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A three-parameter (positive odd integer $s$, thickness factor $\lambda$, and asymmetry factor $a$) family of asymmetric thick brane solutions in five dimensions were constructed from a two-parameter ($s$ and $\lambda$) family of symmetric ones in [R. Guerrero, R.O. Rodriguez, and R. Torrealba, Phys. Rev. D \textbf{72}, 124012 (2005).]. The values $s=1$ and $s\geq3$ correspond to single branes and double branes, respectively. These branes have very rich inner structure. In this paper, by presenting the mass-independent potentials of Kaluza--Klein (KK) modes in the corresponding Schr\"{o}dinger equations, we investigate the localization and mass spectra of fermions on the symmetric and asymmetric thick branes in an AdS background. In order to analyze the effect of gravity-fermion interaction (i.e., the effect of the inner structure of the branes) and scalar-fermion interaction to the spectrum of fermion KK modes, we consider three kinds of typical kink-fermion couplings. The spectra of left chiral fermions for these couplings are consisted of a bound zero mode and a series of gapless continuous massive KK modes, some discrete bound KK modes including zero mode (exist mass gaps) and a series of continuous massive KK modes, infinite discrete bound KK modes, respectively. The structures of the spectra are investigated in detail., Comment: v1: 35 pages, 21 figures; v2: 22 pages, 22 figures, to appear in PRD

An asymmetric thick domain wall solution with de Sitter ($dS$) expansion in five dimensions can be constructed from a symmetric one by using a same scalar (kink) with different potentials. In this paper, by presenting the mass-independent potentials of Kaluza--Klein (KK) modes in the corresponding Schr\"{o}dinger equations, we investigate the localization and mass spectra of various bulk matter fields on the symmetric and asymmetric $dS$ thick branes. It is shown that the spectrum of scalar KK modes on the symmetric $dS$ brane contains only one bound mode (the massless mode). However, for the asymmetric $dS$ brane with a large asymmetric factor $a$, there are two bound scalar KK modes: a zero mode and a massive mode. For spin 1 vectors, the spectra of KK modes on both $dS$ branes consist of a bound massless mode and a set of continuous ones, i.e., the asymmetric factor does not change the number of the bound vector KK modes. For spin 1/2 fermions with the scalar-fermion coupling $\eta\bar\Psi \sin(\phi/\phi_0)\cos^{-\delta}(\phi/\phi_0)\Psi$, there exist some discrete bound KK modes and a series of continuous ones. The asymmetric factor $a$ reduces the number of the bound fermion KK modes., Comment: 28 pages, 28 figures

In this paper, we study localization and mass spectrum of various matter fields on a family of thick brane configurations in a pure geometric Weyl integrable 5-dimensional space time, a non-Riemannian modification of 5-dimensional Kaluza--Klein (KK) theory. We present the shape of the mass-independent potential of the corresponding Schr\"{o}dinger problem and obtain the KK modes and mass spectrum, where a special coupling of spinors and scalars is considered for fermions. It is shown that, for a class of brane configurations, there exists a continuum gapless spectrum of KK modes with any $m^2>0$ for scalars, vectors and ones of left chiral and right chiral fermions. All of the corresponding massless modes are found to be normalizable on the branes. However, for a special of brane configuration, the corresponding effective Schr\"{o}dinger equations have modified P\"{o}schl-Teller potentials. These potentials suggest that there exist mass gap and a series of continuous spectrum starting at positive $m^2$. There are one bound state for spin one vectors, which is just the normalizable vector zero mode, and two bound KK modes for scalars. The total number of bound states for spin half fermions is determined by the coupling constant $\eta$. In the case of no coupling ($\eta=0$), there are no any localized fermion KK modes including zero modes for both left and right chiral fermions. For positive (negative) coupling constant, the number of bound states of right chiral fermions is one less (more) than that of left chiral fermions. In both cases ($\eta>0$ and $\eta, Comment: 18 pages, 2 figures; V2: 19 pages, 12 figures

In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two dimensional compact manifold $S^2$ as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under quite general assumptions about these backgrounds on the bulk. Several special cases of gauge background on the sphere are discussed and some simple fermionic zero modes are obtained., 8 pages, no figures, accepted by Commun. Theor. Phys; V4: one reference added

In light of $\phi$-mapping topological current theory, the inner topological structure of Hopf invariant is investigated. It is revealed that Hopf invariant is just the winding number of Gauss mapping. According to the inner structure of topological current, a precise expression for Hopf invariant is also presented. It is the total sum of all the self-linking and all the linking numbers of the knot family., Comment: 13pages, no figure. Accepted by J.Math.Phys

Based on the $\phi$-mapping topological current theory and the decomposition of gauge potential theory, we investigate knotted vortex lines and monopoles in Skyrme theory and simply discuss the branch processes (splitting, merging and intersection) during the evolution of the monopoles., Comment: 10 pages, 0 figures

Based on the decomposition of U(1) gauge potential theory and the $\phi$-mapping topological current theory, the three-dimensional knot invariant and a four-dimensional new topological invariant are discussed in the U(1) gauge field., Comment: 10 pages, 0 figures accepted by MPLA

Considering that gravitational force might deviate from Newton's inverse-square law and become much stronger in small scale, we present a method to detect the possible existence of extra dimensions in the ADD model. By making use of an effective variational wave function, we obtain the nonrelativistic ground energy of a helium atom and its isoelectronic sequence. Based on these results, we calculate gravity correction of the ADD model. Our calculation may provide a rough estimation about the magnitude of the corresponding frequencies which could be measured in later experiments., 8 pages, no figures, accepted by Mod. Phys. Lett. A

In this note we study fermionic zero modes in gauge and gravity backgrounds taking a two dimensional compact manifold $T^2$ as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under quite general assumptions about these backgrounds on the bulk. Several special cases of gauge background on the torus are discussed and some simple fermionic zero modes are obtained., 8 pages, no figures, v2: more references, accepted by Mod.Phys.Lett.A

We present a new Lorentz gauge invariant U(1) topological field theory in Riemann-Cartan spacetime manifold $U_{4}$. By virtue of the decomposition theory of U(1) gauge potential and the $ \phi $--mapping topological current theory, it is proved that the U(1) complex scalar field $\phi (x)$ can be looked upon as the order parameter field in our Universe, and the set of zero points of $\phi (x)$ create the cosmic strings as the spacetime defects in the early Universe. In the standard cosmology this complex scalar order parameter field possesses negative pressure, provides an accelerating expansion of Universe and be able to explain the inflation in the early Universe. Therefore this complex scalar field is not only the order parameter field created the cosmic strings, but also reasonably behaves as the quintessence, the dark energy., Comment: 10 pages

Based on the decomposition of SU(2) gauge field, we derive a generalization of the decomposition theory for the SU(N) gauge field. We thus obtain the invariant electro-magnetic tensors of SU(N) groups and the extended Wu-Yang potentials. The sourceless solutions are also discussed., 9 pages

In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinors is studied. Using this decomposition, the spinor strutures of the Chern-Simons form and the Chern density are obtained. Furthermore, by these spinor structures, the knot quantum number of non-Abelian gauge theory is discussed, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of $\phi $-mapping., Comment: 11 pages