second quantization of the elliptic calogero sutherland model we construct a quantum field theory model of anyons on a circle and at finite temperature we find an anyon hamiltonian providing a second quantization of the elliptic calogero sutherland model this allows us to prove a remarkable identity which is a starting point for an algorithm to construct eigenfunctions and eigenvalues of the elliptic calogero sutherland hamiltonian

exponential parameter estimation in the presence of known components and noise in the determination of the natural modes of an electromagnetic scatterer the measured time series will contain desired information noise and quite often known transient components introduced by the excitation source or measuring equipment this paper describes a linearly constrained total least squares lctls prony method for extracting the exponential model parameters from observed transient data for such problems the tls criterion yields better parameter estimates than ls moreover the incorporation of known signal information via constraints leads to even greater improvements in performance mathematical connections between lctls prony and a tls variation of time series deflation tsd are used to derive constraints for higher order excitation poles also we use tsd concepts to derive numerically superior data transformations for lctls simulation studies involving idealized test data and synthetic scattering response data of a perfectly conducting sphere demonstrate the advantages of the method

geometric quantization on the super disk in this article we discuss the geometric quantization on a certain type of infinite dimensional super disk such systems are quite natural when we analyze coupled bosons and fermions the large n limit of a system like that corresponds to a certain super homogeneous space first we define an example of a super homogeneous manifold a super disk we show that it has a natural symplectic form and it can be used to introduce classical dynamics once a hamiltonian is chosen existence of moment maps provide a poisson realization of the underlying symmetry super group these are the natural operators to quantize via methods of geometric quantization and we show that this can be done

automorphisms of the canonical anticommutation relations and index theory let h be a complex hilbert space p an orthogonal projection on h and p the complementary projection if g is any symmetrically normed ideal in the ring of bounded operators on h then we consider the group of unitary operators on h such that p up and p u p lie in g when g is the hilbert schmidt class these unitaries define automorphisms of the c algebra b of the canonical anticommutation relations over h which are implementable in the representation of b determined by p we investigate the structure of the group u proving in particular that it has infinitely many connected components uk labelled by the fredholm index of p u p the connected component of the identity u0 is generated by unitaries of the form exp ia with a self adjoint and p a p in g finally we consider an application of these results to two dimensional field theory showing in particular that the charge and chiral charge quantum numbers arise as the fredholm indices of p up for certain unitary u on l2 r c2

loop groups anyons and the calogero sutherland model the positive energy representations of the loop group of u 1 are used to construct a boson anyon correspondence we compute all the correlation functions of our anyon fields and study an anyonic w algebra of unbounded operators with a common dense domain this algebra contains an operator with peculiar exchange relations with the anyon fields this operator can be interpreted as a second quantized calogero sutherland cs hamiltonian and may be used to solve the cs model in particular we inductively construct all eigenfunctions of the cs model from anyon correlation functions for all particle numbers and positive couplings

a superversion of quasifree second quantization i charged particles a formalism comprising and extending quasifree second quantization of charged bosons and fermions is presented the second quantization of one particle observables leads to current superalgebras and a super schwinger term shows up anticommuting parameters are introduced in order to construct super bogoliubov transformations mixing bosons and fermions as an application representations of lie superalgebras are given which are semidirect products of extensions of affine kac moody algebras and the virasoro algebra and of the super virasoro algebra

v algebras a particular class of unbounded operator algebras we consider a weak unbounded commutant for a set of unbounded operators and we examine op algebras which coincide with some of their bicommutant this class of op algebras called v algebras shows some properties close to those which hold true for bounded operator algebras

supersymmetric quantum mechanics defined as sesquilinear forms a formulation of supersymmetric quantum mechanics in terms of sesquilinear forms is presented otherwise occurring rather complicated domain questions are solved in a simple and natural way the authors formulate the axioms and describe a number of models supersymmetry transformations are implemented as superunitary transformations in a space defined over a grassmann algebra generalised bogoliubov transformations acting in that space are also formulated

complex dynamics of derivative free methods for nonlinear equations the dynamical behavior of two iterative derivative free schemes steffensen and m4 methods is studied in case of quadratic and cubic polynomials the parameter plane is analyzed for both procedures on quadratic polynomials different dynamical planes are showed when the mentioned methods are applied on particular cubic polynomials with real or complex coefficients the property of immersion of the basins of attraction in all cases is analyzed

two constructions of affine lie algebra representations and boson fermion correspondence in quantum field theory we establish an isomorphism between the vertex and spinor representations of affine lie algebras for types dl 1 and dl 1 2 we also study decomposition of spinor representations using the infinite family of casimir operators and prove that they are either irreducible or have two irreducible components we show that the vertex and spinor constructions of the representations can be reformulated in the language of two dimensional quantum field theory in this physical context the two constructions yield the generalized sine gordon and thirring models respectively already in renormalized form the isomorphism of representations implies an equivalence of these two models which is known in quantum field theory as the boson fermion correspondence

a new theoretical approach for prony s method abstract the problem treated is that of identifying the poles of a finite order system by observing its transient decay for a limited time after cessation of input the basic method for solving this problem is prony s method we present two new results about prony s method including an extension of the geometric method of henderson to the case of multiple poles and the development of a new method for eliminating known poles from a time series in order to compute the remaining poles

scattering matrix in external field problems we discuss several aspects of second quantized scattering operators s for fermions in external time dependent fields we derive our results on a general abstract level having in mind as a main application potentials of the yang mills type and in various dimensions we present a new and powerful method for proving the existence of s which is also applicable to other situations like external gravitational fields we also give two complementary derivations of the change of phase of the scattering matrix under generalized gauge transformations which can be used whenever our method of proving the existence of s applies the first is based on a causality argument i e s including phase is determined from a time evolution and the second exploits the geometry of certain infinite dimensional group extensions associated with the second quantization of one particle operators as a special case we obtain a hamiltonian derivation of the axial fermion yang mills anomaly and the schwinger terms related to it via the descent equations which is on the same footing and traces them back to a common root

a supersymmetric generalization of von neumann s theorem a formulation of supersymmetric quantum mechanics is given and superunitary and generalized canonical transformations are defined acting in a module next it is assumed that there are operators that give an irreducible representation of the canonical commutation and anticommutation relations respectively and it is proved that two such representations are connected by a uniquely determined superunitary transformation under suitable domain assumptions this extends the well known uniqueness theorem of von neumann to canonical anti commutation relations using anticommuting parameters

computation of exponentials in transient data prony s method is widely used to identify the poles of a time series a numerical implementation of prony s method based on the properties of the least squares solution of the transient data matrices is described and a practical indicator of the accuracy of the computational results that is based on the singular values of the transient data matrices is derived this algorithm can be applied to time series which contain simple or multiple poles

the dirac ramond operator on loops in flat space in this paper a rigorous construction of the s1 equivariant dirac operator i e dirac ramond operator on the space of mean zero loops in rd is given and its equivariant l2 index computed essential use is made of infinite tensor product representations of the canonical anticommutation relations algebra

fermion currents in 1 1 dimensions let f denote the fock space for a free massless fermion field in two space time dimensions if q and q5 denote the charge and chiral charge operators then f n1 n2fn1 n2 where fn1 n2 is the joint eigenspace of q and q5 with corresponding eigenvalues n1 and n2 the smeared time zero free fermion currents formally given by j f x x f x dx 0 1 f s r are in fact self adjoint densely defined operators on f and their exponentials generate a c algebra which leaves each subspace fn1 n2 invariant if a periodic box cutoff for the fermions is introduced uhlenbrock has shown that this c algebra acts irreducibly in each sector fn1 n2 we prove this same result without any cutoffs and determine the properties of the representations in each sector the importance of this result for the problem of constructing fermion fields from observables in two dimensional models such as those of thirring and schwinger is discussed

on the iteration of a rational function computer experiments with newton s method using newton s method to look for roots of a polynomial in the complex plane amounts to iterating a certain rational function this article describes the behavior of newton iteration for cubic polynomials after a change of variables these polynomials can be parametrized by a single complex parameter and the newton transformation has a single critical point other than its fixed points at the roots of the polynomial we describe the behavior of the orbit of the free critical point as the parameter is varied the julia set points where newton s method fail to converge is also pictured these sets exhibit an unexpected stability of their gross structure while the changes in small scale structure are intricate and subtle

a simple procedure to eliminate known poles from a time series an extremely simple procedure is presented for eliminating known or previously computed poles from a time series and for obtaining a deflated time series which contains only the remaining poles time series deflation can be used in combination with any numerical algorithm used to compute poles as an important example it is demonstrated how the time series deflation technique combined with prony s method can produce more accurate results than the use of prony s method alone

some covariant representations of massless boson fields considers the c algebra of the canonical commutation relations ccr acted on by a group g of one particle symmetry transformations v a symplectic operator t defines a representation pi t pi f omicron t where pi f is the fock representation the automorphisms of the ccr algebra that are induced by g are shown to be continuously implemented in pi t if and only if a v g av g is a continuous hilbert schmidt 1 cocycle of g here a is related to t by t exp a a being a suitable bounded antilinear self adjoint operator some new examples of fully poincare covariant representations of massless fields in 1 1 dimensions are constructed

implementability of gauge transformations and quantization of fermions in external fields quantization of fermions in an external soliton field leading to a representation of the canonical anticommutation relation car which is inequivalent to the representation connected to the massive dirac operator is studied classes of gauge and axial gauge transformations that can be unitarily implemented are determined in the latter case quantization conditions for gauge functions are obtained integers entering can be interpreted as winding numbers

groups of automorphisms of the canonical commutation and anticommutation relations observables of supersymmetric quantum mechanics are coded by taking the antisymmetric tensor product with anticommuting parameters next the authors define superunitary transformations which mix bosonic and fermionic degrees of freedom in order to construct automorphisms of the canonical anti commutation relations c a cr conversely every automorphism of the c a cr is implemented by an essentially unique superunitary transformation