arXiv subjects
Publications and source records attributed to A. Zamyatin.
We consider 3 particles on ${\bf Z}{}_{+}$. One of them has infinite mass and stands still at $0$. The particles interact only if all of them are at the point $0$. We give a full description of essential, point and discrete spectra of the corresponding hamiltonian.
We study one particle subspaces for two particles of different masses with ultra local interaction on a lattice of arbitrary dimension.
We give a complete description of the discrete spectrum of one-dimensional Hamiltonian with a general perturbation of the radius $1$.
Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the multidifferential ones, and consider their infinite order jet prolongation. The infinite order jet manifold is endowed with the canonical flat connection that provides the covariant formula of a deformation star-product.