Interatomic forces at very short range.
Electronic energy of interacting atoms at short range, noting Hellman-Feynman theorem for electron density in elliptic coordinates
HELLMANN-FEYNMAN THEOREM↗
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The Internuclear Separation Derivatives of the Energy of a Diatomic Molecule
Hellman-Feynman theorem used for internuclear separation derivatives of diatomic molecule energy
NUCLEAR INTERACTION↗
Diffusion as a problem of statistical path.
Feynman space-time path formulation of nonrelativistic quantum mechanics applied to classical diffusion problem
FEYNMAN DIAGRAM↗
Derivation of relations between temperature- perturbed Thomas-Fermi functions.
Temperature perturbation in Thomas-Fermi functions for atom radius as related by Gilvarry to simpler Feynman-Metropolis-Teller case
TEMPERATURE EFFECT↗
Iterated commutators and functions of operators
Feynman formalisms for expressing iterated commutators and functions of operators
Volkin, H. C.↗
Internuclear separation derivatives of the energy of a diatomic molecule.
Higher order derivatives of energy with respect to internuclear separation for diatomic molecules derived from ordinary and integral Hellmann- Feynman theorems
Kim, H.↗
Development and discussion of Pugh's quantum electrodynamics.
Pugh quantum electrodynamics theory development by precise derivation of equation for S matrix, relating Feynman and Pugh vertex terms
Glover, E. M.↗
Self-consistent Green's-function approach to the electron-gas problem
Electron gas problem in metal physics by self consistent Green function formalism, presenting momentum-space Feynman rules and integral equations derivation
Zmuidzinas, J. S.↗
Production cross section of Lee-Wick hypothetical massive electromagnetic bosons by muons at high energies
Production cross section of Lee-Wick hypothetical massive electromagnetic bosons by muons at high energy, giving Feynman diagrams
Linsker, R.↗
A direct particle theory of weak interactions.
A theory of weak interactions is developed in terms of direct particle action. In its simplest form the theory leads to the formulation given by Feynman and Gell-Mann.
Hoyle, F.↗
Cosmic matter-antimatter asymmetry and gravitational force
Cosmic matter-antimatter asymmetry due to the gravitational interaction alone is discussed, considering the gravitational coupling of fermion matter related to the Yang-Mills (1954) gauge symmetry with the unique generalization of the four-dimensional Poincare group. Attention is given to the case of weak static fields which determines the space-time metric where only large source terms are retained. In addition, considering lowest-order Feynman diagrams, there are presented gravitational potential energies between fermions, between antifermions, and between a fermion and an antifermion. It is concluded that the gravitational force between matter is different from that between antimatter; implications from this concerning the evolution of the universe are discussed.
Hsu, J. P.↗
Functional methods for waves in random media
Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media, and a derivation of approximate moment equations from the functional integral representation.
Chow, P. L.↗
Functional methods for waves in random media
Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media; and a derivation of approximate moment equations from the functional integral representation.
Chow, P. L.↗
Description of quantum noise by a Langevin equation
General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.
Metiu, H.↗
Ladder and cross terms in second-order distorted Born approximation
In the strong fluctuation theory for a bounded layer of random discrete scatterers, the second moments of the fields in the second-order distorted Born approximation are obtained for copolarized and cross-polarized fields. The backscattering cross sections per unit area are calculated by including the mutual coherence of the fields due to the coincidental ray paths, and that due to the opposite ray paths, corresponding to the ladder and cross terms in the Feynman diagramatic representation. It is proved that the contributions from ladder and cross terms for the copolarized backscattering cross sections are the same, while the contributions for the cross-polarized backscattering cross sections are of the same order. The bistatic scattering coefficients in the second-order approximation for both the ladder and cross terms are also obtained. The contributions from the cross terms explain the enhancement in the backscattering direction.
Jin, Y. Q.↗
Remote sensing of earth terrain
Progress on the investigation of the anisotropy of the terrain media, such as vegetation canopy and sea ice, and the study of the fluctuation-dissipation theorem in conjunction with the application of strong fluctuation theory for passive remote sensing of snowpacks is reported. The Feynman diagrammatic technique is used to derive the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field for electromagnetic wave propagation and scattering in an anisotropic random medium. With the random permittivity expressed in a general form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation and the ladder approximation to the Bethe-Salpeter equation. The mean dyadic Green's function for a two layer anisotropic random medium with arbitrary three dimensional correlation function was investigated with the zeroth-order solutions to the Dyson equation under the four characteristic waves associated with the coherent vector fields propagating in an anisotropic random medium layer, which are the ordinary and extraordinary waves with upward and downward propagating vectors.
Kong, J. A.↗
Gauge invariant quantum cosmology
The study of boundary conditions, the Hamiltonian constraint, reparameterization-invariance, and quantum dynamics, is presently approached by means of the path-integral quantization of minisuperspace models. The separation of the wave functions for expansion and contraction by the Feynman boundary conditions is such that there can be no interference between them. This is implemented by the choice of a contour in the complex plane, in order to define the phase of the square-root Arnowitt, Deser, and Misner (1960) Hamiltonian for expansion, collapse, and the classically forbidden region.
Berger, Beverly K.↗
On the choice of the electron-electron potential in relativistic atomic physics
In the calculation of relativistic effects in the structure of many-electron atoms there are two popular choice for the operator V used to represent the electron-electron interaction. One of these, V(I), is associated with the use of the Coulomb gauge propagator for photons; the other, V(II), is associated with the use of the Feynman gauge propagator. In contrast to V(I), the nonperturbative use of V(II) leads to energy levels which are already incorrect in order (alpha exp 4)m. This fact provides a quantitative argument for preferring V(I) to V(II).
Sucher, J.↗