Cartan–Weyl Dirac and Laplacian Operators,Brownian Motions: The Quantum Potential and Scalar Curvature,Maxwell’s and Dirac-Hestenes Equations,and Supersymmetric Systems

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q     

Standing Waves in the Lorentz-Covariant World

When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some nderstanding of plane waves or running waves in the covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincaré group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman’s parton model hadrons moving with a speed close to that of light.     

On the linearized relativistic Boltzmann equation. II. Existence of hydrodynamics

Solutions are analyzed of the linearized relativistic Boltzmann equation for initial data fromL ²(r, p) in long-time and/or small-mean-free-path limits. In both limits solutions of this equation converge to approximate ones constructed with solutions of the set of differential equations called the equations of relativistic hydrodynamics.     

六聚吡咯大环与铀/超铀酰基离子相互作用:成键、热力学和光谱性质

采用全电子相对论密度泛函理论探索多种六聚吡咯大环锕酰基配合物(nAn;n=1~3;An=U,Np and Pu)的电子结构本质、成键规律和化学反应特性。结构优化发现大环配体空穴大小与锕酰离子尺寸相当时,配合物锕酰基采用性对规则的六角双锥结构,而当空穴尺寸相对大时,配合物则采取扭曲结构以降低体系能量。当配体相同时,随着铀、镎、钚变化,An=O伸缩振动频率逐渐变小,这与优化的键长和键级变化规律相一致。QTAIM(quantum theory of atoms in molecule)拓扑分析显示An-N为弱共价单键特征,具有较大离子性成分。依据不同铀源,得到与大环配体的反应自由能均小于146 kJ·mol~(-1),与实验合成配合物的反应能计算数值相当。对含铀配合物电子吸收光谱计算显示,低能(近红外和可见光区)的吸收带具有全部或较大的配体→金属电荷转移性质贡献。     

A superatomic molecule under the spin‐orbit coupling: Insights from the electronic properties in the thiolate‐protected Au38(SR)24 cluster

The role of the spin‐orbit coupling in Au₃₈(SR)₂₄, as a representative case for a superatomic molecules is studied to offer a complete view of the relativistic effect in heavy elements clusters. Its core can be described in as an analog to a diatomic molecule, such as F₂, allowing the electronic structure to be depicted in terms of the D_∞h point group. First, we showed the electronic structure under the spin‐orbit framework using total angular momentum representations ( j = ℓ ± s ; spinors), which allows us to characterize the expected splitting of certain levels derived from the cluster core. Accordingly, the optical properties are evaluated under spin‐orbit coupling regime, revealing differences in the low‐energy region of the absorption spectrum. Lastly, the variation of electron affinity (EA) and ionization potential (IP) properties is evaluated. This reveals characteristic consequences of the inclusion of spin‐orbit coupling in Au₃₈(SR)₂₄, as a bridge to larger thiolate‐protected gold clusters.     

自由电子激光的空间电荷波理论

发展了相对论空间电荷波理论,并首先把空间电荷波理论用于建立自由电子激光的线性理论,揭示出自由电子激光中电子群聚及电子与波互作用机理的物理本质。并首次提出了“相对论去群聚”的物理概念,丰富了自由电子激光理论。同时提出了一些发展自由电子激光的新概念及新建议。     

电子传导不透明度计算

基于含温有界相对论Dirac自洽场原子模型,采用电子-离子散射机制,在Born近似下,计算了部分离化等离子体物质的电子传导不透明度(Electron Conductive Opacity)。以铯(Cs)为例,同他人结果作了比较,给出钛(Ti)元素温度kT=10～10~3eV,密度ρ=0.1ρ_0～10ρ_0范围的电子传导不透明度K_C。     

Particles and “bumps” in quantum field configurations

We study an approach to making a precise identification of particles with bumps in quantum field configurations. The problem requires some effort because typical field configurations are distributions and not elements of the classical configuration space at all. We show that the part of a configuration consisting of vacuum fluctuations may be identified and filtered out in a very natural way, leaving a function which is in the classical configuration space. The filtered field configuration depends on the state of the field, and for ann-particle state withn particles well localized and well separated in the Newton-Wigner sense, the filtered field configuration hasn bumps located where the particles are. We close with a discussion of observation in the Schrödinger representation for the free field in terms of our results.This paper is dedicated to the memory of Paola Calderoni.     

Theoretical study in [C2H4–Tl]+ and [C2H2–Tl]+ complexes

We studied the attraction between [C₂H_n] and Tl(I) in the hypothetical [C₂H_n–Tl]⁺ complexes (n = 2,4) using ab initio methodology. We found that the changes around the equilibrium distance C–Tl and in the interaction energies are sensitive to the electron correlation potential. We evaluated these effects using several levels of theory, including Hartree–Fock (HF), second‐order Møller–Plesset (MP2), MP4, coupled cluster singles and doubles CCSD(T), and local density approximation augmented by nonlocal corrections for exchange and correlation due to Becke and Perdew (LDA/BP). The obtained interaction energies differences at the equilibrium distance R_e (C–Tl) range from 33 and 46 kJ/mol at the different levels used. These results indicate that the interaction between olefinic systems and Tl(I) are a real minimum on the potential energy surfaces (PES). We can predict that these new complexes are viable for synthesizing. At long distances, the behavior of the [C₂H_n]–Tl⁺ interaction may be related mainly to charge‐induced dipole and dispersion terms, both involving the individual properties of the olefinic π‐system and thallium ion. However, the charge‐induced dipole term (R^?4) is found as the principal contribution in the stability at long and short distances. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

CH_2=CH(XM)(X=S,Se,Te;M=H,Li,Na,K,Rb,Cs,-)的从头算研究

应用相对论有效势在ＭＰ２水平上对ＣＨ２ＣＨ（ＸＭ）（Ｘ＝Ｓ，Ｓｅ，Ｔｅ；Ｍ＝Ｈ，Ｌｉ，Ｎａ，Ｋ，Ｒｂ，Ｃｓ，－）进行了从头计算研究．结果表明，所研究的化合物都有平面式和非平面桥式两种构型．分析了碱金属离子对两可亲核底物ＣＨ２ＣＨＸ－（Ｘ＝Ｓ，Ｓｅ，Ｔｅ）离域化的影响，并用自然布局分析方法（ＮＰＡ）研究了电荷分布的变化，得出了有价值的结论．