathematics
• 1992
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent

Covariant Schrödinger Semigroups on Riemannian Manifolds

This monograph develops the theory of covariant Schr\"odinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on

Quantitative C1-estimates by Bismut formulae

• Mathematics
Journal of Mathematical Analysis and Applications
• 2018

Continuity properties of Schrödinger semigroups with magnetic fields

• Mathematics
• 1998
The objects of the present study are one-parameter semigroups generated by Schrodinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the

Schrödinger Semigroups on Manifolds

Abstract We derive uniform upper bounds for the transition density (or parabolic kernel) pV of the Schrodinger operator − 1 2 Δ + V on a Riemannian manifold (with Ricci curvature bounded from below)