superselection in the presence of constraints superselection and constraints occur together in many gauge theories and here we begin a study of such systems our main focus will be to analyze compatibility questions between constraining and superselection and we will develop an example modelled on qed in which our framework is realized we proceed from a generalization of doplicher roberts superselection theory to the case of the nontrivial center and a set of dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form this involves an analysis of the restriction and factorization of superselection structures

high order approximations of the eigenvalues of regular sturm liouville problems abstract in this article we provide high order approximations to the eigenvalues of regular sturm liouville problems with general separable boundary conditions together with their error bounds the approach is based on sampling theory

infrared singular fields and nonregular representations of canonical commutation relation algebras infrared singular variables which often enter in the formulation of models in quantum field theory many body theory and quantum statistical mechanics are described in terms of nonregular representations of canonical commutation relations algebras general properties of such representations are discussed in this way one also obtains insight into the construction and representation of charged field algebras a as canonical extensions of a neutral observable algebra a0 the charged state representations of a0 are obtained through nonregular vacuum representations of the extended field algebra a the above structures are proven to work in several explicit models

eigenvalue and eigenfunction asymptotics for regular sturm liouville problems abstract in this paper we obtain asymptotic formulas for eigenvalues eigenfunctions and the reciprocals of the eigenfunction norms for eigenvalue problems associated with the general sturm liouville equation pu r q u 0 having regular endpoints the method is based on a conversion to liouville normal form and an iterative procedure of solving the associated volterra integral equation producing an asymptotic expansion of the solution in higher powers of 1 1 2 as

corrigendum corrigendum to a tailored solver for bifurcation analysis of ocean climate models j comput phys 227 2007 654 679 this corrigendum contains a correction to some of the results in the article a tailored solver for bifurcation analysis of ocean climate models 2 in which it was demonstrated how the specific mathematical structure of the equations governing oceanic flow can be exploited to build an efficient linear system solver for use in a continuation method compared to earlier work e g 4 an additional novelty was the implementation of the small slope approximation to redi 3 isoneutral diffusion and gent mcwilliams 1 gm stirring these parameterizations provide a physically more realistic description of ocean mixing in z coordinate models than horizontal diffusion unfortunately the formulation of redi and gm mixing in 2 section 2 2 contains several errors which were carried over to the numerical implementation new computations that used the correct formulation revealed qualitative differences with some of the results given in 2 section 4 2 2 in particular fig 7 and fig 8 therefore a correction of these errors will be provided below for completeness we first correct the typographical errors that appeared in 2 section 2 1 in the second term of the momentum equations 2 4a b a factor of r 1 0 where r0 is the earth s radius is missing furthermore the inclusion of the constant s0 in the last term is inappropriate given that the wind stress field s s is defined to have units of pa in the definitions of the operators lu u v and lv u v a factor cos 2h was omitted in the numerator of the first metric term they should read

the operator quantization of the open bosonic string field algebra our aim in this paper is to make explicit the operator theory of the heuristic open bosonic string and to abstract a suitable field algebra for the string this is done on a fock krein space and we examine integrability and j unitary implementability of all the defining transformations of the string i e time translations gauge transformations and poincare transformations the results obtained agree partially with those of bowick and rajeev i e the gauge transformations do not leave the fock krein complex structure invariant once we obtained integrated transformation groups on a suitable symplectic space for the infinitesimal transformations of the string and proved implementability of these for the fock krein representation we are then free to define an abstract c algebra carrying all the algebraic information of the string and to examine different representations

the performance of implicit ocean models on b and c grids fully implicit primitive equation ocean models are useful to study the sensitivity of steady ocean flows to parameters to determine bifurcations of these flows associated with instabilities and to use relatively large time steps in transient flow computations this paper addresses a problem related to the origin of wiggles occurring in fully implicit c grid models the situation considered is the computation of three dimensional thermally driven steady flows in a midlatitude spherical sector we determine the reason why in a coarse resolution c grid implicit model the values of the lateral friction coefficients are restricted to far higher values than for the same b grid model the analysis also reveals why the b grid discretization is superior for the computation of this type of flows

computation of the eigenvalues of sturm liouville problems with parameter dependent boundary conditions using the regularized sampling method the purpose in this paper is to compute the eigenvalues of sturm liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the regularized sampling method an improvement on the method based on shannon sampling theory which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost a few examples shall be presented to illustrate the power of the method and a comparison made with the the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions

asymptotics of eigenvalues for regular sturm liouville problems with eigenvalue parameter in the boundary condition abstract in this paper we obtain asymptotic estimates of eigenvalues for regular sturm liouville problems having the eigenparameter in the boundary condition the method is based on an iterative procedure solving the associated riccati equation and producing an asymptotic expansion of the solution in the higher powers of 1 1 2 as

group actions on c algebras 3 cocycles and quantum field theory we study group extensions where acts on a c algebraa given a twisted covariant representation v of the paira we construct 3 cocycles on with values in the centre of the group generated byv these 3 cocycles are obstructions to the existence of an extension of byv which acts ona compatibly with the main theorems of the paper introduce a subsidiary invariant which classifies actions of onv and in terms of which a necessary and sufficient condition for the the cohomology class of the 3 cocycle to be non trivial may be formulated examples are provided which show how non trivial 3 cocycles may be realised the framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories we show how to interpret our results in that setting in two ways one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups in order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a lie algebra version of the invariant and the 3 cocycle

a fully implicit model of the three dimensional thermohaline ocean circulation 685 in this paper a fully implicit numerical model of the three dimensional thermohaline ocean circulation is presented with this numerical model it is possible to follow branches of steady states in parameter space and monitor their linear stability also transient flows can be computed allowing much larger time steps than those possible with explicit schemes by using recently developed solvers for linear systems of equations and for generalized eigenvalue problems results for reasonable spatial resolution can be obtained bifurcation diagrams and transient flows are computed for typical flows in a single hemispheric basin situation with focus on i the performance of the methodology and ii the new type of information which can be obtained on these flows

algebraic structures of degenerate systems physical requirements and the indefinite metric the basic algebraic structures of systems with a gauge degeneracy have been developed in a c algebra framework in 1 of which the present work is a natural extension we consider the treatment of algebraic conditions in more detail as well as the compatibility conditions between a given constraint set and a given set of physical transformations a list of reasonable physical requirements on the algebraic structure is given we also consider the existence and structure of indefinite inner product representations and obtain various results for obtaining an indefinite inner product representation

systems with outer constraints gupta bleuler electromagnetism as an algebraic field theory since there are some important systems which have constraints not contained in their field algebras we develop here in ac context the algebraic structures of these the constraints are defined as a groupg acting as outer automorphisms on the field algebra g aut g inn and we find that the selection ofg invariant states on is the same as the selection of states onm g m g mathop times limits alpha f by ug 1 g g whereug m g m g mathop times limits alpha f are the canonical elements implementing g these states are taken as the physical states and this specifies the resulting algebraic structure of the physics inm g m g mathop times limits alpha f and in particular the maximal constraint free physical algebra a nontriviality condition is given for to exist and we extend the notion of a crossed product to deal with a situation whereg is not locally compact this is necessary to deal with the field theoretical aspect of the constraints next thec algebra of the ccr is employed to define the abstract algebraic structure of gupta bleuler electromagnetism in the present framework the indefinite inner product representation structure is obtained and this puts gupta bleuler electromagnetism on a rigorous footing finally as a bonus we find that the algebraic structures just set up provide a blueprint for constructive quadratic algebraic field theory

eigenvalues of sturm liouville problems with discontinuity conditions inside a finite interval abstract in this work we use the regularized sampling method to compute the eigenvalues of sturm liouville problems with discontinuity conditions inside a finite interval we work out an example by computing a few eigenvalues and their corresponding eigenfunctions

on the validity of dirac s conjecture regarding first class secondary constraints two examples are presented which clarify dirac s conjecture that all first class secondary constraints generate gauge transformations in the general case the status of this conjecture is ambiguous depending crucially upon the physical interpretation of the lagrangian at hand however the author proposes a consistent general method of interpreting lagrangians such that relative to this interpretative framework dirac s conjecture holds true

some inverse results for hill s equation abstract we consider hill s equation y q y 0 where q l 1 0 we show that if l n the length of the n th instability interval is of order o n k 2 then the real fourier coefficients a n k b n k of q k k th derivative of q are of order o n 2 which implies that q k is absolutely continuous almost everywhere for k 0 1 2

a fully implicit model of the global ocean circulation with the recent developments in the solution methods for large dimensional nonlinear algebraic systems fully implicit ocean circulation models are now becoming feasible in this paper the formulation of such a three dimensional global ocean model is presented with this implicit model the sensitivity of steady states to parameters can be investigated efficiently using continuation methods in addition the implicit formulation allows for much larger time steps than can be used with explicit models to demonstrate current capabilities of the implicit global ocean model we use a relatively low resolution 4 horizontally and 12 levels vertically version for this configuration we present i an explicit calculation of the bifurcation diagram associated with hysteresis behavior of the ocean circulation and ii the scaling behavior of the atlantic meridional overturning versus the magnitude of the vertical mixing coefficient of heat and salt

some remarks on the gupta bleuler triplet indecomposable representations of the poincare group associated to infrared singular field theory models are discussed in the framework of the general theory of the gupta bleuler triplet formulated by araki it is shown that the definition of maximal hilbert space structures related to the infrared properties of the states of the models can be exploited to construct representation spaces for the gupta bleuler triplet the examples of the two dimensional massless scalar field and of the electromagnetic field in the landau gauge are discussed in particular in the first example the relation between the gupta bleuler triplet and the algebraic treatment of the massless scalar field is investigated in the case of electromagnetism the structure of the representation of the poincare group in the landau gauge is clarified the explicit form of the corresponding gupta bleuler triplet for the one particle space of the electromagnetic field is exhibited

reduction of lie jordan banach algebras and quantum states in this paper it is shown that the concept of dynamical correspondence for jordan banach algebras is equivalent to a lie structure compatible with the jordan one then a theory of reduction of lie jordan banach algebras in the presence of quantum constraints is presented and compared to the standard reduction of c algebras of observables of a quantum system the space of states of the reduced lie jordan banach algebra is characterized in terms of dirac states on the physical algebra of observables and its gns representations described in terms of states on the unreduced algebra

the application of jacobian free newton krylov methods to reduce the spin up time of ocean general circulation models in present day forward time stepping ocean climate models capturing both the wind driven and thermohaline components a substantial amount of cpu time is needed in a so called spin up simulation to determine an equilibrium solution in this paper we present methodology based on jacobian free newton krylov methods to reduce the computational time for such a spin up problem we apply the method to an idealized configuration of a state of the art ocean model the modular ocean model version 4 mom4 it is shown that a typical speed up of a factor 10 25 with respect to the original mom4 code can be achieved and that this speed up increases with increasing horizontal resolution

using fourier coefficients to determine the unstable points of hill equation abstract the main purpose of this paper is to determine the unstable points of the hill equation x q t x 0 the approach is based on fourier coefficients combining with a novel form discriminant of hill equation the method is much different from the previous methods employed in the literature

computing the eigenvalues of singular sturm liouville problems using the regularized sampling method abstract this paper deals with singular sturm liouville problems we shall extend the domain of application of the regularized sampling method a method to compute the eigenvalues a few numerical examples will be presented to illustrate the merit of the method

the quantum theory of second class constraints kinematics the problem of second class quantum constraints is here set up in the context ofc algebras utilizing the connection with state conditions as given by the heuristic quantization rules that is a constraint set is said to be first class if all its members can satisfy the same state condition and second class otherwise several heuristic models are examined and they all agree with this definition given then a second class constraint set we separate out its first class part as all those constraints which are compatible with the others and we propose an algebraic construction for imposition of the constraints this construction reduces to the normal one when the constraints are first class moreover the physical automorphisms assumed as conserving the constraints will also respect this construction the final physical algebra obtained is free of constraints gauge invariant unital and with the right choice simple thisc algebra also contains a factor algebra of the usual observables i e the commutator algebra of the constraints the general theory is applied to two examples the elimination of a canonical pair from a boson field theory as in the two dimensional anomalous chiral schwinger model of rajaraman 14 and the imposition of quadratic second class constraints on a linear boson field theory

on the quantization of presymplectic dynamical systems via coisotropic imbeddings we study certain aspects of the problem of quantizing a presymplectic dynamical system such a system is quantized by imbedding the presymplectic manifoldm under consideration into a symplectic manifoldx and then geometrically quantizing the latter it is known that this procedure will yield consistent results provided the imbeddingm x is coisotropic we show that such imbeddings always exist and are locally unique furthermore we investigate the extent to which the resulting quantum dynamics is independent of the choice of coisotropic imbedding that is we examine to what extent the presymplectic phase spacem determines the quantum representation space and the quantization of observables the quantization is carried out within the geometric quantization framework of kostant and souriau

sturm liouville problems with parameter dependent potential and boundary conditions this paper deals with the computation of the eigenvalues of sturm liouville problems with parameter dependent potential and boundary conditions we shall extend the domain of application of the method based on sampling theory to the case where the classical whittaker shannon kotel nikov theorem is not applicable a few numerical examples will be presented

sturm liouville problems with impulse effects abstract this paper deals with the computation of the eigenvalues of sturm liouville problems with several discontinuity conditions inside a finite interval and parameter dependent boundary conditions using the regularized sampling method a few examples are worked out by computing several eigenvalues and their corresponding eigenfunctions

a tailored solver for bifurcation analysis of ocean climate models in this paper we present a new linear system solver for use in a fully implicit ocean model the new solver allows to perform bifurcation analysis of relatively high resolution primitive equation ocean climate models it is based on a block ilu approach and takes special advantage of the mathematical structure of the governing equations in implicit models jacobian matrices have to be constructed analytical construction is hard for complicated but more realistic representations of mixing this is overcome by evaluating the jacobian in part numerically the performance of the new implicit ocean model is demonstrated using i a high resolution model of the wind forced double gyre flow problem in a relatively small midlatitude spherical basin and ii a medium resolution model of thermohaline and wind driven flows in an atlantic size single hemispheric basin

qcd on an infinite lattice we construct a mathematically well defined framework for the kinematics of hamiltonian qcd on an infinite lattice in mathbb r 3 and it is done in a c algebraic context this is based on the finite lattice model for hamiltonian qcd developed by kijowski rudolph e a to extend this model to an infinite lattice we need to take an infinite tensor product of nonunital c algebras which is a nonstandard situation we use a recent construction for such situations developed by grundling and neeb once the field c algebra is constructed for the fermions and gauge bosons we define local and global gauge transformations and identify the gauss law constraint the full field algebra is the crossed product of the previous one with the local gauge transformations the rest of the paper is concerned with enforcing the gauss law constraint to obtain the c algebra of quantum observables for this we use the method of enforcing quantum constraints developed by grundling and hurst in particular the natural inductive limit structure of the field algebra is a central component of the analysis and the constraint system defined by the gauss law constraint is a system of local constraints in the sense of grundling and lledo using the techniques developed in that area we solve the full constraint system by first solving the finite local systems and then combining the results appropriately we do not consider dynamics

computing the spectrum of non self adjoint sturm liouville problems with parameter dependent boundary conditions this paper deals with the computation of the eigenvalues of non self adjoint sturm liouville problems with parameter dependent boundary conditions using the regularized sampling method a few numerical examples among which singular ones will be presented to illustrate the merit of the method and comparison made with the exact eigenvalues when they are available

automatic solution of sturm liouville problems using the pruess method abstract we develop algorithms based on coefficient approximation for the automatic solution of regular and singular sturm liouville problems

algebraic quantization of systems with a gauge degeneracy systems with a gauge degeneracy are characterized either by supplementary conditions or by a set of generators of gauge transformations or by a set of constraints deriving from dirac s canonical constraint method these constraints can be expressed either as conditions on the field algebra or on the states on in ac algebra framework we show that the state conditions give rise to a factor algebra of a subalgebra of the field algebra this factor algebra is free of state conditions in this formulation we show also that the algebraic conditions can be treated in the same way as the state conditions the connection between states on and states on is investigated further within this framework as is also the set of transformations which are compatible with the set of constraints it is also shown that not every set of constraints can give rise to a nontrivial system finally as an example the abstract theory is applied to the electromagnetic field and this treatment can be generalized to all systems of bosons with linear constraints the question of dynamics is not discussed

computing eigenvalues occurring in continuation methods with the jacobi davidson qz method continuation methods are well known techniques for computing several stationary solutions of problems involving one or more physical parameters in order to determine whether a stationary solution is stable and to detect the bifurcation points of the problem one has to compute the rightmost eigenvalues of a related generalized eigenvalue problem the recently developed jacobi davidson qz method can be very effective for computing several eigenvalues of a given generalized eigenvalue problem in this paper we will explain how the jacobi davidson qz method can be used to compute the eigenvalues needed in the application of continuation methods as an illustration the two dimensional rayleigh benard problem has been studied with the rayleigh number as a physical parameter we investigated the stability of stationary solutions and several bifurcation points have been detected the jacobi davidson qz method turns out to be very efficient for this problem

on sinc based method in computing eigenvalues of boundary value problems we aim in this paper to give a complete treatment of the error analysis of the use of the sinc method in computing eigenvalues of second order birkhoff regular eigenvalue problems for this task we study truncation and amplitude errors on bbb c associated with cardinal series representation of band limited functions as well as those of their derivatives these results which seem to be considered for the first time give us the possibility to establish the error analysis when the eigenvalues are not real or not algebraically simple

the resolvent algebra a new approach to canonical quantum systems the standard c algebraic version of the algebra of canonical commutation relations the weyl algebra frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as bounded functions of the hamiltonian here a novel c algebra of the canonical commutation relations is presented which does not suffer from such problems it is based on the resolvents of the canonical operators and their algebraic relations the resulting c algebra the resolvent algebra is shown to have many desirable analytic properties and the regularity structure of its representations is surprisingly simple moreover the resolvent algebra is a convenient framework for applications to interacting and to constrained quantum systems as we demonstrate by several examples