De~Sitter symmetry on quantum level implies that operators describing a given system satisfy commutation relations of the de~Sitter algebra. This approach gives a new perspective on fundamental notions of quantum theory. We discuss applications of the approach to the cosmological constant problem, gravity, and particle theory.

The modular analog of representations of the so(1,4) algebra for a system of two spinless particles is considered in the framework of approach (proposed by the author earlier), in which physical systems are described by the elements of a linear space over a finite field, and operators of physical quantities by linear operators in this space. The eigenvalues of the free mass operator and corresponding eigenvectors are found. It is shown that if the finite field under consideration satisfies some properties then the particles necessarily interact with each other. The corresponding interaction is universal, since it is fully defined by the masses of particles and characteristics of the finite field. The formula for the kernel of the interaction operator is derived, but since the kernel is defined by the sum over the Galois field and this sum cannot be calculated explicitly, then it cannot be determined how far the above interaction manifests itself in the usual conditions.