Liu Yu-Xiao

Fermion localization and resonances on a de Sitter thick brane

In C. A. S. Almeida, R. Casana, M. M. Ferreira, Jr., and A. R. Gomes, Phys. Rev. D 79, 125022 (2009), the simplest Yukawa coupling eta(Psi) over bar phi chi Psi was considered for a two-scalar-generated Bloch brane model. Fermionic resonances for both chiralities were obtained, and their appearance is related to branes with internal structure. Inspired on this result, we investigate the localization and resonance spectrum of fermions on a one-scalar-generated de Sitter thick brane with a class of scalar-fermion couplings eta(Psi) over bar phi(k)Psi with positive odd integer k. A set of massive fermionic resonances for both chiralities is obtained when provided large coupling constant eta. We find that the masses and lifetimes of left and right chiral resonances are almost the same, which demonstrates that it is possible to compose massive Dirac fermions from the left and right chiral resonances. The resonance with lower mass has longer lifetime. For a same set of parameters, the number of resonances increases with k and the lifetime of the lower level resonance for larger k is much longer than the one for smaller k.

Effects of the variation of mass on fermion localization and resonances on thick branes

A few years ago, Campos investigated the critical phenomena of thick branes in warped spacetimes [Phys. Rev. Lett. 88, 141602 (2002)]. Inspired by his work, we consider a toy model of thick branes generated by a real scalar field with the potential V({phi})=a{phi}{sup 2}-b{phi}{sup 4}+c{phi}{sup 6}, and investigate the variation of the mass parameter a on the branes as well as the localization and resonances of fermions. An interesting result is found: there is a critical value for the mass parameter a, and when the critical value of a is reached the solution of the background scalar field is not unique and has the shape of a double kink. This happens in both cases with and without gravity. It is also shown that the numbers of the bound Kaluza-Klein modes of fermions on the gravity-free brane and the resonant states of fermions on the brane with gravity increase with the value of a.

Fermionic Zero Modes in Self-dual Vortex Background on a Torus

We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in (5+1) dimensions. Using the generalized Abelian–Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.

Gravitational Corrections to Energy-Levels of a Hydrogen Atom

The first-order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.

Spinor Field Realizations of W2,6 String and W6 String*

In this paper the spinor field BRST charges of the W2,6 string and W6 string are constructed, where the BRST charges are graded.In this paper the spinor field BRST charges of the W2,6 string and W6 string are constructed, where the BRST charges are graded.

Spinor Field Realizations of Non-critical W2,4 String Based on Linear W1,2,4 Algebra

In this paper, we investigate the spinor field realizations of the W2,4 algebra, making use of the fact that the W2,4 algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the spinor non-critical W2,4 string were built with these realizations.In this paper, we investigate the new spinor field realizations of the W 2,s algebras, making use of the fact that the W 2,s algebras can be linearized through the addition of a spin-1 current. We then use these new realizations to build the nilpotent BRST charges of the spinor non-critical W 2,s strings. The cases of s = 3 and 4 are discussed in detail. 2 1. Introduction As is well known, W algebra has found remarkable applications in W gravity and W string theories since its discovery in 1980s [1,2]. Furthermore, it appears in the quantum Hall effect, black holes, in lattice models of statistical mechanics at criticality, and in other physical models [3,4] and so on. The BRST formalism [5] has turned out to be rather fruitful in the study of the critical and non-critical W string theories. The BRST charge of W 3 string was first constructed in [6], and the detailed studies of it can be found in [6-12]. A natural generalization of the W 3 string, i.e. the W 2,s strings, is a higher-spin string with local spin-2 and spins symmetries on the world-sheet. Much work has been carried out on the scalar field realizations of W 2,s strings [9-18]. The BRST charges for such theories have been constructed for s = 4, 5, 6, 7 [13-15]. Later we discovered the reason that the scalar BRST charge is difficult to be generalized to a general W N string [19]. At the same time, we found the methods to construct the spinor field realization of W 2,s strings and W N strings [19,20]. Subsequently, we studied the exact spinor field realizations of W 2,s (s = 3, 4, 5, 6) strings and W N (N = 4, 5, 6) strings [19-22]. Recently, the authors have constructed the nilpotent BRST charges of spinor non-critical W 2,s (s = 3, 4) strings by taking into account the property of spinor field [23]. These results will be of importance for constructing super W strings, and they will provide the essential ingredients. However, all of these theories about the W 2,s strings mentioned above are based on the non-linear W 2,s algebras. Because of the intrinsic nonlinearity of the W 2,s algebras, their study is a more difficult task compared to linear algebras. Fortunately, it has been shown that certain W algebras can be linearized by the inclusion of …

New Spinor Field Realizations of the Non-Critical W3 String

We investigate the new spinor field realizations of the W3 algebra, making use of the fact that the W3 algebra can be linearized by the addition of a spin-1 current. We then use these new realizations to build the nilpotent Becchi–Rouet–Stora–Tyutin charges of the spinor non-critical W3 string.We investigate the new spinor field realizations of the W-3 algebra, making use of the fact that the W-3 algebra can be linearized by the addition of a spin-1 current. We then use these new realizations to build the nilpotent Becchi-Rouet-Stora-Tyutin charges of the spinor non-critical W-3 string.

Corrections to the Nonrelativistic Ground Energy of a Helium Atom

Considering the nuclear motion, the authors give out the nonrelativistic ground energy of a helium atom by using a simple but effective variational wave function with a flexible parameter

Ruppeiner Geometry of (2 + 1)-Dimensional Spinning Dilaton Black Hole

k

Topological aspect of Chern-Simons p-branes

. Based on this result, the relativistic and radiative corrections to the nonrelativistic Hamiltonian are discussed. The high precision value of the helium ground energy is evaluated to be -2.90338 a.u., and the relative error is 0.00034%.Considering the nuclear motion, we present the nonrelativistic ground energy of a helium atom by using a simple effective variational wavefunction with a flexible parameter k. Based on the result, the relativistic and radiative corrections to the nonrelativistic Hamiltonian are discussed. The high precision value of the helium ground energy is evaluated to be -2.90338 a.u. with the relative error 0.00034%.