## The stochastic Lévy Laplacian and Yang-Mills equation on manifolds.(English)Zbl 1049.58037

It is known that a connection on a vector bundle over $$\mathbb{R}^n$$ satisfies the Yang-Mills equation if and only if its parallel transport is a zero of its Lévy Laplacian.
This work considers two generalisations of this result. Firstly, the space $$\mathbb{R}^n$$ is replaced by a manifold. Secondly, one considers a stochastic framework with stochastic parallel transport and stochastic Lévy Laplacian.

### MSC:

 58J65 Diffusion processes and stochastic analysis on manifolds 53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)

### Keywords:

Lévy Laplacian; Yang-Mills equation
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### References:

 [1] Accardi L., Russ. J. Math. Phys. 2 pp 235– (1994) [2] DOI: 10.1007/BF01018469 · Zbl 0449.53028 [3] Bismut J. M., Prog. Math. pp 45– (1984) [4] DOI: 10.1016/0022-1236(89)90035-9 · Zbl 0676.53033 [5] DOI: 10.1016/0022-1236(92)90035-H · Zbl 0765.60064 [6] DOI: 10.1016/0022-1236(85)90096-5 · Zbl 0624.53021 [7] DOI: 10.1016/0393-0440(93)90075-P · Zbl 0786.60074 [8] DOI: 10.1023/A:1005730013728 · Zbl 0895.60055 [9] DOI: 10.1007/BFb0094642 [10] DOI: 10.1007/BF00353876 · Zbl 0629.60061
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