arXiv subjects

Gen Wang

Publications and source records attributed to Gen Wang.

25 records · Page 2Linked to original sources

arXiv2020

The generalized covariant Hamilton system in complex coordinates

Imitating methods of working on the GCHS and GSPB defined on ${\mathbb{R}^{r}}$ in real coordinates, an attempt to follow this way in complex coordinates is considered, then we try to generalize the PB on ${\mathbb{C}^{n}}$ in complex coordinates to the GSPB with zero restriction of the non-degeneracy expressed in complex coordinates that is compatible with the real case in formulas. Thusly, then the GCHS in complex coordinates defined by the GSPB is self-consistent to the real situation. Meanwhile, we find some difference of the GCHS between the real and complex case in formula. Much of what distinguishes a GCHS in real coordinates from a GCHS in complex coordinates is that the TGHS in complex form has an extra expression.

math-ph↗

arXiv2020

Analogy between geodesic equation and the GCHS on Riemannian manifolds

Enlightened by the similar equation form between the GCHS \footnote{GCHS: Generalized Covariant Hamilton System\\GSPB:Generalized structural Poisson bracket} defined by the GSPB and the geodesic equation expressed by geospin variable, we find a deep connection between the geospin matrix and S-dynamics. In this contrastive way, we actually proves that the GCHS is a compatible theory suitable for the curved spacetime as primitively stated. By contrast, geospin matrix in Riemannian geometry has the same physical nature as S-dynamics in GCHS. We obtain a fact that geodesic equation can be naturally derived by the GCHS in terms of the velocity field. We strictly prove that the geometrio $\hat{S}{{\left( {{x}_{k}},{{p}_{i}},H \right)}^{T}}={{\left( {{b}_{k}},{{A}_{i}},w \right)}^{T}}$ holds by using structural operator $\hat{S}$ directly induced by structural derivative ${A}_{i}$ in terms of position ${x}_{k}$, momentum ${p}_{i}$ and Hamiltonian $H$ respectively. It evidently proves that the GCHS on the Riemannian manifold is certainly determined by the Christoffel symbols. As an application, we consider the GCHS on Riemannian geometry.

math.DS↗

arXiv2020

Some extensive discussions of Liouville's theorem and Cauchy's integral theorem on structural holomorphic

Classic complex analysis is built on structural function $K=1$ only associated with Cauchy-Riemann equations, subsequently various generalizations of Cauchy-Riemann equations start to break this situation. The goal of this article is to show that only structural function $K=Const$ such that Liouville's theorem is held, otherwise, it's not valid any more on complex domain based on structural holomorphic, the correction should be $w=Φ{{e}^{-K}}$, where $Φ=Const$. Those theories in complex analysis which keep constant are unable to be held as constant in the framework of structural holomorphic. Synchronously, it deals with the generalization of Cauchy's integral theorem by using the new perspective of structural holomorphic, it is also shown that some of theories in the complex analysis are special cases at $K=Const$, which are narrow to be applied such as maximum modulus principle.

math.CV↗

arXiv2020

On the nonlinear Cauchy-Riemann equations of structural transformation and nonlinear Laplace equation

This paper aims at studying a functional $K$-transformation $w\left( z \right)\to \widetilde{w}\left( z \right)=w\left( z \right)K\left( z \right)$ that is made to reconsider the complex differentiability for a given complex function $w$ and subsequently we obtain structural holomorphic to judge a complex function to be complex structural differentiable. Since $K\left( z \right)$ can be chosen arbitrarily, thus it has greatly generalized the applied practicability. And we particularly consider $K \left( z \right)= 1+κ\left( z \right)$, then we found an unique Carleman-Bers-Vekua equations which is more simpler that all coefficients are dependent to the structural function $κ\left( z \right)$. The generalized exterior differential operator and the generalized Wirtinger derivatives are simultaneously obtained as well. As a discussion, second-order nonlinear Laplace equation is studied.

math.CV↗

arXiv2020

Geometrodynamics based on geodesic equation with Cartan structural equation on Riemannian manifolds

Motivated by the geospin matrix $W$ as a new variable in Riemannian geometry. Then, we use four real dynamical variables $\left\{ a,α,v,W \right\}$ to show the dynamical essence of Cartan structural equation, we obtain the geometrodynamics on Riemannian manifolds that can be expressed below \begin{align} & Θ/d{{t}^{2}}=a-v\wedge W,\nonumber & dΘ/d{{t}^{3}}=v\wedge α-a\wedge W,\nonumber & Ω/d{{t}^{2}}=α-W\wedge W, \nonumber & dΩ/d{{t}^{3}}=W\wedge α-α\wedge W\nonumber \end{align} that is valid more generally for any connection in a principal bundle. We can see that the first equation explains the geodesic equation very well, the second formula means the first Bianchi identity, while the last equation reveals the dynamical nature of the second Bianchi identity. It implies that Cartan structural equations on Riemannian manifolds can be rewritten in a real geometrodynamical form based on the geospin matrix.

math.DG↗

arXiv2018

Coupling to Multihadron States with Chiral Fermions

Chiral symmerty is presumed to be a crucial component in the strong interaction and QCD, but its role in spectroscopy, especially for baryons, has not been fully explored. Compounding this, chiral fermions are uncommon in lattice calculations due to their expensive nature. We calculate $ηπ$, $Kπ$ and $Nπ$ states with $q\bar{q}$ and $qqq$ interpolation fields at $a=0.114\,\mathrm{fm}$ on a $48^3\times 96$ mixed-action lattice at the physical pion mass, with domain-wall sea quarks and overlap valence quarks. We study the spectral weights of these states as a function of the valence pion mass, which ranges from $m_π=115-665\,\mathrm{MeV}$, to be compared with the results from non-chiral clover valence quarks on the same domain-wall lattice in order to examine their non-chiral effects, which are expected to decrease with the lattice spacing.

hep-lat↗

arXiv2018

Pion Form Factor with Overlap Fermion

We present a calculation of the pion form factor using overlap fermions on 2+1-flavor domain-wall configurations on a $24^3\times 64$ lattice with $a=0.11 \, {\rm{fm}}$ and on a $32^3 \times 64$ lattice with $a=0.143 \, {\rm{fm}}$ generated by the RBC/UKQCD collaboration. Using the multi-mass algorithm, a simulation has been done with various valence quark masses with a range of space-like $Q^2$ from 0.0 to 0.6 ${\rm{GeV^2}}$.

hep-lat↗