On the structure of the relativistic many-body problem and the construction of effective many-hadron theories

The general structure of the bound state problem posed by a Poincaré-invariant quantum field theory is discussed. It is pointed out that the only present-day method which promises to solve this problem is a nonperturbative regularisation and a check of scaling in the continuum limit. It is demonstrated that perturbation procedures like the Green's function methods of “quantum hadro-dynamics” are inconsistent with respect to covariance and do not solve the bound state problem. As a consequence we propose to use for an effective many-hadron theory a regularised Hamiltonian including form factors, the arbitrariness of which may be essentially restricted by a “minimal relativity” condition. Examples for such effective theories are discussed.     

Quantum Theory and the Role of Mind in Nature

Orthodox Copenhagen quantum theory renounces the quest to understand the reality in which we are imbedded, and settles for practical rules describing connections between our observations. Many physicist have regarded this renunciation of our effort describe nature herself as premature, and John von Neumann reformulated quantum theory as a theory of an evolving objective universe interacting with human consciousness. This interaction is associated both in Copenhagen quantum theory and in von Neumann quantum theory with a sudden change that brings the objective physical state of a system in line with a subjectively felt psychical reality. The objective physical state is thereby converted from a material substrate to an informational and dispositional substrate that carries both the information incorporated into it by the psychical realities, and certain dispositions for the occurrence of future psychical realities. The present work examines and proposes solutions to two problems that have appeared to block the development of this conception of nature. The first problem is how to reconcile this theory with the principles of relativistic quantum field theory; the second problem is to understand whether, strictly within quantum theory, a person's mind can affect the activities of his brain, and if so how. Solving the first problem involves resolving a certain non-locality question. The proposed solution to the second problem is based on a postulated connection between effort, attention, and the quantum Zeno effect. This solution explains on the basic of quantum physics a large amount of heretofore unexplained data amassed by psychologists.     

Quasiconfigurations and the theory of effective interactions

Perturbation theory is reformulated. Schrödinger's equation is recast as a non linear integral equation which yields by Neumann expansion a linked cluster series for the degenerate, quasi degenerate or non degenerate problem. An effective interaction theory emerges that can be formulated in a biorthogonal basis leading to a non Hermitian secular problem. Hermiticity can be recovered in a clear and rigorous way. As the mathematical form of the theory is dictated by the request of physical clarity the latter is obtained naturally. When written in diagrammatic many body language, the integral equation produces a set of linked coupled equations for the degenerate case. The classic summations (Brueckner, Bethe-Faddeev and RPA) emerge naturally. Possible extensions of nuclear matter theory are suggested.     

A comparison of the stochastic theory of the crystal growth and the Stefan problem

The stochastic theory of the crystal growth is compared with the solution of the Stefan problem in the case of Sn solidification. It is shown that the stochastic theory gives the same results as the solution of the Stefan problem if kinetic processes at the solidification front are very rapid.     

Mixed problem for the Einstein equations

A question in the theory of gravitation which shares importance with attempts to experimentally observe gravitational waves and to solve various astrophysical problems by means of the general theory of relativity is the question of finding all possible formulations of the various problems, e. g., the Cauchy problem and the mixed problem with various modifications of the boundary conditions.     

Semi-classical approximation and the problem of boundary conditions in the theory of relativistic particle radiation

Abstract

The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is to express the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation.

We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation.

The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics.     

On localization in the theory of the quantized hall effect: A two-dimensional realization of the θ-vacuum

It is shown that the localization problem in the theory of the quantized Hall effect is governed by the zero-component grassmannian U(2m) non-linear σ-model with θ-term, a two-dimensional analogue of the θ-vacuum in Yang-Mills theory. In this case, θ is to be interpreted as the “bare” value for the Hall conductivity, determined by an underlying non-critical theory. A detailed derivation is presented starting from the replica method and a delta function distribution for the impurities.     

A probabilistic study of the influence of parameter uncertainty on solutions of the radiative transfer equation

The influence of uncertainty in the absorption and scattering coefficients on the solution and associated parameters of the radiative transfer equation is studied using polynomial chaos theory. The uncertainty is defined by means of uniform and log-uniform probability distributions. By expanding the radiation intensity in a series of polynomial chaos functions we may reduce the stochastic transfer equation to a set of coupled deterministic equations, analogous to those that arise in multigroup neutron transport theory, with the effective multigroup transfer scattering coefficients containing information about the uncertainty. This procedure enables existing transport theory computer codes to be used, with little modification, to solve the problem. Applications are made to a transmission problem and a constant source problem in a slab. In addition, we also study the rod model for which exact analytical solutions are readily available. In all cases, numerical results in the form of mean, variance and sensitivity are given that illustrate how absorption and scattering coefficient uncertainty influences the solution of the radiative transfer equation.     

The effect of impedance boundary conditions on the potential function of the boundary diffraction wave theory

A novel potential function of the boundary diffraction wave theory is obtained for the impedance surfaces by the asymptotic reduction of the modified theory of physical integrals. The function is expressed in terms of the direction vectors of the incident and scattered rays. The application of the method is performed on the problem of diffraction of plane waves by an impedance half plane for oblique incidence.     

On the simple-source theory of sound from statistical turbulence

A theory for the generation of aerodynamic sound, stated in terms of convected simple sources and dipoles, is presented. The sources are found to depend upon convective derivatives of the hydrodynamic pressure within the turbulent source region. The results are similar to earlier efforts involving simple sources, sometimes called dilatational sources. The results are modified for effects involving measurements on moving flows. The theory shows explicitly the refractive effects of shear flow within the source region, as well as of temperature changes (if any) within the source region. The oscillating cylinder problem is discussed and the results of the present theory are found to agree with those obtained by Lauvstad using a matched asymptotic expansion for the same problem. The theory is used to predict the temperature dependence of sound power for hot jets.Consultant for Bolt Beranek and Newman, Inc.     

On mass-shell renormalizability of the massive Yang-Mills theory

Renormalizable theory of electroweak interactions without scalar particles can be constructed by the modifying the Standard Model. One should remove all terms with the scalar field from the Lagrangian in the unitary gauge. The resulting electroweak theory without the Higgs particle is on mass-shell renormalizable and unitary. Thus the experimental non-observation of the Higgs boson will not mean a problem for the concept of renormalizability in quantum field theory but will confirm the scalar free theory.     

The Observer in the Quantum Experiment

A goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. Such intrusion is usually seen to arise because observation somehow selects a single actuality from among the many possibilities represented by the wavefunction. The issue is typically treated in terms of the mathematical formulation of the quantum theory. We attempt to address a different manifestation of the quantum measurement problem in a theory-neutral manner. With a version of the two-slit experiment, we demonstrate that an enigma arises directly from the results of experiments. Assuming that no observable physical phenomena exist beyond those predicted by the theory, we argue that no interpretation of the quantum theory can avoid a measurement problem involving the observer.     

基于不动点理论的多系统兼容接收机频点选择问题的研究与遗传算法实现

基于不动点理论研究了多系统兼容接收机的频点选择问题,并引入遗传算法解决了这一问题.将Banach不动点理论引入频点空间,提出并证明了频点空间中频点集的遗传进化过程反映了频点空间呈现出的一种不动点物理特性;经过频点空间算子的足够多次的反复遗传进化作用,频点空间中的任一迭代序列源频点集都将最终收敛于唯一不动点目标频点集,而该不动点目标频点集中的目标频点即为该频点选择问题的最优解.完成了遗传算法应用于频点选择问题的理论研究与实现.仿真结果表明,该算法能够有效地解决多系统兼容接收机的频点选择问题. 关键词： 多系统 接收机 遗传算法 不动点     

Formalism of symmetrization operators in the theory of self-broadening of spectral lines

The operators that symmetrize many-particle states in accordance with the quantum statistics of particles are introduced to construct the theory of self-broadening of spectral lines. In this case, the self-broadening problem becomes formally similar to the problem of broadening by a foreign gas. Comparison is made with papers of other authors.     

Ultrasonic characterization of human cancellous bone using the Biot theory: inverse problem

This paper concerns the ultrasonic characterization of human cancellous bone samples by solving the inverse problem using experimental transmitted signals. The ultrasonic propagation in cancellous bone is modeled using the Biot theory modified by the Johnson et al. model for viscous exchange between fluid and structure. The sensitivity of the Young modulus and the Poisson ratio of the skeletal frame is studied showing their effect on the fast and slow wave forms. The inverse problem is solved numerically by the least squares method. Five parameters are inverted: the porosity, tortuosity, viscous characteristic length, Young modulus, and Poisson ratio of the skeletal frame. The minimization of the discrepancy between experiment and theory is made in the time domain. The inverse problem is shown to be well posed, and its solution to be unique. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.     

Rosenberg问题的对称性与守恒量

Rosenberg问题是一个典型而不太复杂的非完整系统问题.本文利用非完整系统的Noether对称性理论来求这个非完整力学问题的守恒量,进而得到问题的最终解.     

Quantum model of the Thomson helium atom

A quantum model of the Thomson helium atom is considered within the framework of stationary perturbation theory. It is shown that from a formal point of view this problem is similar to that of two-electron states in a parabolic quantum dot. The ground state energy of the quantum Thomson helium atom is estimated on the basis of Heisenberg’s uncertainty principle. The ground state energies obtained in the first order of perturbation theory and qualitative estimate provide, respectively, upper and lower estimates of eigenvalues derived by numerically solving the problem for a quantum model. The conditions under which the Kohn theorem holds in this system, when the values of resonance absorption frequencies are independent of the Coulomb interaction between electrons, are discussed.     

Four contemporary interpretations of the nature of science

Instrumentalism is an approach to science that treats a theory as a tool and only as a tool for computation; it dispenses with the concept of truth.Conventionalism treats a theory as true by convention if it forms a pattern of observations from which correct predictions can be made.Operationalism denies meaning to the concepts of a theory unless they can be defined operationally. It is argued in this paper that truth-value is indispensable to science, because a theory can be rejected only if an empirical consequence is false and if falsity of a conclusion entails falsity of a premise. This undermines the above positions. The fourth interpretation isinduction. Induction, by contrast, uses the notion of truth-value. What is focused on here is its reliance on the ultimacy ofobservation. The present thesis is that instrumentalism, conventionalism, and induction are different attempts to handle observations. The common problem is the gap between data and theory.All these interpretations share a philosophy of observationalism. The aim of this paper is to show that the several orthodox interpretations of science all fail to solve the problem of the data-theory gap, and to show that they all presuppose a philosophy of observation.     

Modern aspects of the asymptotic theory for wave radiative transfer in disordered media

Two modern problems of the theory of multiple scattering of electromagnetic wave radiation in discrete randomly inhomogeneous media are discussed. One problem is related to the effective magnetic permeability of a statistical assembly of nonmagnetic conducting particles; the other problem is focused on the regard for the near-field effects of scatterers in the radiative transfer theory.