Dirac Equation under Modified Hylleraas Potential in Noncommutative Spaces

In this paper, we study the interaction of spin 1/2 Dirac particles with the Hylleraas potential based on the noncommutative space framework. Solving the first-order correction of the energy level caused by the noncommutation parameter $\theta$ in the wave equation. The problem of energy level correction under the action of additional weak electric field is further analyzed. Due to the non-commutation parameter, the energy levels are split. The noncommutation parameter $\theta$ has a significant effect on the energy eigenvalues. The effect of $\theta$ on the energy level splitting caused by the electric field is reflected by adding a slight numerical change to the energy level after splitting

Symmetry group at future null infinity I: Scalar theory

We reduce the massless scalar field theory in Minkowski spacetime to future null infinity. We compute the Poincar\'e flux operators, which can be generalized and identified as the supertranslation and superrotation generators. These generators are shown to form a closed symmetry algebra with a divergent central charge. In the classical limit, we argue that the algebra may be interpreted as the geometric symmetry of a Carrollian manifold, i.e., the hypersurface of future null infinity. Our method may be used to find more physically interesting Carrollian field theories.Comment: 51 pages, revised versio

Symmetry group at future null infinity III: Gravitational theory

We reduce the gravitational theory in an asymptotically flat spacetime to future null infinity. We compute the Poincar\'e flux operators at future null infinity and construct the supertranslation and superrotation generators. The generators are shown to form a closed symmetry algebra by including a generalized gravitational duality operator. We could regard all the generators as the Hamiltonians with respect to the symmetry transformation in the boundary field theory. Our construction of the generators may relate to the BMS fluxes defined in the literature by adding counterterms to the Bondi mass and angular momentum aspects.Comment: 67 pages, revised versio