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Conservation of Gravitational Energy-Momentum and Inner diffeomorphism Group Gauge Invariance

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Journal of Modern Physics 2013年第8期4卷 37-47页

作者： Christian Wiesendanger Aurorastr. 24 CH-8032 Zurich Switzerland

Viewing gravitational energy momentum as equal by observation, but different in essence from inertial energy-momentum requires two different symmetries to account for their independent conservations—spacetime and inner translation invariance. Gauging the latter a generalization of non-Abelian gauge theories of compact Lie groups is developed resulting in the gauge theory of the non-compact group of volume-preserving diffeomorphisms of an inner Minkowski space M4. As usual the gauging requires the introduction of a covariant derivative, a gauge field and a field strength operator. An invariant and minimal gauge field Lagrangian is derived. The classical field dynamics and the conservation laws for the new gauge theory are developed. Finally, the theory’s Hamiltonian in the axial gauge is expressed by two times six unconstrained independent canonical variables obeying the usual Poisson brackets and the positivity of the Hamiltonian is related to a condition on the support of the gauge fields.

关键词： Gauge Field Theory Volume-Preserving diffeomorphism Group Inner Minkowski Space

diffeomorphisms with the M0-shadowing Property

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Acta Mathematica Sinica,English Series 2019年第11期35卷 1760-1770页

作者： Xu ZHANG Xin Xing WU Department of Mathematics Shandong UniversityWeihai 264209P.R.China School of Sciences Southwest Petroleum UniversityChengdu 610500P.R.China Department of Electronic Engineering City University of Hong KongHong Kong SARP.R.China

This paper studies the M0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the M0-shadowing property is described by the set of all Anosov diffeomorphisms. The C1-stably M0-shadowing property on a non-trivial transitive set implies the diffeomorphism has a dominated splitting.

关键词： Anosov diffeomorphism average shadowing property Mα-shadowing

Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on Circle diffeomorphisms

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Acta Mathematica Sinica,English Series 2020年第3期36卷 245-272页

作者： Yun Ping JIANG Department of Mathematics Queens College of the City University of New York FlushingNY 11367-1597USA Department of Mathematics Graduate School of the City University of New York365 Fifth A venueNew YorkNY 10016USA

Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit *** study several distortion properties for diffeomorphisms and quasisymmetric *** these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 diffeomorphisms on which we can assign such a ***,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.

关键词： Bers complex manifold structure circle diffeomorphism modulus of continuity quasisymmetric circle homeomorphism Teichmuller space Kobayashi's metric Teichmuller's metric

Two Characterizations of diffeomorphisms of Euclidean Space

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Acta Mathematica Sinica,English Series 2003年第4期19卷 739-744页

作者： LiJunYANG XianWuZENG DepartmentofMathematicalSciences TsinghuaUniversityBeijing100084P.R.China DepartmentofMathematics WuhanUniversityWuhan430072P.R.China

Two characterizations for a local diffeomorphism of R^n to be global one aregiven in terms of associated Wazewski equations. The two characterizations could be useful for theinvestigation of the Jacobian conjecture.

关键词： completeness diffeomorphism Jacobian conjecture properness

Rigidity result on conjugacies of families of diffeomorphisms

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Science China Mathematics 1997年第10期40卷 1036-1044页

作者：李伟固章梅荣 Department of Mathematics Peking UniversityBeijing 100871China Department of Applied Mathematics Tsinghua UniversityBeijing 100084China

Embedding flows are used to obtain a rigidity result on strongly topological conjugacy of families of diffeomorphisms,*** of C4(2≤r≤∞) diffeomorphisms,the strongly topologically conjugating homeomor-phisms near deg... 详细信息

关键词： diffeomorphism topological conjugacy.

关于一类3—连通的12维闭微分流形的同胚分类

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Northeastern Mathematical Journal 1994年第3期10卷 351-358页

作者：方复全

in this paper,we calculate the quotient group of the diffeomorphism group the pseudoisotopy *** using this result,we classify certain 3-connected closed smooth 12-manifolds up to diffeomorphism.

关键词： diffeomorphism Psudoisotopy 3-connected Closed 12-manifold

General Relativity as the Classical Limit of the Renormalizable Gauge Theory of Volume Preserving diffeomorphisms

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Journal of Modern Physics 2014年第10期5卷 948-958页

作者： Christian Wiesendanger Zurich Switzerland

The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an alternative approach to quantum gravity starts with the postulate that inertial energy-momentum and gravitational energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the quantum gauge field theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The classical limit of this theory coupled to a quantized scalar field is derived for an on-shell particle where inertial energy-momentum and gravitational energy-momentum coincide. In that process the symmetry under volume-preserving diffeomorphisms disappears and a new symmetry group emerges: the group of coordinate transformations of four-dimensional spacetime and with it General Relativity coupled to a classical relativistic point particle.

关键词： Quantum Gravity Quantum Gauge Theory of Volume-Preserving diffeomorphism Group GR Emerging as the Classical Limit of Above Different Roles of Inertial and Gravitational Momentum Observability of Spacetime at Microscopic Level

EXCESS FUNCTIONS OF RAYS ON COMPLETE NONCOMPACT MANIFOLDS

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Acta Mathematica Scientia 2003年第3期23卷 339-344页

作者：徐森林徐栩 Department of Mathematics Central China Normal UniversityWuhan 430079China School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

This paper gives an estimate of excess functions of rays on complete non-compact manifolds. By using this estimation, the authors can get the results in [3] as corollaries, which asserts that a complete manifold is diffeomorphic to Rn under some curvature and pinching conditions. At last, they obtain a refinement of them with extra Ricci condition.

关键词： Excess functions rays diffeomorphism

Global smooth solution of multi-dimensional non-homogeneous conservation laws

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Progress in Natural Science:Materials International 2004年第10期14卷 15-22页

作者： YANG Xiaozhou 1 and ZHANG Tong 2 (1.Department of Mathematics,Shantou University,Shantou515063,China 2.Institute of Mathematics,Chinese Academy of Sci-ences,Beijing100080,China) Department of Mathematics Shantou University Shantou 515063 China. Institute of Mathematics Chinese Academy of Sciences Beijing 100080 China

The initial value problem of multi-dimensional non-homogeneous conservation laws is studied and a sufficient condition of the existence of its global smooth solution is ***,three equivalent propositions of the existence of global smooth solution for multi-dimensional homogeneous scalar conservation laws are also *** global smooth solution is uniquely expressed by the global implicit function that is determined by a scalar equation,not by a system as usual methods do.

关键词： conservation laws global smooth solution global implicit function diffeomorphism