In this paper, we construct the nilpotent Becchi-Rouet-Stora-Tyutin(BRST) charges of spinor non-critical W2,s strings. The cases of s = 3, 4 are discussed in detail, and spinor realization for s = 4 is given explicitly. The BRST charges are graded.

It has been shown that certain W algebras can be linearized by the inclusion of a spin-1 current. This Provides a way of obtaining new realizations of the W algebras. In this paper, we investigate the new ghost field realizations of the W2,s(s = 3, 4) algebras, making use of the fact that these two algebras can be linearized. We then construct the nilpotent BRST charges of the spinor non-critical W2,s strings with these new realizations.

By making use of the decomposition of U(1) gauge potential theory and the-mapping method,we propose that a charged two-condensate Bose system possesses vortex lines and two classes of knotted solitons. The topological charges of the vortex lines are characterized by the Hopf indices and the Brower degrees of-mapping, and the knotted solitons are described by the nontrivial Hopf invariant and the BF action, respectively.

The first order perturbations of the energy levels of a stationary hydrogen atom in static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, 4P, 4D and 4F levels. The results show that the energy-level shifts of the states with total angular momentum quantum number 1/2 are all zero, and the ratio of absolute energy shifts with total angular momentum quantum number 5/2 is 1:4:5. This feature can be used to help us to distinguish the gravitational effect from other effect.

In 1997, Liberati and Pollifrone in Phys. Rev. D56 (1997) 6458 (hep-th/9708014) achieved a new formulation of the Bekenstein-Hawking formula, where the entropy and the Euler characteristic are related by S = A/8. In this work we present a relation between the low-energy absorption cross section for minimally coupled fermions and the Euler characteristic of (3+1)-dimensional spherically symmetric black holes, i.e.=g−1 h A. Based on the relation, using the Gauss–Bonnet–Chern theorem and the -mapping method, an absorption cross section density is introduced to describe the topology of the absorption cross section. It is shown that the absorption cross section and its density are determined by the singularities of the timelike Killing vector field of the spacetime and these singularities carry the topological numbers, Hopf indices and Brouwer degrees, naturally.