Conformal invariance and conserved quantities of a general holonomic system with variable mass

Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal one-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.     

Unified Free Quantum Fields for Massive and for Massless Particles

For any mass m ≧ 0 and arbitrary spin, free relativistic quantum fields are constructed using the same formulas for m > 0 and for m = 0. The transformation properties of these fields under P, C, T and some questions concerning super-selection rules are discussed.     

Statistical Mechanics in Collective Coordinates

We study the transformation of the statistical mechanics of N particles to the statistical mechanics of fields, that are the collective coordinates, describing the system. We give an explicit expression for the functional Fourier transform of the Jacobian of the transformation from particle to collective coordinate and derive the Fokker–Planck equation in terms of the collective coordinates. Simple approximations, leading to Debye–Huckel theory and to the hard sphere Percus–Yevick equation are discussed.     

New Concepts from the Evans Unified Field Theory. Part One: The Evolution of Curvature,Oscillatory Universe Without Singularity,Causal Quantum Mechanics,and General Force and Field Equations

No Heading The Evans field equation is solved to give the equations governing the evolution of scalar curvature R and contracted energy-momentum T. These equations show that R and T are always analytical, oscillatory, functions without singularity and apply to all radiated and matter fields from the sub-atomic to the cosmological level. One of the implications is that all radiated and matter fields are both causal and quantized, contrary to the Heisenberg uncertainty principle. The wave equations governing this quantization are deduced from the Evans field equation. Another is that the universe is oscillatory without singularity, contrary to contemporary opinion based on singularity theorems. The Evans field equation is more fundamental than, and leads to, the Einstein field equation as a particular example, and so modifies and generalizes the contemporary Big Bang model. The general force and conservation equations of radiated and matter fields are deduced systematically from the Evans field equation. These include the field equations of electrodynamics, dark matter, and the unified or hybrid field.     

Quantum Noether identities for non-local transformationsin higher-order derivatives theories

Based on the phase-space generating functional of the Green function for a system with a regular/singular higher-order Lagrangian, the quantum canonical Noether identities (NIs) under a local and non-local transformation in phase space have been deduced, respectively. For a singular higher-order Lagrangian, one must use an effective canonical action I_eff^P in quantum canonical NIs instead of the classical I^P in classical canonical NIs. The quantum NIs under a local and non-local transformation in configuration space for a gauge-invariant system with a higher-order Lagrangian have also been derived. The above results hold true whether or not the Jacobian of the transformation is equal to unity or not. It has been pointed out that in certain cases the quantum NIs may be converted to conservation laws at the quantum level. This algorithm to derive the quantum conservation laws is significantly different from the quantum first Noether theorem. The applications of our formulation to the Yang-Mills fields and non-Abelian Chern-Simons (CS) theories with higher-order derivatives are given, and the conserved quantities at the quantum level for local and non-local transformations are found, respectively.Received: 12 February 2002, Revised: 16 June 2003, Published online: 25 August 2003Z.-P. Li: Corresponding authorAddress for correspondence: Department of Applied Physics, Beijing Polytechnic University, Beijing 100022, P.R. China     

A dynamical approach to the information content of collinear inelastic scattering

The information content of collinear inelastic scattering is discussed in terms of (a) the nature of the classical transformation in internal angle-action space induced by the collision, (b) the number of parameters required to characterize the transformation, and (c) the number and choice of trajectories required to determine the parameters. The constraints of time reversal symmetry, energy and flux conservation are embodied in the transformation equations. In a model application the full S matrix is successfully estimated in terms of a single information parameter deduced from knowledge of the purely elastic scattering trajectories.     

Two-field coset space realization of the spin-4 current algebra

A two-field realization of the spin-4 current algebra is obtained through the coset space approach. The transformation properties of these two fields are also deduced through the composition law, which turns out to be a simple generalization of the corresponding diffeomorphic transformation.     

Material parameter equation for rotating elliptical spherical cloaks

By using the coordinate transformation method, we have deduced the material parameter equation for rotating elliptical spherical cloaks and carried out simulation as well. The results indicate that the rotating elliptical spherical cloaking shell, which is made of meta-materials whose permittivity and permeability are governed by the equation deduced in this paper, can achieve perfect invisibility by excluding electromagnetic fields from the internal region without disturbing any external field.     

Analytic expression for the magnetization curve and hysteresis loop

In a real ferromagnet there are a large number of domains differing greatly in energy, so that a domain energy distribution can be introduced. The nonvanishing initial permeability and saturation on the magnetization curve allow an analytic expression to be found for this function and thus for the magnetization curve. Taking the domain interaction into account by introducing a starting field allows the B(H) dependence found to be generalized to weak fields. Analysis of ideal magnetization curves shows that the superposition on a constant field of varying fields having nonvanishing amplitudes reduces the starting field to zero, i.e., removes the magnetic interaction. The B, H plane can be thought of as a complex plane, each point of which is associated with some state of the ferromagnet. A transformation is made from the magnetization curve to the remagnetization curve by a linear transformation of this complex point. In this manner, a transformation can be made from the B(H) dependence found for weak fields to an analytic expression for the hysteresis loop in the same field range.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 59–62, November, 1970.     

Scaling for the discrete Mathieu equation

The scaling of the total width of the band for the discrete Mathieu equation is studied in the critical region near the transition between localized and extended states, for the special case in which there is one period of the modulation forp lattice spacings. A general expression for the bandwidthW in the critical region is found. At the critical point an analytic expression forpW is found which agrees to one part in 10⁸ with the result deduced from numerical work.     

Energy of free and bound excitons in GaAs in a magnetic field

We have measured in photoluminescence the energy shift of free, weakly and tightly bound excitons in high purity GaAs in magnetic fields up to 12T. In the weak binding limit we find a surprising result: the mass obtained from the magnetic shift is the electron-heavy hole reduced mass in contrast to the results obtained from k · p calculation in zincblende type semiconductors in zero magnetic field. In the tight binding limit the mass deduced from the magnetic shift is the effective electron mass.     

Radiation Reaction of the Classical Off-Shell Relativistic Charged Particle

It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham–Lorentz–Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields of the 0, 1, 2, 3 components correspond to the Maxwell fields). Without additional constraints, the particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous non-linear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that mass-shell deviation is bounded when the external field is removed.     

A New Variational Principle for the Fundamental Equations of Classical Physics

In this paper we introduce a variational principle from which the fundamental equations of classical physics can be deduced. This principle permits a sort of unification of the gravitational and the electromagnetic fields. The basic point of this variational principle is that the world-line of a material point is parametrized by a parameter a which carries some physical information, namely it is related to the rest mass and to the charge. In particular, the (inertial) rest mass will not be a property of a material point, but it will be a constant of the motion which is determined by the initial conditions. In this framework the equality between the inertial and gravitational mass can be deduced.     

Dendrimer-magnetic nanostructure: a Monte Carlo simulation

In this paper, the magnetic properties of ternary mixed spins (σ,S,q) Ising model on a dendrimer nanostructure are studied using Monte Carlo simulations. The ground state phase diagrams of dendrimer nanostructure with ternary mixed spins σ = 1/2, S = 1 and q = 3/2 Ising model are found. The variation of the thermal total and partial magnetizations with the different exchange interactions, the external magnetic fields and the crystal fields have been also studied. The reduced critical temperatures have been deduced. The magnetic hysteresis cycles have been discussed. In particular, the corresponding magnetic coercive filed values have been deduced. The multiples hysteresis cycles are found. The dendrimer nanostructure has several applications in the medicine.     

A dilemma in the physics of gravitational fields

It is shown that improper use of local quantities for nonlocal situations in fields leads to traditional errors. Nonlocal theoretical quantities referred to standards in a fixed field are defined in order to obtain reliable results. Nonlocal properties of gravitational fields and matter located in it are deduced with the help of physical principles and an electromagnetic model for matter. In spite of the fact that the local velocity of light should be constant, the field is a space of variable nonlocal velocity of light, which accounts for its properties. Matter and light virtually propagate themselves without exchanging energy with the external field, in disagreement with traditional assumptions. Matter becomes contracted by the field. The results are self-consistent and consistent with the observed facts. Bodies withr2GM would be different from black holes and they may account for the peak of highest energy of cosmic radiation and other astronomical facts.     

Gravimagnetism,causality, and aberration of gravity in the gravitational light-ray deflection experiments

Experimental verification of the existence of gravimagnetic fields generated by currents of matter is important for a complete understanding and formulation of gravitational physics. Although the rotational (intrinsic) gravimagnetic field has been extensively studied and is now being measured by the Gravity Probe B, the extrinsic gravimagnetic field generated by the translational current of matter is less well studied. The present paper uses the post-Newtonian parametrized Einstein and light geodesics equations to show that the extrinsic gravimagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay and/or light deflection caused by the moving mass. We prove that the extrinsic gravimagnetic field is generated by the relativistic effect of the aberration of the gravity force caused by the Lorentz transformation of the metric tensor and the Levi–Civita connection. We show that the Lorentz transformation of the gravity field variables is equivalent to the technique of the retarded Lienard–Wiechert gravitational potentials predicting that a light particle is deflected by gravitational field of a moving body from its retarded position so that both general-relativistic phenomena—the aberration and the retardation of gravity—are tightly connected and observing the aberration of gravity proves that gravity has a causal nature. We explain in this framework the 2002 deflection experiment of a quasar by Jupiter where the aberration of gravity from its orbital motion was measured with accuracy 20%. We describe a theory of VLBI experiment to measure the gravitational deflection of radio waves from a quasar by the Sun, as viewed by a moving observer from the geocentric frame, to improve the measurement accuracy of the aberration of gravity to a few percent.     

高阶微商场论中奇异拉氏量系统的量子正则对称性

给出了高阶徽商场论中奇异拉氏量系统规范生成元的构成.从相空间中Green函数的生成泛函出发,导出了约束Hamilton系统正则形式的Ward恒等式.指出该系统的量子正则方程与由Dirac猜想得到的经典正则方程不同.给出了与Chern-Simons理论等价的一个广义动力学系统的量子化.将正则Ward恒等式初步应用于该系统,不作出对正则动量的路径积分,也可导出场的传播子与正规顶角之间的某些关系.     

Local Fields Without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. One may assume the existence of such fields only if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT-invariance. Restrictions on mass-spectrum of CPT-violating fields are found. Local fields that annihilate vacuum state and violate CPT-invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particularly needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed.     

Gravitationally stabilized nucleons in the theory of the generalized gravitational potential

From the field equation in of the author's general-relativistic scalar field theory in the complex Weyl space an infinite set of Yukawa type equations, representing potential fields, arising from zero rest mass particles is obtained. The simplest of these equations is solved and is used in a nucleon model as the origin of a gravitationally stabilized nucleon. This procedure leads directly to an expression that predicts the representative nucleon radius of 1.21 fm.