Showing papers on "Operator (computer programming) published in 1979"

Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem

Abstract: A manifestly covariant and local canonical operator formalism of non-Abelian gauge theories is presented in its full detail. This formalism, applicable to Yang-Mills theories as well as to gravity, not only provides us a transparent understanding in the scattering theoretical aspects, but also makes it possible to discuss other important problems directly related to the (Heisenberg) operators and the state vectors: As for the former, the physical S-matrix unitarity is proved quite generally on the basis of the representation of the algebra of the BRS charge, and asymptotic field analysis is explicitly performed for some examples. As for the latter, the problems of observables and the well-definedness of charge operators are discussed and clear results are obtained, where the locality and covariance of the formalism are indispensable. Observables are shown to be invariant under the BRS transformation as well as the unbroken global gauge groups. By analyzing the structure of “Maxwell” equations in YM theories, the converse of the Higgs theorem is found to hold. This turns out to lead to a remarkably simple criterion of quark confinement in QCD. The present formalism is found useful also for the U(1) problem and the charge universality proof in the Weinberg-Salam model. General theory of indefinite metric quantum fields is developed to some extent.

Constructive techniques for accretive and monotone operators

Abstract: Publisher Summary This chapter describes the constructive techniques for accretive and monotone operators. It highlights new and recent convergence results, error estimates, applications, and open problems. The chapter presents a new result for strongly accretive operators. The chapter presents an assumption that E is a uniformly convex Banach space with a uniformly convex dual and a duality mapping that is weakly sequentially continuous at zero and A ⊂ E × E is an w-accretive operator with a zero. Zeros of certain monotone operators correspond to solutions of certain partial differential equations. Convergent schemes may be used to prove existence. In probabilistic analysis, they may be used to establish existence of random solutions to random equations.

Expansion and completeness theorems for operator manifolds

Abstract: Some expansion and completeness theorems for operator manifolds, which are currently being employed in propagator theory, are derived. It is shown that excitation or ionization operators satisfying the conditions Q|0〉 = |Λ〉 and QΛ|0〉 = 0 for general excited states |Λ〉 and reference state |0〉 may be expanded uniquely in particular sets of basis operators. These results are then used to discuss rigorous expressions for fermion propagators.

Fortsetzungen von C...-Funktionen, welche auf einer abgeschlossenen Menge in ...n definiert sind.

Abstract: In this paper the problem is considered of finding linear, continuous extension operators which extend Whitney-functions of type C∞ on a closed set in ℝn to C∞-functions on the whole space. It is shown that a sort of horn condition for the closed set A is sufficient for the existence of an extension operator on ξ(A). The methods are different from Bierstone's [2] who recently proved the same extension result for closed sets A for instance whose boundary ∂A is locally the graph of a function of Lipschitz class ℒ. A further result is an equivalent description for the existence of an extension operator by the topology of ξ(K) in the case of a compact set K. From this there are derived some examples of compact sets which are the closures of their interiors such that there exists no extension operator.

Functional integral methods for stochastic fields

Abstract: We study a method proposed recently that gives a unified view of the properties of stochastic fields determined by Langevin-type equations. The functional integrals involved are shown to need an additional prescription to be defined, this prescription being related to the relative order of noncommuting operators in the corresponding operator formalism which we characterize in detail. It is proved that the prescription is responsible for an additional term which has given rise to difficulties of interpretation in the Onsager-Machlup path probability density. We prove that all results are independent of this term. In particular in perturbation theory the cancellation mechanism of the prescription dependence is studied in detail.

Linearized analysis of inhomogeneous plasma equilibria: General theory

Abstract: A generalized framework is presented for analyzing the linearized equations for perturbations of inhomogeneous plasma equilibria in which there is a collisionless species, some properties of the solutions of the linearized equations are described, and a basis is provided for numerical computations of the linearized properties of such equilibria. It is useful to expland the perturbation potentials in eigenfunctions of the field operator which appears in the linearized equations, and to define a dispersion matrix whose analytical properties determine the nature of the solutions of the initial‐value problem. It is also useful to introduce auxiliary functions to replace the usual perturbation distribution functions, and to expand the auxiliary functions in eigenfunctions of the equilibrium Liouville operators. By introducing the auxiliary functions, great freedom is achieved in the choice of the field operator which appears in the linearized equations. This freedom can be useful in some problems to define expansion functions for the potentials that are particularly suitable for studying specific normal modes.

Bound states in a Yukawa potential: A Sturmian group-theoretical approach

Abstract: The Schr\"odinger eigenvalue problem for a Yukawa potential is reexamined from a group-theoretical perspective. By using the Fock transformation, the Schr\"odinger operator is transformed into a compact or "inverse Sturmian" operator which is a linear superposition of local representation operators of SL(2,$R$). It may be approximated by finite-rank techniques, which provide a very useful method for obtaining accurate numerical results.

Coercive singular perturbations

Abstract: We consider general boundary value problems with small parameter ɛ in the operator and boundary conditions. Both the perturbed and reduced operators are supposed to be elliptic. We point outnecessary andsufficient conditions of Shapiro-Lopatinsky type for the singularly perturbed problem to be coercive, i.e. for a two-sided a priori estimate to hold for its solutions uniformly with respect to ɛ.

Invariant subspaces of clustering operators

Abstract: A class of clustering operators is defined which is a generalization of a transfer matrix of a Gibbs lattice field with an exponential decay of correlations. It is proved that for small values ofβ the clustering operator has invariant subspaces which are similar tok-particle subspaces of the Fock space. The restriction of the clustering operator onto these subspaces resembles the operator exp(-H k, whereH k is thek- particle Schrodinger Hamiltonian in nonrelativistic quantum mechanics. The spectrum of eachH k,k⩾1, is contained in the interval (C 1βk,C 2βk). These intervals do not intersect with each other.

Higher Euler operators and some of their applications

Abstract: A set of operators which are associated with the Euler–Lagrange operator is introduced. An analysis of the commutation properties of these new operators, which will be referred to as the higher Euler operators, leads to a generalization of the necessary conditions for an expression to be an Euler–Lagrange expression. A product rule is derived for the higher Euler operators. In the special case of the Euler–Lagrange operator this product rule is basic to simple proofs of sufficiency theorems for the existence of a Lagrangian given the potential Euler–Lagrange expressions. By considering a certain homogeneity property, a characterization of Lagrangians in terms of their Euler–Lagrange expressions is established. Examples of applications of this characterization are given. A general procedure is given for constructing equivalent (not necessarily scalar density) Lagrangians when the field functions are tensorial and the Euler–Lagrange expressions are tensor densities. These results give particular significance to one of the higher Euler operators.

Models of the process operator

Abstract: The process control literature is reviewed for evidence on the following aspects of the process operator: characteristics of human control behaviour, development of process control skills, individual differences between process operators, task factors that affect performance, the organization of operator control behaviour. The various theoretical constructs which have been proposed to model these aspects of operator behaviour are described and discussed. Since the majority of the models are based on an analysis of verbal report data, a discussion of some of the methodological problems in using verbal protocols is presented. The review concludes that an information processing approach based on protocol data seems to be the most fruitful technique for modelling the human process controller.

Cylindrical lens systems described by operator algebra.

Abstract: In a recent work, an operator algebra was developed for the description of axially symmetrical coherent optical systems. The present work extends the operator representation to incorporate cylindircal lenses and is used to analyze the transforming properties of an arbitrarily oriented cylindrical lens. The results provide the basis for synthesizing various systems for signal processing, such as convolution and correlation operations.

On the Specification of Operator or Occupational Workload with Performance-Measurement Methods:

Abstract: Five system-output or performance-measurement methods have been described in the literature for use in operator or occupational workload specifications: laboratory, analytic, synthetic, simulation,...

Automatic portable pH meter and method with calibration receptacle

Abstract: A portable self-calibrating pH meter particularly adapted for use by unskilled operators in adverse environment conditions is disclosed which has a minimum of operator controls while preventing operator errors and while providing effective and accurate pH measurement.

Operator waves in Hilbert space and related partial differential equations

Abstract: The success of the theory of characteristic functions of nonselfadjoint operators and its applications to the System Theory [1–17] is the inspiration for attempts towards creating a general theory in the much more complicated case of several commuting nonselfadjoint operators. In this paper we study the close relations between sets of commuting operators in Hilbert space and related systems of partial differential equations. At the same time a generalization of the classical Cayley Hamilton Theorem, in the case of two commuting operators, is obtained which leads to unexpected connections with the theory of algebraic curves.

The charged sectors of quantum electrodynamics in a framework of local observables

Abstract: The construction of charged sectors in Quantum Electrodynamics (QED) is analyzed within a framework of algebras of local observables. It is argued that charged sectors arise by composing a vacuum state with charged * morphisms of an algebra of (neutral) quasi-local observables. Charged * morphisms, in turn, are obtained as weak limits of charge transfer cocycles. These are non-local elements of the algebra of all quasi-local observables obeying “topological” commutation relations with the local charge operators. It is shown that in this framework, charged sectors are invariant under the time evolution and satisfy the relativistic spectrum condition. The total charge operator is well defined and time-independent (conserved) on all charged sectors. Under an additional hypothesis the spectrum of the total charge operator is shown to be a discrete subgroup of the real line. A generalized Haag-Ruelle scattering theory for charged infra-particles is suggested, and some comments on non-abelian gauge theories are described.

On integral representations for the Neumann operator.

Abstract: This paper is devoted to the derivation of an approximate formula for the kernel of the Neumann operator N on strongly pseudo-convex domains. In particular, a new class of singular integral operators arises that are infinitely smoothing in the interior and preserve singular supports at the boundary and whose kernels are products of isotropic kernels with parabolic ones.

Characterization of parallel subtraction.

Abstract: Parallel subtraction is an operation defined on pairs of positive operators. In terms of electrical networks, one may pose the following problem: Given an electrical network, represented by a specified positive operator, determine the set of positive operators which when connected in parallel with the specified operator yield another prescribed operator. The set of solutions of this electrical network problem is shown to have a minimum. The minimum is termed “the parallel difference of the fixed operators,” and the operation is termed “parallel subtraction.” The parallel difference is used to obtain explicit error estimates for an iteration procedure which approximates the geometric mean of positive operators. This concept of the geometric mean reduces to the square root of the product of the operators if the operators commute. Finally, by using the geometric mean, an operator version of the Gaussian mean is presented.

An application of the maximum principle to the study of essential self‐adjointness of Dirac operators. II

Abstract: We formulate a theorem saying that the Dirac operator corresponding to a one‐electron atomic ion is essentially self‐adjoint on the usual domain, provided that the nuclear charge Z is less than 118. Furthermore, for such nuclear charges the domains of the closure of the free particle and total Dirac operators are equal. In the present part I of this paper we prove this theorem for the part of the operator over each of the usual reducing subspaces.

Compactness principles in nonlinear operator approximation theory

Abstract: This paper is concerned with the approximate solution of nonlinear operator equations in abstract settings and with applications to integral and differential equations. A given operator with certain continuity and compactness or inverse compactness properties is a suitable limit of a sequence of operators with analogous properties which hold uniformly or asymptotically. Both fixed point equations and inhomogeneous equations are treated. Solutions of approximate problems converge to solutions of the given problem. This is an appropriate type of set convergence when solutions are not unique.

Apparatus for and method of operating a well

Abstract: Apparatus and system for testing and producing a well in which the well is controlled adjacent the producing formation and may be shut-in or permitted to flow at the discretion of the operator. The well may be tested under flowing or shut-in conditions and after testing is completed the tubing may be hung off in the well with the well shut-in adjacent the producing formation.

Convertible switch operator

Abstract: A convertible switch operator for use as a pull momentary and as a push-pull momentary operation characterized by a tubular selector longitudinally movable in a housing and spring biased by a first spring for operation as a pull operator; and spring biased by two springs in an intermediate position as a push-pull operator.