Massive gravity as a quantum gauge theory

We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F⁺ (H_graviton) where the one-particle Hilbert space H_graviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space H_graviton generated by the gravitational field h and some ghosts fields u, (which are vector Fermi fields) and v (which is a vector Bose field).Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theory.     

Affine connection in Hilbert space

A concise geometrodynamic approach to quantum theory is introduced, via a quo;quantum connectionQ _µ , which is the affine connection in Hilbert space. It is emphasized that this is the simplest and most natural interpretation of quantum mechanics in general relativity and yet has been largely neglected, so that much work remains to be done on it. The generalized Hilbert space has a simple Hermitian metric, but the precise form ofQ _µ remains to be determined. The quantum connection is matheamtically analogous to the spinor connection, which is discussed here for that reason, although the spinor connection arises in the first quantization, whereasQ _µ geometrizes the second quantization.     

On the renormalization of the quantum field theory of point-like monopoles and charges

The quantum field theory of point-like monopoles and charges is first formulated on a euclidean lattice for a convenient regularization. The regularization preserves the peculiar features of the theory, namely those related to the invariance and to the quantization condition. The partition function is expressed as a path integral over the particle's closed paths and the action is constructed in terms of arbitrary surfaces having those paths as boundaries. The possible divergences of the continuum limit are discussed, in particular the vacuum polarization ones. It is found that, although both the electric charge Q and the magnetic charge G are renormalized as Q = Z_QQ_R and G = Z_GG_R, the quantization condition is preserved by the renormalization i.e. Z_QZ_G = 1 so that QG = Q_RG_R = 2πn. Due to the dual symmetry of the theory, then, for Q = G we get Z_Q = Z_G = 1.     

All Stable Characteristic Classes of Homological Vector Fields

An odd vector field Q on a supermanifold M is called homological, if Q ² = 0. The operator of Lie derivative L _Q makes the algebra of smooth tensor fields on M into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator L _Q and are represented by Q-invariant tensors made up of the homological vector field and a symmetric connection on M by means of the algebraic tensor operations and covariant differentiation.     

The argon nuclear quadrupole moments

New standard values -116(2) mb and 76(3) mb are suggested for the nuclear quadrupole moments (Q) of the ³⁹Ar and ³⁷Ar nuclei, respectively. The Q values were obtained by combining optical measurements of the quadrupole coupling constant (B or eqQ/h) of the 3s²3p⁵4s[3/2]₂ (³P^o) and 3s²3p⁵4p[5/2]₃ (³D^e) states of argon with large scale numerical complete active space self-consistent field and restricted active space self-consistent field calculations of the electric field gradient at the nucleus (q) using the LUCAS code, which is a finite-element based multiconfiguration Hartree–Fock program for atomic structure calculations.     

Q 2 dependence of the measured asymmetry A 1: A test of the Bjorken sum rule

We analyze the proton and deutron data on the spin-dependent asymmetry A ₁(x, Q ²), supposing that the DIS structure functions g ₁(x, Q ²) and F ₃(x, Q ²) have a similar Q ² dependence. As a result, we have found that Λ ₁ ^p −Λ ₁ ⁿ =0.190±0.038 at Q ²=10 GeV² and Λ ₁ ^p −Λ ₁ ⁿ =0.165±0.026 at Q ²=3 GeV²; these values are in the best agreement with the Bjorken sum rule predictions. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 9–14 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Peierls Instability for the Holstein Model with Rational Density

We consider the static Holstein model, describing a chain of fermions interacting with a classical phonon field, when the interaction is weak and the density is a rational number p = P/Q, with P, Q relative prime integers. We show that the energy of the system, as a function of the phonon field, has one (if Q is even) or two (if Q is odd) stationary points, defined up to a lattice translation, which are local minima in the space of fields periodic with period equal to the inverse of the density.     

相干态在参数量子相空间的两维正态分布

把量子力学与数理统计的正态分布联系起来进行初步的尝试.用数理统计的观点和有序算符内的积分技术研究相干态,指出在依赖一个实参数k的量子化方案中,相干态|z??z|在相空间呈现出以(q,p)为随机变量的两维正态分布,z=(q+ip)/√2.两个随机变量的相关系数为ik.在k=±1的参数相空间中,|z??z|分别表现出P排序(P在Q左)和Q排序的形式(Q在P左),而在k=0的参数相空间中,|z??z|表现出Weyl排序的形式.在P排序和Q排序的情况下,量子算符|z??z||z=(q+ip)/√2的经典对应函数中随机变量(q,p)是关联的,只有在Weyl对应时,随机变量(q,p)是独立的.也就是说,算符的Weyl排序有利于其经典对应的随机变量解脱关联.     

Implications of the JLab proton polarization data for the behavior of strange nucleon form factors

A special eight-resonance unitary and analytic model of nucleon electromagnetic structure is used to analyze first the classical proton form factor data obtained by the Rosenbluth technique, and then also the contradictory JLab proton polarization data on the ratio μ_p G _Ep(Q ²)/G _Mp(Q ²) , with the aim to investigate the implications of the latter for the behavior of strange nucleon form factors.     

A new approach to calculate the gluon polarization

We derive the Leading-Order (LO) master equation to extract the polarized gluon distribution G(x,Q ²)=xδg(x,Q ²) from polarized proton structure function, g^p₁(x,Q²)g^{p}_{1}(x,Q^{2}). By using a Laplace-transform technique, we solve the master equation and derive the polarized gluon distribution inside the proton. The test of accuracy which is based in our calculations on two different methods, confirms that we achieve to the correct solution for the polarized gluon distribution. To determine the polarized gluon distribution xδg(x,Q ²) more accurately, we only need to have more experimental data on the polarized structure functions, g₁^p(x,Q²)g_{1}^{p}(x,Q^{2}). Our result for polarized gluon distribution is in good agreement with some phenomenological models.     

Surface quantization effect on the macroscopic characteristics of semiconductor space-charge layers

A numerical study of the dependence of the space-charge density Q_sc on the surface potential Ψ_s in a two-dimensional electron inversion layer on Si(100) is presented. The dependence Q_sc(Ψ)_s being a macroscopic characteristic of semiconductor space-charge layers is found to be considerably influenced by the surface quantization in a wide temperature range up to room temperature. The conditions for the appearance of appreciable differences in the behaviour of the Q_sc(Ψ)_s curves in the quantum-mechanical and quasi-classical cases are determined and discussed.     

Expanding color flux tubes and instabilities

We present an analytic study of the physics of the glasma which is a strong classical gluon field created at early stage of high-energy heavy-ion collisions. Our analysis is based on the picture that the glasma just after the collision is made of color electric and magnetic flux tubes extending in the longitudinal direction with their diameters of the order of 1/Q_s (Q_s is the saturation scale of the colliding nuclei). We find that both the electric and magnetic flux tubes expand outwards and the field strength inside the flux tube decays rapidly in time. Next we investigate whether there exist instabilities against small rapidity-dependent perturbations for a fixed color configuration. We find that the magnetic background field exhibits an instability induced by the fluctuations in the lowest Landau level, and it grows exponentially in the time scale of 1/Q_s. For the electric background field we find no apparent instability while the possible relation to the Schwinger mechanism for particle pair creations is suggested.     

Virtuality evolution and rapidity structure of a simplified parton shower

We have studied transverse momentum distributions for exclusive ⁰ muoproduction on protons and heavier nuclei at 2Q ²<25>². TheQ ² dependence of the slopes of thep _t ² andt distributions is discussed. The influence of the non-exclusive background is investigated. Thep _t ² -slope for exclusive events is 4.3±0.6±0.7 GeV^–2 at largeQ ². Thep _t ² spectra are much softer than inclusivep _t ² spectra of leading hadrons produced in deep inelastic scattering.Supported by Bundesministerium für Forschung und Technologie     

The BFKL-Regge phenomenology of deep inelastic scattering

We calculate the Regge trajectories of the subleading BFKL singularities and eigenfunctions for the running BFKL pomeron in the color dipole representation. We obtain a viable BFKL-Regge expansion of the proton structure function F _2p (x,Q ²) in terms of several rightmost BFKL singularities. We find large subleading contributions to F _2p (x,Q ²) in the HERA kinematical region which explain the lack of predictive power of GLDAP extrapolations of F _2p (x,Q ²) to the region of small x. We point out the relation of our early finding of precocious BFKL asymptotic behavior to the nodal structure of subleading BFKL eigenfunctions. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 134–138 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit     

Minimum-wear characteristics for boundary friction between solids

A new parameter is proposed for characterizing boundary friction between solids—the probability Q that some contact spot will be converted to a wear particle as the real contact area shifts by one mean contact-spot diameter. A method is proposed for the phenomenological detection of optimum regimes of boundary friction, which are characterized by the minimum wear intensity of the sample material, and for measuring the corresponding quantity Q=Q ^opt. For babbitt, one of the most frictionless materials, the value of Q ^opt is found to be ≈2×10⁻¹⁰. When data on the linear wear intensity I _h , the contact pressure p _n , and the hardness H are available, Q can be calculated for the given test conditions. Deviations of Q from the value Q ^opt (for a given material) can serve as a criterion for how closely a prepared surface structure approaches the optimal. Zh. Tekh. Fiz. 68, 48–52 (April 1998)     

再论时域的量子化及其物理本质

本文在提出时域吸收过程、时域辐射过程和时域无辐射跃迁过程等概念的基础上,进一步揭示出时域量子化的本质含义.对时间不可逆性问题进行了详细论证,并在给出“时间量子”t与光子能量ε_t之间的关系式t=h/ε_t(式中h为普朗克常量)的同时,进一步提出了时域量子化的新观点.利用t=h/ε_t这一关系对超快科学研究领域中的新时间尺度(诸如超短激光脉冲的脉宽压缩、阿秒界限的突破等)问题进行了详细讨论.最后,在对时空对称性以及时空对称结构等问题进行详细分析的基础上,进一步提出了量子时空观和量子化时空结构的基本观点.     

用超短光脉冲简并四波混频测量介质弛豫率的研究

本文讨论用ps光脉冲简并四波混频测量非线性介质弛豫率和在适度或强的相位调制情况下测量激光脉冲宽度的方法,通过用计算机模拟及与实验结果比较,得出结论:对t_p>>τ_r和t_p<<τ_r两种极限情况,该方法是足够精确的.对τ_r/t_p的中间情况,该方法只能给出一个估计.     

Quenching Evolution in a Quantum-Classical Hybrid System

The adiabatic theorem, an important theory in quantum mechanics, tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In this paper, we study the quench evolution that is another extreme circumstance where the external conditions vary rapidly such that the quantum system can not follow the change and remains in its initial state (or wavefunction). We examine the matter-wave pressure and derive the requirement for such an evolution. The study is conducted by considering a quantum particle in an infinitely deep potential, the potential width Q is assumed to be change rapidly. We show that the total energy of the quantum subsystem decreases as Q increases, and this rapidly change exerts a force on the wall which plays the role of boundary of the potential. For Q < Q₀ (Q₀ is the initial width of the potential), the force is repulsive, and for Q > Q₀, the force is positive. The condition for the quenching evolution evolution is given via a spin-\( \frac{1}{2} \) in a rotating magnetic field.

     

The Stark effect in molecules with strong nuclear quadrupole coupling

The Hamiltonian for a rotating molecule containing one nuclear quadrupole in a uniform electric field is H ₀ + H_E + H_Q , where H ₀ describes the unperturbed rotator, H_E the interaction with the electric field and H_Q the coupling of the nuclear quadrupole to the rotating molecule. The energy is evaluated, up to and including terms in H_EH_Q in symmetric tops in which the quadrupolar nucleus is on the axis, and H_E ² H_Q in linear molecules, by treating H_E and H_Q as perturbations to H ₀. Dipole moments determined through studies of the Stark effect in microwave spectra can be significantly affected by the higher-order terms, even in weak electric fields, if the nuclear quadrupole coupling energy is not small relative to the separation of the rotational energy levels.

Dipole moments determined from Stark splittings of the J = 2←J = 1 lines are reduced by approximately 1 per cent in AsF₃ and from 1·647 to 1·618D in CH₃I.