Spectral asymmetry of Dirac Hamiltonian in a five-dimensional Kaluza-Klein theory

It is shown that the fermion number in a five-dimensional Kaluza-Klein theory (M⁴×S¹) in which the fermion is interacting with a monopole field, is quantized in units of (ϕR)² where the scalar ϕ is asymptotically constant andR is the radius of S¹.     

Equivalence and hermiticity of Dirac Hamiltonians in the Kerr gravitational field

In the paper, for the Kerr field, we prove that Chandrasekhar's Dirac Hamiltonian and the self‐adjoint Hamiltonian with a flat scalar product of the wave functions are physically equivalent. Operators of transformation of Chandrasekhar's Hamiltonian and wave functions to the η representation with a flat scalar product are defined explicitly. If the domain of the wave functions of Dirac's equation in the Kerr field is bounded by two‐dimensional surfaces of revolution around the z axis, Chandrasekhar's Hamiltonian and the self‐adjoint Hamiltonian in the η representation are Hermitian with equality of the scalar products, .

     

高阶微商系统中正则Ward恒等式和Abel规范理论中动力学质量的产生

基于含复合场的正则Ward恒等式，研究了含高阶微商的Abel理论中动力学规范对称破缺.得到了包括费米子和束缚态的质量谱.讨论了高阶微商项的影响. 关键词： 正则Ward恒等式 约束 动力学对称破缺 Abel规范理论     

Divergence structure of the statistical entropy of the Dirac field in a plane symmetry black hole geometry

The divergences at all levels for the statistical entropy of a plane symmetry black hole arising from the massless Dirac field are considered using the brick-wall model. It is shown that if we ignore the usual contribution from the vacuum surrounding the system, then the statistical entropy consists of two parts: one is the linearly divergent term which has the geometric character, the other consists of two logarithmically divergent terms which are not proportional to the surface area of the horizon. The entropy of the Dirac field on extremal plane symmetry spacetime background has higher divergence than usual.     

Dirac operators in Boson-Fermion Fock spaces and supersymmetric quantum field theory

Infinite dimensional analysis is developed on an abstract Boson-Fermion Fock space. A general class of Dirac operators acting there is introduced and properties of them are investigated. An index theorem for the Dirac operators is established in terms of a path integral on a loop space. It is shown that the abstract formalism presented here gives a mathematical unification for some models of supersymmetric quantum field theory.     

重力场中原子的衍射态及其概率分布

使用量子力学中Feynman的路径积分方法,导出了重力场中原子经单缝、双缝及多缝衍射后的量子态及其概率分布.在一定近似条件下,证明了干涉条纹的移动与重力加速度有关,而条纹间隔与重力加速度无关.     

Mass generation in the aether: Neutrino oscillations and massive gauge fields

Neutrino mixing is studied in an absolute spacetime conception based on a dispersive aether. The effect of the frequency-dependent permeability of the aether on the interference phase of neutrino mass eigenstates is analyzed. Neutrinos are treated as massless Dirac spinors, and mass eigenstates are due to the neutrino permeability of spacetime. The aether can also generate effective gauge masses, resulting in massive dispersion relations preserving the gauge symmetry. The propagators of gauge and spinor fields are derived, illustrating mass generation by isotropic permeability tensors in the aether frame, the rest frame of the cosmic background radiation.     

The physical role of gravitational and gauge degrees of freedom in general relativity – II: Dirac versus Bergmann observables and the objectivity of space-time

This is the second of a couple of papers in which we aim to show the peculiar capability of the Hamiltonian ADM formulation of metric gravity to grasp a series of conceptual and technical problems that appear to have not been directly discussed so far. In this paper we also propose new viewpoints about issues that, being deeply rooted into the foundational level of Einstein theory, seem particularly worth of clarification in connection with the alternative programs of string theory and loop quantum gravity. The achievements of the present work include: (1) the analysis of the so-called Hole phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of spatially non-compact Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the weak ADM energy. It is crucial to our analysis the re-interpretation of active diffeomorphisms as passive and metric-dependent dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (nearly unknown) connection to gauge transformations on-shell; this is expounded in the first paper (gr-qc/0403081); (2) the utilization of the Bergmann-Komar intrinsic pseudo-coordinates, defined as suitable functionals of the Weyl curvature scalars, as tools for a specific gauge-fixing to the super-hamiltonian and super-momentum constraints; (3) the consequent construction of a physical atlas of 4-coordinate systems for the 4-dimensional mathematical manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent Dirac observables). Such construction embodies the physical individuation of the points of space-time as point-events, both in absence and presence of matter, and associates a non-commutative structure to each gauge fixing or 4-dimensional coordinate system; (4) a clarification of the multiple definition given by Peter Bergmann of the concept of (Bergmann) observable in general relativity. This clarification leads to the proposal of a main conjecture asserting the existence of: i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) change in the observable quantities of general relativity; (5) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a standard of space-time more or less like atomic clocks define standards of time. In the end, against the well-known Einstein's assertion according to which general covariance takes away from space and time the last remnant of physical objectivity, we conclude that point-events maintain a peculiar sort of objectivity. Also, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of participating directly in the individuation process, being involved in the determination of the Dirac observables. Finally, some hints following from our approach for the quantum gravity programme are suggested.     

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.     

有重弹性体形变与质量分布规律的简明推导

依据胡克定律与串联弹性体的劲度系数计算公式,直观简便地导出了弹性体在重力场中的形变规律、质量分布规律及其质心位置.     

Density dependence of nucleon radius and mass in the global color symmetry model of QCD with a sophisticated effective gluon propagator

Making use of the global color symmetry model (GCM) at finite chemical potential and with a sophisticated effective gluon propagator, the density dependence of the bag constant, the total energy and the radius of a nucleon in nuclear matter is investigated. A maximal nuclear matter density for the existence of the bag with three quarks confined within is given as about 8 times the normal nuclear matter density. The calculated results indicate that, before the maximal density is reached, the bag constant and the total energy of a nucleon decrease, and the radius of a nucleon increases, with the increasing of the nuclear matter density. As the maximal nuclear matter density is reached, the mass and the bag constant of the nucleon vanish and the radius becomes infinite suddenly. It manifests that a phase transition from nucleons to quarks takes place. Meanwhile, shortening the interaction range among quarks can induce the phase transition to happen easier.     

The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory

We study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, we show that the critical exponentv describing the vanishing of the physical mass at the critical point is equal tov /d_w, whered _w is the Hausdorff dimension of the walk, andv is the exponent describing the vanishing of the energy per unit length of the walk at the critical point. For the case ofO(N) models, we show thatv ₀=, where is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is/v forO(N) models.