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Showing papers on "Configuration space published in 1970"


Book ChapterDOI
01 Jan 1970
TL;DR: In this paper, the superspace of a fixed closed 3D manifold M is defined as the orbit space of the group of diffeomorphisms, Diff (M), acting by coordinate-transformation on the space of Riemannian metrics, Riem (M).
Abstract: In this work a theory of superspace is introduced. The superspace, or space of all geometries, of a fixed closed (compact without boundary) 3-dimensional manifold M is defined as the orbit space \(S(M) = \frac{{Riem (M)}}{{Diff (M)}}\) of the group of diffeomorphisms, Diff (M), acting by “coordinate-transformation” on the space of Riemannian metrics, Riem (M). A geometry is then a point in S(M), i.e. an equivalence class of isometric Riemannian metrics. Superspace, as the space of physically distinguishable states, is the proper configuration space for a dynamical theory of relativity. It is the space in which the momentary geometries of space itself evolve. Our first result states that this space is in fact a metric space.

118 citations


Journal ArticleDOI
TL;DR: In this article, a perturbative treatment of electron correlation in N −electron atoms is devised, where the unperturbed starting point is a central-force "hydrogenic" problem in the full dN −dimensional configuration space.
Abstract: A novel perturbative treatment of electron correlation in N‐electron atoms is devised. The unperturbed starting point is a central‐force “hydrogenic” problem in the full dN‐dimensional configuration space (d = dimensionality). The central potential in this solvable “hydrogenic” problem is obtained by averaging the actual electron–electron and electron–nucleus potentials over all dN − 1 hyperspherical polar angles in the configuration space. The relevant projected Green's functions are computed for the ground states of the model one‐dimensional two‐electron atom (with delta function interactions), as well as for the real three‐dimensional helium isoelectronic sequence. The corresponding first‐order wavefunctions exhibit weakly singular logarithmic behavior (at three‐particle confluence) of the type first advocated by Fock. Second‐order energies are evaluated for both of these two‐electron problems. The basic ingredients of our hyperspherical coordinate method for three‐electron atoms are displayed, in preparation for later application. Explicit suggestions are made for inclusion of singular terms in high‐accuracy atomic and molecular variational wavefunctions.

45 citations



Journal ArticleDOI
TL;DR: In this article, the Van Hove self-correlation function Gs(r, t) is calculated in configuration space (analogous to generalized hydrodynamic equations) and phase space (kinetic equations) which are then suitably approximated and solved using either perturbation or modeling methods.
Abstract: Projection operator techniques have been applied to study the diffusion of a test particle in a classical many‐particle system such as a liquid or a plasma. Particular attention has been directed towards the calculation ot the Van Hove self‐correlation function Gs(r, t). This calculation proceeds through the development of exact descriptions of Gs(r, t), both in configuration space (analogous to generalized hydrodynamic equations) and phase space (kinetic equations) which are then suitably approximated and solved using either perturbation or modeling methods. These results compare quite favorably with molecular dynamics computer experiments.

22 citations


Journal ArticleDOI
B. Lorazo1
TL;DR: In this article, the broken-pair coupling scheme was proposed for the ground state wave function of the 2 n identical particles system being described by a superposition of n identical J π = 0 + coupled pairs I +, the total configuration space of the shell model was divided into subspaces according to the number of pairs I+ they contain.

18 citations


Journal ArticleDOI
TL;DR: In this paper, the three-body elastic scattering rate when three initially free independently moving particles collide under the influence of short-range forces is computed. But the results for the volume-independent threebody reaction coefficient are not given.
Abstract: Results are quoted for the 'physical' three-body transition operator yielding the volume-independent three-body reaction coefficient, in terms of which one computes the three-body elastic scattering rate when three initially free independently moving particles collide under the influence of short-range forces.

13 citations


Journal ArticleDOI
TL;DR: In this article, an off-shell effective-rangelike theory for the low-energy two-nucleon matrix was developed, and the parameters in the theory can be determined from on-shell scattering data.
Abstract: An off-shell effective-rangelike theory is developed for the low-energy two-nucleon $T$ matrix. It is shown that the parameters in the theory can be determined from on-shell scattering data. The parameters are determined from the $^{3}S_{1}$ and $^{1}S_{0}$ two-nucleon phase shifts, and the validity of the off-shell formula is tested by means of examples. For the cases considered, the formula is found to work very well. A new proof for the separability of the two-body $T$ matrix near bound-state and resonance energies is given. This proof is based on the properties of the $T$ matrix in configuration space. A theorem on the factorization of the Jost function is developed and used to solve the inversion problem for rank-two separable potentials. Results are given for phase shifts that become hard-core phase shifts at high energies and for tensor forces. These results allow one to construct a separable potential that has the same on-shell $T$ matrix and bound-state wave function as a realistic local potential.

12 citations


Journal ArticleDOI
TL;DR: In this article, the connection between matrix elements of one body operators in odd nuclei and vertex functions is demonstrated and the renormalization of the external field, necessistated by configuration space limitations, is carried through for scalar, local fields, acting on the density and for radiation fields of the electric multipole type.
Abstract: We demonstrate the connection between matrix elements of one body operators in odd nuclei and vertex functions. The procedure is free of assumptions on the pole distribution of the two point functions and it does not use perturbation theory. The renormalization of the external field, necessistated by configuration space limitations, is carried through for scalar, local fields, acting on the density and for radiation fields of the electric multipole type using the requirement of gauge invariance. It is shown that this renormalization is possible, even if the renormalized field is strongly energy dependent due to configuration mixing.

7 citations


Journal ArticleDOI
TL;DR: For a tentative choice of configuration space Ω, it is proved that the Yang-Mills field has states with a nonvanishing isospin component if gauge-invariant quantization is used as mentioned in this paper.
Abstract: For a tentative choice of configuration space Ω, it is proved that the Yang‐Mills field, self‐interacting but not coupled to other fields, has states with a nonvanishing isospin component if gauge‐invariant quantization is used. This is shown by proving existence of a solution for the elliptic boundary‐value problem ▿β▿βζi(x) = 0 on all of 3‐dimensional Euclidean space, subject to the asymptotic condition ζi = ci + O(r−1), ∂β∂βζi = O(r−4) as r → ∞, where ci are constants; ▿β is the covariant derivative belonging to the spatial Yang‐Mills potentials bβi(x). The existence proof is a modification of Schauder's proof to an unbounded domain. Ω consists of all numerical real multiplet functions bβi(x) which are of order O(r−2) as r → ∞, have ∂βbβi = O(r−4), and satisfy certain smoothness conditions. Also, for this configuration space, the problem of existence of equivalent transverse potentials is reduced to a simpler uniqueness problem. In the classical theory, the existence of solutions ζi implies that the co...

7 citations


Journal ArticleDOI
TL;DR: In this paper, the Hartree-Fock without exchange (H-FOCK) method was used to derive the total wave function and energy of a many-electron system from the successive eigenfunctions and eigenvalues of this equation which involves of the number of electrons as a parameter only.
Abstract: By a proper approximation of the interaction term in the Hartree energy expression a simple differential equation can be derived for the one-electron orbitals of a many-electron system. The total wave function and energy of the system are constructed from the successive eigenfunctions and eigenvalues of this equation which involves of the number of electrons as a parameter only. The method shows common features with others (Hartree-Fock without exchange, theory of geminals). The difficulties of the numerical calculations arising with other methods can be vastly reduced and, in spite of the great simplicity for He, Li and Be, promising accuracy is reached.

2 citations


01 Jan 1970
TL;DR: Configuration space theory of nonrelativisitic three body scattering - transition amplitudes as discussed by the authors, which is a generalization of the three body-scattering theory of configuration space theory.
Abstract: Configuration space theory of nonrelativisitic three body scattering - transition amplitudes

Journal ArticleDOI
TL;DR: In this article, the Schrodinger equation is studied in a finite subspace of the Hilbert space, where the truncation of the configuration space makes the effective interaction energy-dependent.
Abstract: The Schrodinger equation is studied in a finite subspace of the Hilbert space. The truncation of the configuration space makes the (effective) interaction energy-dependent. This dependency is investigated. An analytic expression for the matrix elements of the effective interaction is established for the schematic model, for the displaced harmonic oscillator, for a simple random-phase problem and for a pairing force model. Thereby the phase transitions from bound to unbound states and from normal to superconducting states are analysed.

Journal ArticleDOI
TL;DR: In this article, the level density of a random Hamiltonian H such that the total configuration space can be split into irreducible subspaces using for example invariance properties is studied.
Abstract: We study the level density of a random HamiltonianH such that the total configuration space can be split into irreducible subspaces using for example invariance properties. The level density is supposed to be known for each individual subspace and the matrix elements connecting the various subspaces are treated as random variables. A similar problem arises when the Hamiltonian may be written in the formH0 +V, whereH0 has a known level density andV, the residual interaction, is a random matrix. In both cases, we start from the relation of the level density to the average of the resolvent. We expand the latter in powers of the interaction, and by scaling considerations we get the dominant contributions. The final result is easily obtained when the matrix elements of the residual interaction are statistically independent. Some simple algebraic examples are given; in particular, we recover the « semi-circle » law and indicate some generalizations.