Magnetic cochains Laplacians and their essential self-adjointness.

In this paper, we introduce the notion of oriented triangular faces F , the notion of edges potential P E and the notion of triangular faces potential P F in a connected oriented locally finite graph (V , E) in order to construct a new framework that's we call the magnetic weighted 2 -simplicial complex M = (V , E , F , P E , P F). On this new magnetic weighted framework, we introduce the magnetic 0 -cochains set, the magnetic 1 -cochains set, the magnetic 2 -cochains set and the magnetic cochains set. After that, we construct the magnetic 0 -cochains Laplacian, the magnetic 1 -cochains Laplacian, the magnetic 2 -cochains Laplacian and the magnetic cochains Laplacian. Finally, we ensure essential self-adjointness for our new magnetic cochains Laplacians using the Stieltjes vectors. [ABSTRACT FROM AUTHOR]