Extended Configuration Space Research Articles

Study of electronic correlations in the Auger cascade decay from Ne*1s−13p

We present an experimental and theoretical study of the angular correlation between resonant Auger and subsequent Coster–Krönig electrons emitted in the cascade decay of Ne (1s−13p) resonance excited by linearly polarized light. The angular correlation has been measured for different relative orientations between the light polarization, the emission direction of the Coster–Krönig electron and the emission angle of the resonant Auger electron. All the experimental angular patterns are measured as a function of the resonant Auger emission angle and are compared with multi-configuration Dirac–Fock model numerical results, which include electron correlations in each step of the cascade. The agreement between theory and experiment is different for the different considered decay channels; for the cases in which disagreement is larger it is argued that an extended configuration space must be taken into account to reproduce the experimental data.

Lagrangian description of the variational equations

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. After discussing certain features of the formulation, we introduce the so-called inherited constants of the motion and relate them to the Noether constants of the extended system.

Spacetime states and covariant quantum theory

In its usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended configuration space. Such covariant formulations are natural for relativistic gravitational systems, where general covariance conflicts with the notion of a preferred physical-time variable. The standard presentation of quantum mechanics, in turn, again gives time a very special role, raising well known difficulties for quantum gravity. Is there a covariant form of (canonical) quantum mechanics? We observe that the preferred role of time in quantum theory is the consequence of an idealization: that measurements are instantaneous. Canonical quantum theory can be given a covariant form by dropping this idealization. States prepared by noninstantaneous measurements are described by ``spacetime smeared states.'' The theory can be formulated in terms of these states, without making any reference to a special time variable. The quantum dynamics is expressed in terms of the propagator, an object covariantly defined on the extended configuration space.

Partial observables

We discuss the distinction between the notion of partial observable and the notion of complete observable. Mixing up the two is frequently a source of confusion. The distinction bears on several issues related to observability, such as (i) whether time is an observable in quantum mechanics, (ii) what are the observables in general relativity, (iii) whether physical observables should or should not commute with the Wheeler-DeWitt operator in quantum gravity. We argue that the extended configuration space has a direct physical interpretation, as the space of the partial observables. This space plays a central role in the structure of classical and quantum mechanics and the clarification of its physical meaning sheds light on this structure, particularly in context of general covariant physics.

Extended cluster algorithm in quantum simulations

We propose an extension of the quantum cluster algorithm by a combined use of the Fortuin-Kasteleyn mapping and the Hubbard-Stratonovich transformation. To describe the idea, we consider the $S=\frac{1}{2}$ $\mathrm{XXZ}$ chain model and express the partition function as the sum in an extended configuration space of spins, graphs, and fields. Then it is clarified that this algorithm possesses a computationally tractable continuous-time limit and maintains virtues of the quantum cluster algorithm. Numerical simulations are performed and its applicability is demonstrated. Further, we discuss potential gains in our algorithm.

Quantum mechanics of periodic systems

The quantum description of a periodic system can be naturally embedded in an auxiliary problem with an extended configuration space. Standard methods applied to the solution of the extended Schrödinger equation yield the results usually obtained by the use of group theory or extensions of Floquet’s theorem. This method is used to prove Bloch’s theorem and to construct a multimode Floquet method for the semiclassical theory of lasers interacting with atoms.

Picosecond lifetime measurement of neutron core-excited states in the N = 50 nucleus 95Rh

Lifetimes of high-spin states in the N = 50 nucleus 95Rh were measured using the recoil-distance Doppler-shift technique. The nuclei were produced via the reaction 58Ni( 40Ca,3p) at 145 MeV beam energy and the γ radiation was detected in six EUROBALL cluster detectors. Reduced transition probabilities for seventeen γ transitions and limits for nine further transitions were extracted and compared with the predictions of the spherical shell model based on the extended configuration space, ( 0f 5 2 , 1p 3 2 , 1p 1 2 , 0g 9 2 ) for protons and ( 0g 9 2 , 1d 5 2 ) for neutrons relative to a hypothetical 68Ni core. The results indicate that all observed states with 27 2 ⩽ I ⩽ 39 2 are built from a neutron g 9 2 → d 5 2 excitation across the N = 50 shell closure, coupled to up to five valence protons in different configurations. Evidence of stretched dipole cascades having large M1 strengths was found and explained by spin recoupling within the ν( g 9 2 ) −1ν( d 5 2 ) neutron part of the wavefunctions.

“Worm” algorithm in quantum Monte Carlo simulations

We present a novel quantum Monte Carlo scheme which allows efficient calculations of the Green function at finite temperature and the study of large disordered systems. The scheme is ergodic, works with non-zero winding numbers and in the grand canonical ensemble. The central idea is using a pair of worldline discontinuities for sampling the extended configuration space of the system which includes both closed and disconnected worldlines. The method is illustrated by simulations of pure and disordered bosonic Hubbard models in 1D.

Multipole oscillations in sodium clusters: Separable ansatz in the random-phase-approximation description

The modified random-phase-approximation (RPA) method with the self-consistent separable residual forces (SRPA) is proposed for the description of multipole electric oscillations of valence electrons in sodium clusters. The method allows one to study the coupling of different kinds of collective motion. As a particular case, the coupling of surface and volume modes is considered. The SRPA is applied to neutral and singly charged spherical sodium clusters in a wide size region ${(N}_{e}=8,20,40,58,92,138,196,440,952)$ and good agreement with experimental data is achieved. This testifies to the applicability of the separable ansatz, which has the essential advantage of avoiding diagonalization of the RPA matrices and thus drastically simplifies the RPA calculations. The latter could be quite urgent for very large and deformed clusters where an extended configuration space and, consequently, high-rank RPA matrices are used. The predictions for $E2$ and $E3$ collective excitations are presented. The results obtained with the self-consistent Kohn-Sham and phenomenological Woods-Saxon single-particle schemes are exhibited and different parameters for the Woods-Saxon potential are proposed.

Modified formulation for a green-schwarz superstring having irreducible links of the first kind

A space which receives covariant action is proposed for aD=10, N=1 superstring in a suitably extended configuration space having the following properties: a) a theory can be constructed dynamically equivalent to the Green-Schwarz superstring, and b) the fermion links may be separated into types in an explicitly covariant fashion, where the links of the first kind are irreducible.

Contact Transformations in Classical Mechanics

Transformations of coordinates of points in an infinite-dimensional graded vector space, the so-called contact transformations, are examined. An infinite jet prolongation of the extended configuration space of N spinless particles is the subspace of this vector space. The dynamical equivalence among Lagrangian N-body systems connected by an invertible jet transformation is established. As an example of the invertible jet transformations, a class of gauge transformations of Lagrangian variables is investigated. The method of contact transformations is applied to the Wheeler-Feynman electrodynamics for two point charges.

Green-Schwarz superstring in extended configuration space and the infinitely reducible first class constraints problem.

The Green--Schwarz superstring action is modified to include some set of additional (on-shell trivial) variables. A complete constraints system of the theory turns out to be reducible both in the original and in additional variable sectors. The initial $8s$ first class constraints and $8c$ second class ones are shown to be unified with $8c$ first and $8s$ second class constraints from the additional variables sector, resulting with $SO(1,9)$-covariant and linearly independent constraint sets. Residual reducibility proves to fall on second class constraints only.

On the lowest electronic states of the C2F radical

The adiabatic energy surfaces of the lowest three electronic states [2(2A′ and 2A′)] and 2Σ+[2A′] of the C2F radical were investigated by the Hartree-Fock multiconfiguration self-consistent field (HF—MCSCF) ab initio method using a large set of atomic natural orbitals (ANO) and an extended configuration space, and the results were shown to be in agreement with the predictions of valence theory for this radical. The electronic ground state was found to have a bent equilibrium structure, hence contradicting the Walsh rule which predicts for the isoelectronic molecules a 2 linear state. The three states were found to be nearly degenerate and the potential energy surfaces of the two lowest electronic states exhibit an avoided crossing at an energy ∼2000 cm−1 above the ground-state minimum, lower than the highest vibrational fundamental. The strong adiabatic interaction which is responsible for the ordering of the electronic states and their equilibrium geometry involves not only the bending coordinate as normally found for Renner-Teller pairs of states, but also the C—C stretching coordinate, due to the near degeneracy of the 2Σ+ and the 2 lowest electronic states at linear geometries. © 1996 John Wiley & Sons, Inc.

11-DIMENSIONAL SUPERMEMBRANE IN A SPINOR MOVING REPERE FORMALISM

Twistor-like formulations for super p-brane theories in the D-dimensional space-time including D=11 supermembrane are suggested in an extended configuration space. This extension is carried out by the addition of auxiliary spinor coordinates of the moving repere (the Newman-Penrose dyades for D=4). The spinor coordinates are realized as the Lorentz harmonics and necessary for the irreducible covariant description of the κ-symmetry. Using this harmonical realization a generalization of the Newman-Penrose dyades for the case D=11 is suggested.

Strings with zero tension

We describe bosonic strings by using a kind of Lagrangian compatible with the zero tension limit. The work is developed on an extended configuration space and the quantization is carried out with details.

Path integrals in parametrized theories: Newtonian systems

Constraints in dynamical systems typically arise either from gauge or from parametrization. We study Newtonian systems moving in curved configuration spaces and parametrize them by adjoining the absolute time and energy as conjugate canonical variables to the dynamical variables of the system. The extended canonical data are restricted by the Hamiltonian constraint. The action integral of the parametrized system is given in various extended spaces: Extended configuration space or phase space and with or without the lapse multiplier. The theory is written in a geometric form which is manifestly covariant under point transformations and reparametrizations. The quantum propagator of the system is represented by path integrals over different extended spaces. All path integrals are defined by a manifestly covariant skeletonization procedure. It is emphasized that path integrals for parametrized systems characteristically differ from those for gauge theories. Implications for the general theory of relativity are discussed.

The Einstein Equations of Evolution-A Geometric Approach

In this paper the exterior Einstein equations are explored from a differential geometric point of view. Using methods of global analysis and infinite-dimensional geometry, we answer sharply the question: ``In what sense are the Einstein equations, written as equations of evolution, a Lagrangian dynamical system?'' By using our global methods, several aspects of the lapse function and shift vector field are clarified. The geometrical significance of the shift becomes apparent when the Einstein evolution equations are written using Lie derivatives. The evolution equations are then interpreted as evolution equations as seen by an observer in space coordinates. Using the notion of body-space transitions, we then find the relationship between solutions with different shifts by finding the flow of a time-dependent vector field. The use of body and space coordinates is shown to be somewhat analogous to the use of such coordinates in Euler's equations for a rigid body and the use of Eulerian and Lagrangian coordinates in hydrodynamics. We also explore the geometry of the lapse function, and show how one can pass from one lapse function to another by integrating ordinary differential equations. This involves integrating what we call the ``intrinsic shift vector field.'' The essence of our method is to extend the usual configuration space M=Riem(M) of Riemannian metrics to T×D×M, where T=C∞(M,R) is the group of relativistic time translations and D=Diff(M) is the group of spatial coordinate transformations of M. The lapse and shift then enter the dynamical picture naturally as the velocities canonically conjugate to the configuration fields (ξt,ηt)∈T×D. On this extended configuration space, a degenerate Lagrangian system is constructed which allows precisely for the arbitrary specification of the lapse and shift functions. We reinterpret a metric given by DeWitt for M as a degenerate metric on D×M. On D×M, however, the metric is quadratic in the velocity variables. The groups T and D also serve as symmetry groups for our dynamical system. We establish that the associated conserved quantities are just the usual ``constraint equations.'' A precise theorem is given for a remark of Misner that in an empty space-time we must have H=0. We study the relationship between the evolution equations for the time-dependent metric gt and the Ricci flat condition of the reconstructed Lorentz metric gL. Finally, we make some remarks about a possible ``superphase space'' for general relativity and how our treatment on T×D×M is related to ordinary superspace and superphase space.

Time evolving theory of the mechanics of single particles and single photons

We introduce space-time ensemble methods to formulate definitions of single particles and single photons as local abstractions of constant processes. We find the general form of the corresponding Stueckelberg Lagrangian for Riemannian and Newtonian spacetimes and supply a physical interpretation for the worldline parameter. We develop the corresponding mechanical theories over the extended configuration space and the extended phase space. We suppose that the background can be represented by an ‘external field’ and we study several general examples. Certain phenomenological forms do not describe particles, others do not seem to describe theories in which the representation of the background is process independent (Riemannian case). At the canonical level the elimination of second-class constraints associated with null processes generates restrictions on the domain of definition of photon coordinates which correspond to the absence of zero energies. The requirement that the canonical process-anti-process classification exist leads to a factorization condition on the extended phase space which is satisfied for all the cases studied in which the configuration formalisms entail no difficulties, except one, which is the ‘minimally’ coupled external vector field case over Riemannian space-times. We discuss the observation theoretical significance of our results.