## 7 Citations

### Stability of the Yang-Mills heat equation for finite action

- Mathematics
- 2017

The existence and uniqueness of solutions to the Yang-Mills heat equation over domains in Euclidean three space was proven in a previous paper for initial data lying in the Sobolev space of order…

### The Yang-Mills heat equation with finite action in three dimensions

- MathematicsMemoirs of the American Mathematical Society
- 2022

The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over
R
3
\mathbb {R}^3
and over a bounded open convex set in
R
3
\mathbb {R}^3…

### A Functional Integral Approaches to the Makeenko–Migdal Equations

- MathematicsCommunications in Mathematical Physics
- 2019

Makeenko and Migdal (Phys Lett B 88(1):135–137, 1979) gave heuristic identities involving the expectation of the product of two Wilson loop functionals associated to splitting a single loop at a…

### Equivalence of helicity and Euclidean self-duality for gauge fields

- MathematicsNuclear Physics B
- 2019

### The Yang-Mills Heat Equation on Three-Manifolds with Boundary

- Mathematics
- 2020

In this short note we provide an expository account of the work of Leonard Gross and the author on the Yang-Mills heat equation over smooth three-manifolds with boundary.

### The Yang-Mills heat flow with random distributional initial data

- Mathematics, Computer ScienceCommunications in Partial Differential Equations
- 2023

The main idea, which goes back to work of Bourgain as well as work of Da Prato-Debussche, is to decompose the solution into a rougher linear part and a smoother nonlinear part and to control the latter by probabilistic arguments.

### Yang–Mills for Probabilists

- MathematicsProbability and Analysis in Interacting Physical Systems
- 2019

The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is…

## References

SHOWING 1-10 OF 13 REFERENCES

### Neumann domination for the Yang-Mills heat equation

- Mathematics
- 2014

Long time existence and uniqueness of solutions to the Yang-Mills heat equation have been proven over a compact 3-manifold with boundary for initial data of finite energy. In the present paper, we…

### The Yang-Mills Heat Semigroup on Three-Manifolds with Boundary

- Mathematics
- 2010

Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued…

### Regularity theory for the generalized Neumann problem for Yang-Mills Connections – Non-trivial examples in dimensions 3 and 4

- Mathematics
- 2000

Abstract. We develop the existence and regularity theory for the generalized Neumann problem for Yang-Mills connections. This is the most general boundary value problem for connections on a compact…

### Dirichlet and neumann boundary value problems for Yang-Mills connections

- Mathematics
- 1992

The Yang-Mills equations have been extensively studied on compact Riemannian manifolds without boundary. A substantial amount of work has also been done on non-compact examples with a boundary…

### Elliptic Partial Differential Equations of Second Order

- Mathematics
- 1997

We study in this chapter a class of partial differential equations that generalize and are to a large extent represented by Laplace’s equation. These are the elliptic partial differential equations…

### The generalized neumann problem for yang-mills connections

- Mathematics
- 1999

The purpose of this paper is defining a new boundary value problem for Yang-Mills connections, which is the most general in the context of Neumann-type problems for forms. We achieve this by…

### The Yang-Mills heat equation with finite action, (2016)

- 2016