A simple proof of the perturbative uniqueness of the Kerr solution

We present a mathematically simple and coordinate-free proof, based on the GHP spin-coefficient formalism, that a small stationary perturbation of a Kerr solution results in a new Kerr solution. Thus, under physically reasonable assumptions, we give a new and simple proof that a stationary black hole is given by a Kerr solution.     

On a Generalization of the Trèves Criterion for the First Integrals of the KdV Hierarchy to Higher GD Hierarchies

First, a new proof of the necessity of the Trèves criterion for a differential polynomialto be a first integral of the KdV hierarchy is given. This proof is much shorter than the original one and admits generalizations. Second, a similar criterion is suggested and its necessity proven for the next of the GD hierarchies which is generated by the third-order linear operator.     

A proof of the Nielsen-Ninomiya theorem

The Nielsen-Ninomiya theorem asserts the impossibility of constructing lattice models of non-selfinteracting chiral fermions. A new proof is given here. This proof fills a technical gap in the two proofs presented by the authors of the theorem. It also serves as prelude to an investigation of the chiral properties of the general lattice model.     

A proof of the indeterminary relation of lifetime and energy

A new proof of the indeterminacy relation of the standard energy deviation and lifetime of a pure quantum state is given by means of the Mandelstam-Tamm inequality.     

A new proof for the convergent iterative solution of the degenerate quantum double-well potential and its generalization

We present a new and simpler proof for the convergent iterative solution of the one-dimensional degenerate double-well potential. This new proof depends on a general theorem, called the hierarchy theorem, that shows the successive stages in the iteration to form a monotonically increasing sequence of approximations to the energy and to the wavefunction at any point x. This important property makes possible a much simpler proof of convergence than the one given before in the literature. The hierarchy theorem proven in this paper is applicable to a much wider class of potentials which includes the quartic potential.     

Adiabatic theorem for finite dimensional quantum mechanical systems

A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. An explicitly integrable two-level system is considered as an example. It is demonstrated that the error estimate given by the adiabatic theorem cannot be improved.     

精确配置离散动力系统的所有Lyapunov指数

针对给定的确定性离散时间动力学系统,提出一种可以精确配置受控系统所有Lyapunov指数的混沌控制与反控制新方法.本文不限制给定系统的具体形式,仅利用取模运算和预设的一组Lyapunov指数,设计出一种新的状态反馈控制器.在控制器的作用下,受控系统的Lyapunov指数与预设的Lyapunov指数一致.控制器的形式简单,可以用于解决混沌控制和混沌反控制两种问题.给出了数学证明和两个实例,仿真结果显示了算法的有效性.     

The infinite cluster method in the two-dimensional Ising model

By studying infinite clusters in the two dimensional ferromagnetic Ising model some new results on the problem of existence of non-translation invariant equilibrium states are obtained. Furthermore a new proof of a theorem by Abraham and Reed is given.This work was supported in part by C.N.R., G.N.F.M.     

Branching space-time analysis of the GHZ theorem

Greenberger. Horne. Shimony, and Zeilinger gave a new version of the Bell theorem without using inequalities (probabilities). Mermin summarized it concisely; but Bohm and Hiley criticized Mermin's proof from contextualists' point of view. Using the branching space-time language, in this paper a proof will be given that is free of these difficulties. At the same time we will also clarify the limits of the validity of the theorem when it is taken as a proof that quantum mechanics is not compatible with a deterministic world nor with a world that permits correlated space-related events without a common cause.Supported by OTKA Foundation. Nos. T-015606 and T-017176.     

Regularity of gauge equivalence in quantum mechanics and the Aharonov-Bohm effect

A general new proof of the Aharonov-Bohm effect is given. The proof is essentially based on the regularity theorem for elliptic operators and does not depend on the geometry or symmetry of the system. We also establish the inequivalence of the different canonical quantum realizations of classical systems whose configuration spaces are multiply connected.     

Asymptotic Behavior for the Liouville Equations

A new proof of the diffusion approximation for ordinary differential equations is given. It is based on an asymptotic expansion of the solution of the corresponding Liouville partial differential equations. In contrast to previous results obtained for the suspension under Holderian mappings of subshift of finite type or Fourier analysis techniques, our proof relies only on symbolic dynamics.     

Inconsistency of Quantum—Classical Dynamics, and What it Implies

A new proof of the impossibility of a universal quantum-classical dynamics is given. It has at least two consequences. The standard paradigm “quantum system is measured by a classical apparatus” is untenable, while a quantum matter can be consistently coupled only with a quantum gravity.     

A simple derivation of Borland's locality result

A new proof of Borland's localization theorem is given, which is simpler, less rigorous, but gives more quantitative results.     

Study of Lamination Characteristics for Rapid Prototyping

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构造Birkhoff表示的Hojman方法与Birkhoff对称性

讨论了构造Birkhoff表示的Hojman方法.利用该方法重新研究Birkhoff对称性,提出一种关于该对称性的新见解,给出Birkhoff守恒量的新证明,并对该守恒量仅与Birkhoff张量相关作出解释.举例说明所得结果的应用.     

Adler's theorem in finite massless QED and possible extensions to non-Abelian gauge theories

A new proof of Adler's theorem in finite massless QED is given and generalizations to non-Abelian gauge theories are studied.     

Asymptotic completeness for quantum mechanical potential scattering

A new (geometrical) proof is given for the asymptotic completeness of the wave operators and the absence of a singular continuous spectrum of the Hamiltonian for potentials which decrease faster than in the Coulomb case, the space dimension is arbitrary.Partially supported by a travel grant from the Deutsche ForschungsgemeinschaftOn leave from Department of Theoretical Physics, University of Bielefeld, Federal Republic of Germany     

On the finiteness of a new topological model in D=3

A new topological model is proposed in three dimensions as an extension of the BF-model. It is a three-dimensional counterpart of the two-dimensional model introduced by Chamseddine and Wyler ten years ago. The BFK-model, as we shall call it, shows to be quantum scale invariant at all orders in perturbation theory. The proof of its full finiteness is given in the framework of algebraic renormalization.     

A Geometrical Approach to Hojman Theorem of a Rotational Relativistic Birkhoffian System

A geometrical approach to the Hojman theorem of a rotational relativistic Birkhoffian system is presented.The differential equations of motion of the system are established. According to the invariance of differential equations under infinitesimal transformation, the determining equations of Lie symmetry are constructed. A new conservation law of the system, called Hojman theorem, is obtained, which is the generalization of previous results given sequentially by Hojman, Zhang, and Luo et al. In terms of the theory of modern differential geometry a proof of the theorem is given.