arXiv subjects

Han-Ying Guo

Publications and source records attributed to Han-Ying Guo.

At least 37 records · Page 2Linked to original sources

arXiv2005

Conformal Triality of de Sitter, Minkowski and Anti-de Sitter Spaces

We describe how conformal Minkowski, dS- and AdS-spaces can be united into a single submanifold [N] of RP^5. It is the set of generators of the null cone in M^{2,4}. Conformal transformations on the Mink-, dS- and AdS-spaces are induced by O(2,4) linear transformations on M^{2,4}. We also describe how Weyl transformations and conformal transformations can be resulted in on [N]. In such a picture we give a description of how the conformal Mink-, dS- and AdS-spaces as well as [N] are mapped from one to another by conformal maps. This implies that a CFT in one space can be translated into a CFT in another. As a consequence, the AdS/CFT-correspondence should be extended.

hep-th↗

arXiv2005

Three Kinds of Special Relativity via Inverse Wick Rotation

Since the special relativity can be viewed as the physics in an inverse Wick rotation of 4-d Euclid space, which is at almost equal footing with the 4-d Riemann/Lobachevski space, there should be important physics in the inverse Wick rotation of 4-d Riemann/Lobachevski space. Thus, there are three kinds of special relativity in de Sitter/Minkowski/anti-de Sitter space at almost equal footing, respectively. There is an instanton tunnelling scenario in the Riemann-de Sitter case that may explain why $\La$ be positive and link with the multiverse.

hep-th↗

arXiv2005

A new single-dynamical-scalar-field model of dark energy

A new single-dynamical-scalar-field model of dark energy is proposed, in which either higher derivative terms nor structures of extra dimension are needed. With the help of a fixed background vector field, the parameter for the effective equation of state of dark energy may cross $w=-1$ in the evolution of the universe. After suitable choice of the potential, the crossing $w=-1$ and transition from decelerating to accelerating occur at $z\approx 0.2$ and $z\approx 1.7$, respectively.

astro-ph↗

arXiv2005

Mechanics and Newton-Cartan-Like Gravity on the Newton-Hooke Space-time

We focus on the dynamical aspects of Newton-Hooke space-time ${\cal NH}_+$ mainly from the viewpoint of geometric contraction of the de Sitter spacetime. We first discuss the Newton-Hooke classical mechanics, especially the continuous medium mechanics, in this framework. Then, we establish a consistent theory of gravity on the Newton-Hooke space-time as a kind of Newton-Cartan-like theory, parallel to the Newton's gravity in the Galilei space-time. Finally, we give the Newton-Hooke invariant Schrödinger equation from the geometric contraction, where we can relate the conservative probability in some sense to the mass density in the Newton-Hooke continuous medium mechanics. Similar consideration may apply to the Newton-Hooke space-time ${\cal NH}_-$ contracted from anti-de Sitter spacetime.

hep-th↗

arXiv2004

Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm

We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This approach keeps both symplicticity and energy conservation discretely. We show that there exists the discrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existence in finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodic perturbation. The numerical results are satisfactory.

math-ph↗

arXiv2004

The Generalized Liouville's Theorems via Euler-Lagrange Cohomology Groups on Symplectic Manifold

Based on the Euler-Lagrange cohomology groups $H_{EL}^{(2k-1)}({\cal M}^{2n}) (1 \leqslant k\leqslant n)$ on symplectic manifold $({\cal M}^{2n}, ω)$, their properties and a kind of classification of vector fields on the manifold, we generalize Liouville's theorem in classical mechanics to two sequences, the symplectic(-like) and the Hamiltonian-(like) Liouville's theorems. This also generalizes Noether's theorem, since the sequence of symplectic(-like) Liouville's theorems link to the cohomology directly.

math-ph↗

arXiv2004

On de Sitter Invariant Special Relativity and Cosmological Constant as Origin of Inertia

Weakening the Euclidean assumption in special relativity and the coordinate-independence hypothesis in general relativity for the de Sitter space, we propose a de Sitter invariant special relativity with two universal constants of speed $c$ and length $R$ based on the principle of relativity and the postulate of universal constants $c$ and $R$ on de Sitter space with Beltrami metric. We also propose a postulate on the origin of the inertial motions and inertial systems as a base of the principle of relativity. We show that the Beltrami-de Sitter space provides such a model that the origin of inertia should be determined by the cosmological constant $Λ$ if the length $R$ is linked with $Λ$. In addition, via the `gnomonic' projection the uniform straight-line motion on Beltrami-de Sitter space is linked with the uniform motion along a great `circle' on de Sitter space embedded in 5-d Minkowski space.

hep-th↗

arXiv2004

On Special Relativity with Cosmological Constant

Based on the principle of relativity and the postulate of invariant speed and length, we propose the theory of special relativity with cosmological constant ${\cal SR}_{c,R}$ if the invariant length whose square is the inverse of the one-third cosmological constant of the universe. It is on the Beltrami-de Sitter spacetime ${\cal B}_R$ with de Sitter invariance. We define the observables of free particles and generalize famous Einstein's formula. We also define two kinds of simultaneity. The first is for local experiments and inertial motions. The second is for cosmological observations. Thus there is a relation between the relativity principle and the cosmological principle. We predict that the 3-d cosmic space is then of positive spatial curvature of order cosmological constant. The relation between ${\cal SR}_{c,R}$ and the doubly special relativity is briefly disucssed.

hep-th↗

arXiv2003

On Beltrami Model of de Sitter Spacetime

Based on some important properties of $dS$ space, we present a Beltrami model ${\cal B}_Λ$ that may shed light on the observable puzzle of $dS$ space and the paradox between the special relativity principle and cosmological principle. In ${\cal B}_Λ$, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson-Walker-like metric. It is of positive spatial curvature of order $Λ$. This is more or less indicated already by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.

hep-th↗

arXiv2003

(Super)gravity and Yang-Mills Theories as Generalized Topological Fields with Constraints

We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand.

hep-th↗

arXiv2003

The Euler-Lagrange Cohomology Groups on Symplectic Manifolds

The definition and properties of the Euler-Lagrange cohomology groups $H^{2k-1}$, $1 \leqslant k \leqslant n$, on a symplectic manifold $({\cal M}^{2n},ω)$ are given and studied. For $k = 1$ and $k = n$, they are isomorphic to the corresponding de Rham cohomology groups $H_{dR}^1({\cal M}^{2n})$ and $H_{dR}^{2n-1}({\cal M}^{2n})$, respectively. The other Euler-Lagrange cohomology groups are different from either the de Rham cohomology groups or the harmonic cohomology groups on $({\cal M}^{2n},ω)$, in general. The general volume-preserving equations on $({\cal M}^{2n},ω)$ are also presented from cohomological point of view. In the special cases, these equations become the ordinary canonical equations in the Hamilton mechanics. Therefore, the Hamilton mechanics has been generalized via the cohomology.

physics.class-ph↗

arXiv2003

On Diffeomorphism Invariance and Black Hole Entropy

The Noether-charge realization and the Hamiltonian realization for the $\diff({\cal M})$ algebra in diffeomorphism invariant gravitational theories are studied in a covariant formalism. For the Killing vector fields, the Nother-charge realization leads to the mass formula as an entire vanishing Noether charge for the vacuum black hole spacetimes in general relativity and the corresponding first law of the black hole mechanics. It is analyzed in which sense the Hamiltonian functionals form the $\diff({\cal M})$ algebra under the Poisson bracket and shown how the Noether charges with respect to the diffeomorphism generated by vector fields and their variations in general relativity form this algebra. The asymptotic behaviors of vector fields generating diffeomorphism of the manifold with boundaries are discussed. In order to get more precise estimation for the "central extension" of the algebra, it is analyzed in the Newman-Penrose formalism and shown that the "central extension" for a large class of vector fields is always zero on the Killing horizon. It is also checked whether the Virasoro algebra may be picked up by choosing the vector fields near the horizon. The conclusion is unfortunately negative.

gr-qc↗

arXiv2003

The Euler-Lagrange Cohomology and General Volume-Preserving Systems

We briefly introduce the conception on Euler-Lagrange cohomology groups on a symplectic manifold $(\mathcal{M}^{2n}, ω)$ and systematically present the general form of volume-preserving equations on the manifold from the cohomological point of view. It is shown that for every volume-preserving flow generated by these equations there is an important 2-form that plays the analog role with the Hamiltonian in the Hamilton mechanics. In addition, the ordinary canonical equations with Hamiltonian $H$ are included as a special case with the 2-form $\frac{1}{n-1} H ω$. It is studied the other volume preserving systems on $({\cal M}^{2n}, ω)$. It is also explored the relations between our approach and Feng-Shang's volume-preserving systems as well as the Nambu mechanics.

hep-th↗

arXiv2002

General Volume-Preserving Mechanical Systems

In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, ω). It is shown that every volume-preserving flow has some 2-forms acting the role of the Hamiltonian functions in the Hamiltonian mechanics and the ordinary Hamilton equations are included as a special case with a 2-form \frac{1}{n-1} H ωwhere H is the corresponding Hamiltonian.

math-ph↗

arXiv2002

Noether-Charge Realization of Diffeomorphism Algebra

It is shown in the covariant phase space formalism that the Noether charges with respect to the diffeomorphism generated by vector fields and their horizontal variations in general relativity form a diffeomorphism algebra. It is also shown with the help of the null tetrad which is well defined everywhere that the central term of the reduced diffeomorphism algebra on the Killing horizon for a large class of vector fields vanishes.

gr-qc↗

arXiv2002

Chern-Simons Term for BF Theory and Gravity as a Generalized Topological Field Theory in Four Dimensions

A direct relation between two types of topological field theories, Chern-Simons theory and BF theory, is presented by using ``Generalized Differential Calculus'', which extends an ordinary p-form to an ordered pair of p and (p+1)-form. We first establish the generalized Chern-Weil homomormism for generalized curvature invariant polynomials in general even dimensional manifolds, and then show that BF gauge theory can be obtained from the action which is the generalized second Chern class with gauge group G. Particularly when G is taken as SL(2,C) in four dimensions, general relativity with cosmological constant can be derived by constraining the topological BF theory.

hep-th↗

arXiv2002

Discrete mechanics Based on Finite Element Methods

Discrete Mechanics based on finite element methods is presented in this paper. We also explore the relationship between this discrete mechanics and Veselov discrete mechanics. High order discretizations are constructed in terms of high order interpolations.

hep-th↗

arXiv2002

Black Hole Mass Formula Is a Vanishing Noether Charge

The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respectively. For Einstein's GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived from this Noether current although it definitely vanishes. This indicates that the mass formula of black holes is a vanishing Noether charge in this case. The first law of black hole thermodynamics can also be derived from the variation relation of this vanishing Noether current.

gr-qc↗