Direct calculation of ionization energies

The advantages of the propagator formalism, as a direct method of calculating ionization energies, are stressed. The propagator equations are derived for closed-shell systems using an operator method instead of the usual diagrammatic derivations. The equations enable the development of an interpretation of the ionization energies in terms of conceptually simple quantities, such as pair correlation energies and associated relaxation effects, and retain the idea of orbital ionization. Infinite summations appearing in the self-energy terms are replaced by finite expressions involving functions satisfying uncoupled inhomogeneous differential equations. Certain high-order propagator equations are derived, and a connection with the Bethe-Goldstone formulation of pair correlation is made. Several computational procedures are advocated as forming the basis for balanced calculations of atomic and molecular ionization energies.     

高频波激发低频磁场和离子声波的重整化强湍动理论

本文给出了高温等离子体中高频波激发低频磁场和离子声波强湍动过程的重整化理论,以便改善通常的弱非线性处理方法,从Vlasov-Maxwell方程组出发,在Fourier表象中得到了包含“最发散”和“次发散”效应互相耦合的高频和低频传播于重整化方程组,从而获得了高、低频振荡粒子重整化分布函数和场的耦合关系。在“最发散”重整化近似下,我们求解了高低频传播子方程组,得到了展开到v₄(高频湍动场能密度与等离子体热能密度之比)一次方的近似解和重整化介电函数等表达式。然后,在Fourier逆变换下导得了我们所要的时空表用中重整化强湍动方程组。最后,作为一个说明重整化作用的例子,在一维稳态下求解了孤立子的形式。 关键词：     

Lie algebraic approach for Fokker-Planck dynamics with space-dependent diffusion and mean-reverting drift

Using the Lie algebraic approach we have derived the exact diffusion propagator of the Fokker-Planck equation with a time-dependent variable diffusion coefficient and a time-dependent mean-reverting force between two absorbing boundaries. The exact diffusion propagator not only enables us to study the time evolution of the corresponding stochastic system, but the knowledge of the propagator can also provide a benchmark for testing approximate numerical or analytical procedures. Furthermore, the Lie algebraic method is very simple and could be easily extended to the more general Fokker-Planck equations with well-defined algebraic structures. Received 18 December 2002 / Received in final form 3 March 2003 Published online 24 April 2003     

Functional integral formulation of classical wave equations

It is shown in this paper that classical wave equations admit path integral formulations. For this, the evolution of the system is first set-up in terms of a fundamental solution or propagator. We choose this last name because it suggests a connection with functional integrals, which are exploited in this work. A functional integral in terms of non-singular functions is then proposed and shown to converge to the propagator in the appropriate limit for the case of scalar wave equations. One of the advantages of such formulation is that it provides an adequate framework for mesh-free numerical methods. This is demonstrated through a computational implementation that combines a simple second-degree polynomial local approximation of the continuous field and an approximate statement of the exact evolution equations. Numerical simulations of modal analysis and transient dynamics indicate the feasibility of the technique.     

Renormalization of QED in an external field

The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these equations are given in terms of appropriate Feynman diagrams. The Green function that is used as an electron propagator in each case is discussed in detail. The general renormalization rules for each of the three equations are provided both in a non perturbative way (Dyson relations) and for Feynman diagrams.     

Projection Operator and Feynman Propagator for a Free MassiVe Particle of Arbitrary Spin

Based on the solution to the Bargmann-Wigner equations, a direct derivation of the projection operator and Feynman propagator for a free massive particle of arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin, the general commutation rules and Feynman propagator with additional non-covariant terms for a free massive particle with any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, and 4 are provided.     

Free vibration of three-dimensional anisotropic layered composite nanoplates based on modified couple-stress theory

Based on the modified couple-stress theory, three-dimensional analytical solutions of free vibration of a simply supported, multilayered and anisotropic composite nanoplate are derived by solving an eigenvalue system and using the propagator matrix method. By expanding the solutions of the extended displacements in terms of two-dimensional Fourier series, the final governing equations of motion with modified couple-stress effect are reduced to an eigenvalue system of ordinary differential equations. Analytical expressions for the natural frequencies and mode shapes of multilayered anisotropic composite plates with modified couple-stress effect are then derived via the propagator matrix method. Numerical examples are carried out for homogeneous thick-plates and sandwich composite plates to show the effect of the non-local parameter in different layers and stacking sequence on the mode shapes. The present solutions can serve as benchmarks to various thick-plate theories and numerical methods, and could be further useful for designing layered composite structures involving small scale.     

Intermediate Range Force Contributions to Dynamical Chiral Symmetry Breaking in QCD

We propoee the intermediate range QCD force singular like δ(q) by analysing the gluon propagator in the nonperturbative region from QCD sum rules. With the help of the Slavnov- Taylor-Ward identity we derive the equations for the nonperturbative quark propagator from the Schwinger-Dyson (SD) equation. Solutione for the quark propagator in two special cases are given. We find that the intermediate range force L also responsible for the chiral symmetry breaking in QCD.     

Nonstationary motion of electrons in a double plasma layer subjected to the self-consistent electric field of the space charge

Nonstationary 1D equations describing the motion of electrons in a double plasma layer subjected to the self-consistent electric field of the space charge are investigated with allowance for friction force. Analytical solutions to a set of nonlinear hydrodynamic equations for plasma electrons are derived. The variation of the electric field strength, as well as of the electron velocity and concentration, in space and time is found. Electron plasma motions of different types of symmetry are characterized in terms of dynamic parameters.     

Renormalization constants and asymptotic behaviour in quantum electrodynamics

Using dimensional regularization, a field theory contains at least one parameter less than usual with the dimension of mass. The Callan-Symanzik equations for the renormalization constants then become solvable entirely in terms of the coefficient functions. Explicit expressions are obtained for all the renormalization constants in quantum electrodynamics. At non-exceptional momenta the infrared behaviour and the three leading terms in the asymptotic expansion of any Green function are controlled by the Callan-Symanzik equations. For the propagators the three leading terms are computed explicitly. The gauge dependence of the asymptotic electron propagator in momentum space is calculated in all orders of perturbation theory.     

Causal green function in relativistic quantum mechanics

The causal Green function or Feynman propagator for the free-field Klein-Gordon equation and related singular functions, defined as distributions, are related to the causal time-boundary data. Probability densities and amplitudes are defined in terms of the solutions of the Klein-Gordon equation for a complex scalar field interacting with an electromagnetic field. The convergence of the perturbation expansion of the solution of the Klein-Gordon equation for a charged scalar particle in an external field is shown for well-behaved electromagnetic potentials. Other relativistic wave equations are discussed briefly.     

On the Summation of Non-leading Logarithms in QCD

Exploiting the relations between the expansion coefficients of Green's functions and those of β and γ functions in massless QFT, the summation up to the n-th non-leading logarithms is reduced to the solution of a system of linear differential equations, which in general differ from renormalization group equations. Applying this procedure to the gluon propagator the leading log approximation is modified near the mass shell by a constant factor only. Furthermore for the gluon propagator exponentiation in terms of the running coupling constant is argued to be restricted to leading logarithms.     

Path Integral Solution for a Dirac Particle in Non-Abelian SU(N) Gauge Field

The propagator of a Dirac particle in interaction with a non-Abelian SU(N) gauge field is determined according to the path integral formalism of Alexandrou et al. by using the representation so called “local projection” and the wave functions are extracted. Furthermore, it is shown that certain selected equations obtained during the integrations can also be classically derived.     

Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime

In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identities. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space.     

Neutrino propagator in matter and its spin properties

The spectral representation for the neutrino propagator in moving matter with a constant density has been derived. It has been found that matter includes a four-dimensional axis of complete polarization and all poles of the propagator are classified in terms of the projection of the spin on this axis.     

Semiclassical propagator of the Wigner function

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.     

Path integration of the harmonic oscillator with a two-time quadratic action

Path integration of the harmonic oscillator with a two-time quadratic action characterizing memory effects is given in terms of the solutions of some integrodifferential equations. The exact propagator in closed form is then obtained for the specific kernel introduced by Feynman in the polaron problem.     

Renormalized Hartree-Fock equations in a nuclear relativistic quantum field theory

Renormalized Hartree-Fock equations are derived for an infinite system of mesons and baryons in the framework of a relativistic quantum field theory. Direct and exchange diagrams in the baryon propagator are summed self-consistently to all orders, and the effects of occupied negative-energy states in the Dirac sea are included. The required counterterm subtractions are defined by conventional renormalization conditions, but they need not be evaluated explicitly. The result is a set of finite nonlinear integral equations for the baryon self-energy that includes vacuum fluctuation effects from virtual N$\text{N}$ pairs in the many-body wavefunction at finite density.     

Exact propagator for an electron in a quadratic saddle-point potential and a magnetic field

We study the propagator for an electron moving in a two-dimensional (2D) quadratic saddle-point potential,in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is derived using the Feynmann path integrals.     

Gauge and Lorentz covariant quark propagator in an arbitrary gluon field

The quark propagator in the presence of an arbitrary gluon field is calculated gauge and Lorentz covariantly order by order in terms of powers of the gluon field and its derivatives. The result is independent of the path connecting the ends of the propagator, and the leading order result coincides with the exact propagator in the trivial case of a vanishing gluon field. Received: 5 February 2003 / Published online: 23 May 2003