Schwinger Dyson equations: Dynamical chiral symmetry breaking and confinement

International Nuclear Information System (INIS)

Roberts, C.D.

1992-01-01

A representative but not exhaustive review of the Schwinger-Dyson equation (SDE) approach to the nonperturbative study of QCD is presented. The main focus is the SDE for the quark self energy but studies of the gluon propagator and quark-gluon vertex are also discussed insofar as they are important to the quark SDE. The scope of this article is the application of these equations to the study of dynamical chiral symmetry breaking, quark confinement and the phenomenology of the spectrum and dynamics of QCD

Resummation of the 1/N-expansion of the non-linear σ-model by Dyson-Schwinger equations

International Nuclear Information System (INIS)

Drouffe, J.M.; Flyvbjerg, H.

1988-02-01

Dyson-Schwinger equations for the O(N)-symmetric non-linear σ-model are derived and expanded in 1/N. A closed set of equations is obtained by keeping only the leading term and the first correction term in this expansion. These equations are solved numerically in 2 dimensions on square lattices of sizes 50x50 and 100x100. Results for the magnetic susceptibility and the mass gap are compared with predictions of the ordinary 1/N-expansion and with Monte Carlo results. The results obtained with the Dyson-Schwinger equations show the same scaling behavior as found in the Monte Carlo results. This is not the behavior predicted by the perturbative renormalization group. (orig.)

Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques.

Science.gov (United States)

Han, Seungsuk; Yarkony, David R

2011-05-07

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.

Exact solutions of linearized Schwinger endash Dyson equation of fermion self-energy

International Nuclear Information System (INIS)

Zhou, B.

1997-01-01

The Schwinger endash Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the independent solutions, which, respectively, submit to irregular and regular ultraviolet boundary condition are derived and expounded. copyright 1997 American Institute of Physics

Coupled Dyson-Schwinger equations and effects of self-consistency

International Nuclear Information System (INIS)

Wu, S.S.; Zhang, H.X.; Yao, Y.J.

2001-01-01

Using the σ-ω model as an effective tool, the effects of self-consistency are studied in some detail. A coupled set of Dyson-Schwinger equations for the renormalized baryon and meson propagators in the σ-ω model is solved self-consistently according to the dressed Hartree-Fock scheme, where the hadron propagators in both the baryon and meson self-energies are required to also satisfy this coupled set of equations. It is found that the self-consistency affects the baryon spectral function noticeably, if only the interaction with σ mesons is considered. However, there is a cancellation between the effects due to the σ and ω mesons and the additional contribution of ω mesons makes the above effect insignificant. In both the σ and σ-ω cases the effects of self-consistency on meson spectral function are perceptible, but they can nevertheless be taken account of without a self-consistent calculation. Our study indicates that to include the meson propagators in the self-consistency requirement is unnecessary and one can stop at an early step of an iteration procedure to obtain a good approximation to the fully self-consistent results of all the hadron propagators in the model, if an appropriate initial input is chosen. Vertex corrections and their effects on ghost poles are also studied

Single-site Green function of the Dirac equation for full-potential electron scattering

Energy Technology Data Exchange (ETDEWEB)

Kordt, Pascal

2012-05-30

I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

Single-site Green function of the Dirac equation for full-potential electron scattering

International Nuclear Information System (INIS)

Kordt, Pascal

2012-01-01

I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

Gauge-independent bifurcation to the chiral-symmetry-breaking solution of the Dyson-Schwinger equation in continuum QED

International Nuclear Information System (INIS)

Rembiesa, P.

1990-01-01

The Dyson-Schwinger equation for the fermion propagator can be effectively solved in the approximation of the small-momentum-transfer vertex function. There exists a critical value of the coupling constant above which the ordinary infrared-divergent solution for massless quantum electrodynamics bifurcates to another, massive solution. With a proper transverse part included in the vertex function, the bifurcation point is gauge independent, the new solution is finite in all gauges, and does not require momentum cutoffs of any kind

Dyson-Schwinger equations and N = 4 SYM in Landau gauge

Energy Technology Data Exchange (ETDEWEB)

Maas, Axel; Zitz, Stefan [University of Graz, Institute of Physics, NAWI Graz, Graz (Austria)

2016-03-15

N = 4 Super Yang-Mills theory is a highly constrained theory, and therefore a valuable tool to test the understanding of less constrained Yang-Mills theories. Our aim is to use it to test our understanding of both the Landau gauge beyond perturbation theory and the truncations of Dyson-Schwinger equations in ordinary Yang-Mills theories. We derive the corresponding equations within the usual one-loop truncation for the propagators after imposing the Landau gauge. We find a conformal solution in this approximation, which surprisingly resembles many aspects of ordinary Yang-Mills theories. We furthermore discuss which role the Gribov-Singer ambiguity in this context could play, should it exist in this theory. (orig.)

Estimations for the Schwinger functions of relativistic quantum field theories

International Nuclear Information System (INIS)

Mayer, C.D.

1981-01-01

Schwinger functions of a relativistic neutral scalar field the basing test function space of which is S or D are estimated by methods of the analytic continuation. Concerning the behaviour in coincident points it is shown: The two-point singularity of the n-point Schwinger function of a field theory is dominated by an inverse power of the distance of both points modulo a multiplicative constant, if the other n-2 points a sufficiently distant and remain fixed. The power thereby, depends only on n. Using additional conditions on the field the independence of the power on n may be proved. Concerning the behaviour at infinite it is shown: The n-point Schwinger functions of a field theory are globally bounded, if the minimal distance of the arguments is positive. The bound depends only on n and the minimal distance of the arguments. (orig.) [de

Time-ordered products and Schwinger functions

International Nuclear Information System (INIS)

Eckmann, J.P.; Epstein, H.

1979-01-01

It is shown that every system of time-ordered products for a local field theory determines a related system of Schwinger functions possessing an extended form of Osterwalder-Schrader positivity and that the converse is true provided certain growth conditions are satisfied. This is applied to the phi 3 4 theory and it is shown that the time-ordered functions and S-matrix elements admit the standard perturbation series as asymptotic expansions. (orig.) [de

Multiplicative renormalizability and self-consistent treatments of the Schwinger-Dyson equations

International Nuclear Information System (INIS)

Brown, N.; Dorey, N.

1989-11-01

Many approximations to the Schwinger-Dyson equations place constraints on the renormalization constants of a theory. The requirement that the solutions to the equations be multiplicatively renormalizable also places constraints on these constants. Demanding that these two sets of constraints be compatible is an important test of the self-consistency of the approximations made. We illustrate this idea by considering the equation for the fermion propagator in massless quenched quantum electrodynamics, (QED), checking the consistency of various approximations. In particular, we show that the much used 'ladder' approximation is self-consistent, provided that the coupling constant is renormalized in a particular way. We also propose another approximation which satisfies this self-consistency test, but requires that the coupling be unrenormalized, as should be the case in the full quenched approximation. This new approximation admits an exact solution, which also satisfies the renormalization group equation for the quenched approximation. (author)

Resurgent transseries & Dyson–Schwinger equations

Energy Technology Data Exchange (ETDEWEB)

Klaczynski, Lutz, E-mail: klacz@mathematik.hu-berlin.de

2016-09-15

We employ resurgent transseries as algebraic tools to investigate two self-consistent Dyson–Schwinger equations, one in Yukawa theory and one in quantum electrodynamics. After a brief but pedagogical review, we derive fixed point equations for the associated anomalous dimensions and insert a moderately generic log-free transseries ansatz to study the possible strictures imposed. While proceeding in various stages, we develop an algebraic method to keep track of the transseries’ coefficients. We explore what conditions must be violated in order to stay clear of fixed point theorems to eschew a unique solution, if so desired, as we explain. An interesting finding is that the flow of data between the different sectors of the transseries shows a pattern typical of resurgence, i.e. the phenomenon that the perturbative sector of the transseries talks to the nonperturbative ones in a one-way fashion. However, our ansatz is not exotic enough as it leads to trivial solutions with vanishing nonperturbative sectors, even when logarithmic monomials are included. We see our result as a harbinger of what future work might reveal about the transseries representations of observables in fully renormalised four-dimensional quantum field theories and adduce a tentative yet to our mind weighty argument as to why one should not expect otherwise. This paper is considerably self-contained. Readers with little prior knowledge are let in on the basic reasons why perturbative series in quantum field theory eventually require an upgrade to transseries. Furthermore, in order to acquaint the reader with the language utilised extensively in this work, we also provide a concise mathematical introduction to grid-based transseries.

Resurgent transseries & Dyson-Schwinger equations

Science.gov (United States)

Klaczynski, Lutz

2016-09-01

We employ resurgent transseries as algebraic tools to investigate two self-consistent Dyson-Schwinger equations, one in Yukawa theory and one in quantum electrodynamics. After a brief but pedagogical review, we derive fixed point equations for the associated anomalous dimensions and insert a moderately generic log-free transseries ansatz to study the possible strictures imposed. While proceeding in various stages, we develop an algebraic method to keep track of the transseries' coefficients. We explore what conditions must be violated in order to stay clear of fixed point theorems to eschew a unique solution, if so desired, as we explain. An interesting finding is that the flow of data between the different sectors of the transseries shows a pattern typical of resurgence, i.e. the phenomenon that the perturbative sector of the transseries talks to the nonperturbative ones in a one-way fashion. However, our ansatz is not exotic enough as it leads to trivial solutions with vanishing nonperturbative sectors, even when logarithmic monomials are included. We see our result as a harbinger of what future work might reveal about the transseries representations of observables in fully renormalised four-dimensional quantum field theories and adduce a tentative yet to our mind weighty argument as to why one should not expect otherwise. This paper is considerably self-contained. Readers with little prior knowledge are let in on the basic reasons why perturbative series in quantum field theory eventually require an upgrade to transseries. Furthermore, in order to acquaint the reader with the language utilised extensively in this work, we also provide a concise mathematical introduction to grid-based transseries.

A Dyson-Schwinger approach to finite temperature QCD

Energy Technology Data Exchange (ETDEWEB)

Mueller, Jens Andreas

2011-10-26

The different phases of quantum chromodynamics at finite temperature are studied. To this end the nonperturbative quark propagator in Matsubara formalism is determined from its equation of motion, the Dyson-Schwinger equation. A novel truncation scheme is introduced including the nonperturbative, temperature dependent gluon propagator as extracted from lattice gauge theory. In the first part of the thesis a deconfinement order parameter, the dual condensate, and the critical temperature are determined from the dependence of the quark propagator on the temporal boundary conditions. The chiral transition is investigated by means of the quark condensate as order parameter. In addition differences in the chiral and deconfinement transition between gauge groups SU(2) and SU(3) are explored. In the following the quenched quark propagator is studied with respect to a possible spectral representation at finite temperature. In doing so, the quark propagator turns out to possess different analytic properties below and above the deconfinement transition. This result motivates the consideration of an alternative deconfinement order parameter signaling positivity violations of the spectral function. A criterion for positivity violations of the spectral function based on the curvature of the Schwinger function is derived. Using a variety of ansaetze for the spectral function, the possible quasi-particle spectrum is analyzed, in particular its quark mass and momentum dependence. The results motivate a more direct determination of the spectral function in the framework of Dyson-Schwinger equations. In the two subsequent chapters extensions of the truncation scheme are considered. The influence of dynamical quark degrees of freedom on the chiral and deconfinement transition is investigated. This serves as a first step towards a complete self-consistent consideration of dynamical quarks and the extension to finite chemical potential. The goodness of the truncation is verified first

A Dyson-Schwinger approach to finite temperature QCD

International Nuclear Information System (INIS)

Mueller, Jens Andreas

2011-01-01

The different phases of quantum chromodynamics at finite temperature are studied. To this end the nonperturbative quark propagator in Matsubara formalism is determined from its equation of motion, the Dyson-Schwinger equation. A novel truncation scheme is introduced including the nonperturbative, temperature dependent gluon propagator as extracted from lattice gauge theory. In the first part of the thesis a deconfinement order parameter, the dual condensate, and the critical temperature are determined from the dependence of the quark propagator on the temporal boundary conditions. The chiral transition is investigated by means of the quark condensate as order parameter. In addition differences in the chiral and deconfinement transition between gauge groups SU(2) and SU(3) are explored. In the following the quenched quark propagator is studied with respect to a possible spectral representation at finite temperature. In doing so, the quark propagator turns out to possess different analytic properties below and above the deconfinement transition. This result motivates the consideration of an alternative deconfinement order parameter signaling positivity violations of the spectral function. A criterion for positivity violations of the spectral function based on the curvature of the Schwinger function is derived. Using a variety of ansaetze for the spectral function, the possible quasi-particle spectrum is analyzed, in particular its quark mass and momentum dependence. The results motivate a more direct determination of the spectral function in the framework of Dyson-Schwinger equations. In the two subsequent chapters extensions of the truncation scheme are considered. The influence of dynamical quark degrees of freedom on the chiral and deconfinement transition is investigated. This serves as a first step towards a complete self-consistent consideration of dynamical quarks and the extension to finite chemical potential. The goodness of the truncation is verified first

Dyson-Schwinger equations for the non-linear σ-model

International Nuclear Information System (INIS)

Drouffe, J.M.; Flyvbjerg, H.

1989-08-01

Dyson-Schwinger equations for the O(N)-symmetric non-linear σ-model are derived. They are polynomials in N, hence 1/N-expanded ab initio. A finite, closed set of equations is obtained by keeping only the leading term and the first correction term in this 1/N-series. These equations are solved numerically in two dimensions on square lattices measuring 50x50, 100x100, 200x200, and 400x400. They are also solved analytically at strong coupling and at weak coupling in a finite volume. In these two limits the solution is asymptotically identical to the exact strong- and weak-coupling series through the first three terms. Between these two limits, results for the magnetic susceptibility and the mass gap are identical to the Monte Carlo results available for N=3 and N=4 within a uniform systematic error of O(1/N 3 ), i.e. the results seem good to O(1/N 2 ), though obtained from equations that are exact only to O(1/N). This is understood by seeing the results as summed infinite subseries of the 1/N-series for the exact susceptibility and mass gap. We conclude that the kind of 1/N-expansion presented here converges as well as one might ever hope for, even for N as small as 3. (orig.)

Schwinger-Dyson loop equations as the w1+∞-like constraints for hermitian multi-matrix chain model at finite N

International Nuclear Information System (INIS)

Cheng, Yi-Xin

1992-01-01

The Schwinger-Dyson loop equations for the hermitian multi-matrix chain models at finite N, are derived from the Ward identities of the partition functional under the infinitesimal field transformations. The constraint operators W n (m) satisfy the w 1+∞ -like algebra up to a linear combination of the lower spin operators. We find that the all the higher spin constraints are reducible to the Virasoro-type constraints for all the matrix chain models. (author)

On the Lippmann--Schwinger equation for atom--diatom collisions: A rotating frame treatment

International Nuclear Information System (INIS)

Kouri, D.J.; Heil, T.G.; Shimoni, Y.

1976-01-01

The use of a rotating frame description of molecular collisions is reconsidered within the framework of the Lippmann--Schwinger equation for the transition or T operator. The present approach explicitly displays the proper boundary conditions which apply to descriptions of such collisions in the rotating frame whose Z axis follows the scattering vector. The resulting body frame equations are shown to lead naturally to the introduction of ''body frame Bessel and Hankel functions,'' J/subJ//subj//sup lambda//sup lambda//sup prime/ and H/subJ//subj//sup lambda//sup lambda//sup prime/ (BFBF), which are solutions of the unperturbed Hamiltonian for the collision transformed to the rotating frame. It is found that the BFBF can be defined in several ways differing by phase factors that affect their asymptotic form. Two particular choices are examined, one of which leads to a simple asymptotic form of the wavefunction, and the other leads to a somewhat more complicated form. Both are shown to yield the j/subz/-conserving coupled states equations of McGuire and Kouri but slightly different approximations are required in the two cases. The implication of these results as to the accuracy of the j/subz/CCS method are discussed

Schwinger variational principle in the nuclear two-body problem and multichannel theory

International Nuclear Information System (INIS)

Zubarev, A.L.; Podkopaev, A.P.

1978-01-01

The aim of the investigation is to study the Schwinger variational principle in the nuclear two-body problem and the multichannel theory. An approach is proposed to problems of the potential scattering based on the substitution of the exact potential operator V by the finite rank operator Vsup((n)) with which the dynamic equations are solved exactly. The functionals obtained for observed values coincide with corresponding expressions derived by the Schwinger variational principle with the set of test functions. The determination of the Schwinger variational principle is given. The method is given for finding amplitude of the double-particle scattering with the potential Vsup((n)). The corresponding amplitudes are constructed within the framework of the multichannel potential model. Interpolation formula for determining amplitude, which describes with high accuracy a process of elastic scattering for any energies, is obtained. On the basis of the above method high-energy amplitude may be obtained within the range of small and large scattering angles

Application and development of the Schwinger multichannel scattering theory and the partial differential equation theory of electron-molecule scattering

Science.gov (United States)

Weatherford, Charles A.

1993-01-01

One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.

Wilsonian Renormalization Group and the Lippmann-Schwinger Equation with a Multitude of Cutoff Parameters

Science.gov (United States)

Epelbaum, E.; Gegelia, J.; Meißner, Ulf-G.

2018-03-01

The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed. Supported in part by BMBF under Grant No. 05P2015 - NUSTAR R&D), DFG and NSFC through Funds Provided to the Sino- German CRC 110 “Symmetries and the Emergence of Structure in QCD”, National Natural Science Foundation of China under Grant No. 11621131001, DFG Grant No. TRR110, the Georgian Shota Rustaveli National Science Foundation (grant FR/417/6-100/14) and the CAS President’s International Fellowship Initiative (PIFI) under Grant No. 2017VMA0025

Schwinger-Keldysh superspace in quantum mechanics

Science.gov (United States)

Geracie, Michael; Haehl, Felix M.; Loganayagam, R.; Narayan, Prithvi; Ramirez, David M.; Rangamani, Mukund

2018-05-01

We examine, in a quantum mechanical setting, the Hilbert space representation of the Becchi, Rouet, Stora, and Tyutin (BRST) symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals in coarse-grained systems with dissipation, or in open quantum systems. Operationally, this entails uplifting the standard Schwinger-Keldysh two-copy formalism into superspace by appending BRST ghost degrees of freedom. These statements were previously argued at the level of the correlation functions. We provide herein a complementary perspective by working out the Hilbert space structure explicitly. Our analysis clarifies two crucial issues not evident in earlier works: first, certain background ghost insertions necessary to reproduce the correct Schwinger-Keldysh correlators arise naturally, and, second, the Schwinger-Keldysh difference operators are systematically dressed by the ghost bilinears, which turn out to be necessary to give rise to a consistent operator algebra. We also elaborate on the structure of the final state (which is BRST closed) and the future boundary condition of the ghost fields.

Calculation of the fermionic determinant in the Schwinger model

International Nuclear Information System (INIS)

Dias, S.A.; Linhares, C.A.

1991-01-01

We compute explicitly the fermionic determinant and the effective action for the generalized Schwinger model in two dimensions and compare it with respective results for the particular cases of the Schwinger, chiral Schwinger and axial Schwinger models. The parameters that signal the ambiguity in the regularization scheme fo the determinant are introduced through the point-splitting method. The Wess-Zumino functional is also obtained and compared with the known expressions for the above-mentioned particular cases. (author)

On Schwinger terms in (3+1)-dimensions

International Nuclear Information System (INIS)

Langmann, E.

1991-02-01

Schwinger terms arise in current algebras due to regularisations required for a consistent construction of the currents. In (1+1)-dimensions one has to normal order, and the resulting Schwinger term is the well-known Kac-Peterson cocycle. In higher dimensions, an additional wave function renormalisation is necessary leading to operator valued Schwinger terms. A rigorous, nonperturbative construction of such Schwinger terms was given by Mickelsson and Rajeev [Commun. Math. Phys. 116, 365 (1988)] in terms of determinant bundles over infinite dimensional Grassmannians. We present an alternative construction of this Schwinger term by means of quasi-free second quantization of fermions. First, we review this formalism and the construction of current algebras in (1+1)-dimensions within this framework: gauge transformations correspond to unitarily implementable Bogoliubov transformations (BTS), and the currents can be obtained from the implementers of these BTS. It is argued that in higher dimensions, gauge transformations give rise to BTS which are not unitarily implementable. We propose an implementation of such BTS by quadratic forms which allows us to obtain current algebras in (3+1)-dimensions and the Mickelsson-Rajeev Schwinger term in a simple and natural way. (author)

Nature of the Schwinger term in spinor electrodynamics. [Dispersion formulation,dimensions,green functions,c-number,linear unitarity condition

Energy Technology Data Exchange (ETDEWEB)

Nishijima, K; Sasaki, R [Tokyo Univ. (Japan). Dept. of Physics

1975-06-01

On the basis of the dispersion formulation of field theories the Schwinger term in spinor electrodynamics is shown to be a c-number. The essence of the proof consists in the dimensional argument and the characteristic features of the linear unitarity condition for a set of Green's functions involving the Schwinger term.

Schwinger's formula and the partition function for the bosonic and fermionic harmonic oscillators

International Nuclear Information System (INIS)

Albuquerque, L.C. de; Farina, C.; Rabello, S.J.

1994-01-01

We use Schwinger's formula, introduced by himself in the early fifties to compute effective actions for Qed, and recently applied to the Casimir effect, to obtain the partition functions for both the bosonic and fermionic harmonic oscillators. (author)

Quantum statistical field theory an introduction to Schwinger's variational method with Green's function nanoapplications, graphene and superconductivity

CERN Document Server

Morgenstern Horing, Norman J

2017-01-01

This book provides an introduction to the methods of coupled quantum statistical field theory and Green's functions. The methods of coupled quantum field theory have played a major role in the extensive development of nonrelativistic quantum many-particle theory and condensed matter physics. This introduction to the subject is intended to facilitate delivery of the material in an easily digestible form to advanced undergraduate physics majors at a relatively early stage of their scientific development. The main mechanism to accomplish this is the early introduction of variational calculus and the Schwinger Action Principle, accompanied by Green's functions. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green's function equations-of-motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and nonequilibrium Green's functions...

Phase structure of hot and/or dense QCD with the Schwinger-Dyson equation

Energy Technology Data Exchange (ETDEWEB)

Takagi, Satoshi [Nagoya Univ., Nagoya, Aichi (Japan)

2002-09-01

We investigate the phase structure of the hot and/or dense QCD using the Schwinger-Dyson equation (SDE) with the improved ladder approximation in the Landau gauge. We solve the coupled SDE for the Majorana masses of the quark and antiquark (separately from the SDE for the Dirac mass) in the finite temperature and/or chemical potential region. The resultant phase structure is rather different from those by other analyses. In addition to this analysis we investigate the phase structure with the different two types of the SDE, in one of which the Majorana mass gap of the antiquark is neglected, while in the other of which the Majorana mass gap of the quark and that of the antiquark are set to be equal. The effect of the Debye mass of the gluon on the phase structure is also investigated. (author)

Hamiltonian formulation of QCD in the Schwinger gauge

International Nuclear Information System (INIS)

Schutte, D.

1989-01-01

The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a specially suited framework for the computation of bound-state (hadron) properties. The most important reasons are the manifest rotation invariance, the lack of a Gribov horizon (giving standard many-body techniques a better chance), and the fact that a regularization analogous to the lattice regularization is easily implementable. Some details of the Schwinger-gauge Hamiltonian theory are discussed

Aliasing modes in the lattice Schwinger model

International Nuclear Information System (INIS)

Campos, Rafael G.; Tututi, Eduardo S.

2007-01-01

We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considered with boundaries new modes appear due to aliasing effects. In the continuum limit, however, this lattice yields also a Klein-Gordon equation with a reduced mass

Supersymmetric two-particle equations

International Nuclear Information System (INIS)

Sissakyan, A.N.; Skachkov, N.B.; Shevchenko, O.Yu.

1986-01-01

In the framework of the scalar superfield model, a particular case of which is the well-known Wess-Zumino model, the supersymmetric Schwinger equations are found. On their basis with the use of the second Legendre transformation the two-particle supersymmetric Edwards and Bethe-Salpeter equations are derived. A connection of the kernels and inhomogeneous terms of these equations with generating functional of the second Legendre transformation is found

Faddeev-Jackiw Hamiltonian reduction for free and gauged Rarita-Schwinger theories

Energy Technology Data Exchange (ETDEWEB)

Dengiz, Suat [Massachusetts Institute of Technology, Center for Theoretical Physics, Cambridge, MA (United States)

2016-10-15

We study the Faddeev-Jackiw symplectic Hamiltonian reduction for 3 + 1-dimensional free and Abelian gauged Rarita-Schwinger theories that comprise Grassmannian fermionic fields. We obtain the relevant fundamental brackets and find that they are in convenient forms for quantization. The brackets are independent of whether the theories contain mass or gauge fields, and the structures of constraints and symplectic potentials largely determine characteristic behaviors of the theories. We also note that, in contrast to the free massive theory, the Dirac field equations for free massless Rarita-Schwinger theory cannot be obtained in a covariant way. (orig.)

On the equivalence between the Schwinger and axial models

International Nuclear Information System (INIS)

Souza Dutra, A. de.

1991-01-01

We show the equivalence between the Schwinger and axial models, in the sense that all Green's functions of one model can be obtained from those of the other, and that both models have the same effective Lagrangian density (and so they have equal partition functions associated with them). In particular, we show that the two models have the same chiral anomaly. Finally it is demonstrated that the Schwinger model can keep gauge invariance for an arbitrary mass, dispensing with an additional gauge group integration. (author)

Color-superconductivity from a Dyson-Schwinger perspective

International Nuclear Information System (INIS)

Nickel, M.D.J.

2007-01-01

Color-superconducting phases of quantum chromodynamics at vanishing temperatures and high densities are investigated. The central object is the one-particle Green's function of the fermions, the so-called quark propagator. It is determined by its equation of motion, the Dyson-Schwinger equation. To handle Dyson-Schwinger equations a successfully applied truncation scheme in the vacuum is extended to finite densities and gradually improved. It is thereby guaranteed that analytical results at asymptotically large densities are reproduced. This way an approach that is capable to describe known results in the vacuum as well as at high densities is applied to densities of astrophysical relevance for the first time. In the first part of the thesis the framework of the investigations with focus on the extension to finite densities is outlined. Physical observables are introduced which can be extracted from the propagator. In the following a minimal truncation scheme is presented. To point out the complexity of our approach in comparison to phenomenological models of quantum chromodynamics the chirally unbroken phase is discussed first. Subsequently color-superconducting phases for massless quarks are investigated. Furthermore the role of finite quark masses and neutrality constraints at moderate densities is studied. In contrast to phenomenological models the so-called CFL phase is found to be the ground state for all relevant densities. In the following part the applicability of the maximum entropy method for the extraction of spectral functions from numerical results in Euclidean space-time is demonstrated. As an example the spectral functions of quarks in the chirally unbroken and color-superconducting phases are determined. Hereby the results of our approach are presented in a new light. For instance the finite width of the quasiparticles in the color-superconducting phase becomes apparent. In the final chapter of this work extensions of our truncation scheme in

Color-superconductivity from a Dyson-Schwinger perspective

Energy Technology Data Exchange (ETDEWEB)

Nickel, M.D.J.

2007-12-20

Color-superconducting phases of quantum chromodynamics at vanishing temperatures and high densities are investigated. The central object is the one-particle Green's function of the fermions, the so-called quark propagator. It is determined by its equation of motion, the Dyson-Schwinger equation. To handle Dyson-Schwinger equations a successfully applied truncation scheme in the vacuum is extended to finite densities and gradually improved. It is thereby guaranteed that analytical results at asymptotically large densities are reproduced. This way an approach that is capable to describe known results in the vacuum as well as at high densities is applied to densities of astrophysical relevance for the first time. In the first part of the thesis the framework of the investigations with focus on the extension to finite densities is outlined. Physical observables are introduced which can be extracted from the propagator. In the following a minimal truncation scheme is presented. To point out the complexity of our approach in comparison to phenomenological models of quantum chromodynamics the chirally unbroken phase is discussed first. Subsequently color-superconducting phases for massless quarks are investigated. Furthermore the role of finite quark masses and neutrality constraints at moderate densities is studied. In contrast to phenomenological models the so-called CFL phase is found to be the ground state for all relevant densities. In the following part the applicability of the maximum entropy method for the extraction of spectral functions from numerical results in Euclidean space-time is demonstrated. As an example the spectral functions of quarks in the chirally unbroken and color-superconducting phases are determined. Hereby the results of our approach are presented in a new light. For instance the finite width of the quasiparticles in the color-superconducting phase becomes apparent. In the final chapter of this work extensions of our truncation scheme in

Lattice-QCD based Schwinger-Dyson approach for Chiral phase transition

International Nuclear Information System (INIS)

Iida, Hideaki; Oka, Makoto; Suganuma, Hideo

2005-01-01

Dynamical chiral-symmetry breaking in QCD is studied with the Schwinger-Dyson (SD) formalism based on lattice QCD data, i.e., LQCD-based SD formalism. We extract the SD kernel function K(p 2 ) in an Ansatzindependent manner from the lattice data of the quark propagator in the Landau gauge. As remarkable features, we find infrared vanishing and intermediate enhancement of the SD kernel function K(p 2 ). We apply the LQCD-based SD equation to thermal QCD with the quark chemical potential μ q . We find chiral symmetry restoration at T c ∼100MeV for μ q =0. The real part of the quark mass function decreases as T and μ q . At finite density, there appears the imaginary part of the quark mass function, which would lead to the width broadening of hadrons

What is the trouble with Dyson-Schwinger equations?

International Nuclear Information System (INIS)

Kreimer, D.

2004-01-01

We discuss similarities and differences between Green Functions in Quantum Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint equations which originate from an underlying Hopf algebra structure. Typically, the equation is linear for the polylog, and non-linear for Green Functions. We argue though that the crucial difference lies not in the non-linearity of the latter, but in the appearance of non-trivial representation theory related to transcendental extensions of the number field which governs the linear solution. An example is studied to illuminate this point

On the algebraic structure of covariant anomalies and covariant Schwinger terms

International Nuclear Information System (INIS)

Kelnhofer, G.

1992-01-01

A cohomological characterization of covariant anomalies and covariant Schwinger terms in an anomalous Yang-Mills theory is formulated and w ill be geometrically interpreted. The BRS and anti-BRS transformations are defined as purely differential geometric objects. Finally the covariant descent equations are formulated within this context. (author)

Supersymmetry and the chiral Schwinger model

International Nuclear Information System (INIS)

Amorim, R.; Das, A.

1998-01-01

We have constructed the N= (1) /(2) supersymmetric general Abelian model with asymmetric chiral couplings. This leads to a N= (1) /(2) supersymmetrization of the Schwinger model. We show that the supersymmetric general model is plagued with problems of infrared divergence. Only the supersymmetric chiral Schwinger model is free from such problems and is dynamically equivalent to the chiral Schwinger model because of the peculiar structure of the N= (1) /(2) multiplets. copyright 1998 The American Physical Society

The generalized chiral Schwinger model on the two-sphere

International Nuclear Information System (INIS)

Bassetto, A.

1995-01-01

A family of theories which interpolate between vector and chiral Schwinger models is studied on the two-sphere S 2 . The conflict between the loss of gauge invariance and global geometrical properties is solved by introducing a fixed background connection. In this way the generalized Dirac-Weyl operator can be globally defined on S 2 . The generating functional of the Green functions is obtained by taking carefully into account the contribution of gauge fields with non-trivial topological charge and of the related zero-modes of the Dirac determinant. In the decompactification limit, the Green functions of the flat case are recovered; in particular the fermionic condensate in the vacuum vanishes, at variance with its behaviour in the vector Schwinger model. ((orig.))

Some physical applications of fractional Schroedinger equation

International Nuclear Information System (INIS)

Guo Xiaoyi; Xu Mingyu

2006-01-01

The fractional Schroedinger equation is solved for a free particle and for an infinite square potential well. The fundamental solution of the Cauchy problem for a free particle, the energy levels and the normalized wave functions of a particle in a potential well are obtained. In the barrier penetration problem, the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined. In the quantum scattering problem, according to the fractional Schroedinger equation, the Green's function of the Lippmann-Schwinger integral equation is given

Schwinger-Dyson operator of Yang-Mills matrix models with ghosts and derivations of the graded shuffle algebra

NARCIS (Netherlands)

Krishnaswami, G.S.

2008-01-01

We consider large-N multi-matrix models whose action closely mimics that of Yang-Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G( ), are quadratic equations

Comparison of the anomalous and non-anomalous generalized Schwinger models via functional formalism

International Nuclear Information System (INIS)

Souza Dutra, A. de.

1992-01-01

The Green functions of the two versions of the two versions of the generalized Schwinger model, the anomalous and the non-anomalous one, in their higher order Lagrangian density form are calculated. Furthermore it is shown through a sequence of transformations that the bosonized Lagrangian density is equivalent to the former, at least for the bosonic correlation functions. The introduction of the sources from the beginning, leading to a gauge-invariant source term is also considered. It is verified that the two models have the same correlation functions only of the gauge-invariant sector is taken into account. Finally it is presented a generalization of the Wess-Zumino term, and its physical consequences are studied, in particular the appearance of gauge-dependent massive excitations. (author)

Kinetic equations with pairing correlations

International Nuclear Information System (INIS)

Fauser, R.

1995-12-01

The Gorkov equations are derived for a general non-equilibrium system. The Gorkov factorization is generalized by the cumulant expansion of the 2-particle correlation and by a generalized Wick theorem in the case of a perturbation expansion. A stationary solution for the Green functions in the Schwinger-Keldysh formalism is presented taking into account pairing correlations. Especially the effects of collisional broadening on the spectral functions and Green functions is discussed. Kinetic equations are derived in the quasi-particle approximation and in the case of particles with width. Explicit expressions for the self-energies are given. (orig.)

SU(N) Irreducible Schwinger Bosons

OpenAIRE

Mathur, Manu; Raychowdhury, Indrakshi; Anishetty, Ramesh

2010-01-01

We construct SU(N) irreducible Schwinger bosons satisfying certain U(N-1) constraints which implement the symmetries of SU(N) Young tableaues. As a result all SU(N) irreducible representations are simple monomials of $(N-1)$ types of SU(N) irreducible Schwinger bosons. Further, we show that these representations are free of multiplicity problems. Thus all SU(N) representations are made as simple as SU(2).

Integral equation for Coulomb problem

International Nuclear Information System (INIS)

Sasakawa, T.

1986-01-01

For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems

The gravitational Schwinger effect and attenuation of gravitational waves

Science.gov (United States)

McDougall, Patrick Guarneri

This paper will discuss the possible production of photons from gravitational waves. This process is shown to be possible by examining Feynman diagrams, the Schwinger Effect, and Hawking Radiation. The end goal of this project is to find the decay length of a gravitational wave and assert that this decay is due to photons being created at the expense of the gravitational wave. To do this, we first find the state function using the Klein Gordon equation, then find the current due to this state function. We then take the current to be directly proportional to the production rate per volume. This is then used to find the decay length that this kind of production would produce, gives a prediction of how this effect will change the distance an event creating a gravitational wave will be located, and shows that this effect is small but can be significant near the source of a gravitational wave.

Dynamically Assisted Schwinger Mechanism

International Nuclear Information System (INIS)

Schuetzhold, Ralf; Gies, Holger; Dunne, Gerald

2008-01-01

We study electron-positron pair creation from the Dirac vacuum induced by a strong and slowly varying electric field (Schwinger effect) which is superimposed by a weak and rapidly changing electromagnetic field (dynamical pair creation). In the subcritical regime where both mechanisms separately are strongly suppressed, their combined impact yields a pair creation rate which is dramatically enhanced. Intuitively speaking, the strong electric field lowers the threshold for dynamical particle creation--or, alternatively, the fast electromagnetic field generates additional seeds for the Schwinger mechanism. These findings could be relevant for planned ultrahigh intensity lasers

A Csup(*)-algebra approach to the Schwinger model

International Nuclear Information System (INIS)

Carey, A.L.; Hurst, C.A.

1981-01-01

If cutoffs are introduced then existing results in the literature show that the Schwinger model is dynamically equivalent to a boson model with quadratic Hamiltonian. However, the process of quantising the Schwinger model destroys local gauge invariance. Gauge invariance is restored by the addition of a counterterm, which may be seen as a finite renormalisation, whereupon the Schwinger model becomes dynamically equivalent to a linear boson gauge theory. This linear model is exactly soluble. We find that different treatments of the supplementary (i.e. Lorentz) condition lead to boson models with rather different properties. We choose one model and construct, from the gauge invariant subalgebra, a class of inequivalent charge sectors. We construct sectors which coincide with those found by Lowenstein and Swieca for the Schwinger model. A reconstruction of the Hilbert space on which the Schwinger model exists is described and fermion operators on this space are defined. (orig.)

The Schwinger variational principle in the quantum-mechanical three-body problem

International Nuclear Information System (INIS)

Podkopaev, A.P.; Subarev, A.I.; Wrzecionko, J.

1978-01-01

The Schwinger variational principle (SVP) is applied to problems of atomic (e + H scattering), mesoatomic (p(dμ) scattering) and nuclear (pion-deuteron scattering) physics. The convergence of the Schwinger variational iterative method is investigated. It is shown that in some cases there occurs a pathological convergence. It means that the iterative procedure is convergent, but not to the exact solution. The method of strong coupling of channels is reformulated on the basis of SVP. it permits the summation over all closed channels. The obtained equations are applied to the calculations of the low energy scattering parameters of the following processes: e + H → e + H; πd → πd. The dependence on πN scattering lengths and effective radii is investigated. It is shown that the contribution of closed channels to the π - d scattering length is 30 percent

Hadronic contribution to the muon g-2: A Dyson-Schwinger perspective

Science.gov (United States)

Goecke, T.; Fischer, C. S.; Williams, R.

2012-04-01

We summarize our results for hadronic contributions to the anomalous magnetic moment of the muon (aμ), the one from hadronic vacuum-polarization (HVP) and the light-by-light scattering contribution (LBL), obtained from the Dyson-Schwinger equations (DSEs) of QCD. In the case of HVP we find good agreement with model independent determinations from dispersion relations for aμHV P as well as for the Adler function with deviations well below the ten percent level. From this we conclude that the DSE approach should be capable of describing aμLBL with similar accuracy. We also present results for LBL using a resonance expansion of the quark-anti-quark T-matrix. Our preliminary value is aμLBL=(217±91)×10-11.

Running coupling constant of a gauge theory in the framework of the Schwinger-Dyson equation: Infrared behavior of three-dimensional quantum electrodynamics

International Nuclear Information System (INIS)

Kondo, K.

1997-01-01

We discuss how to define and obtain the running coupling of a gauge theory in the approach of the Schwinger-Dyson (SD) equation, in order to perform a nonperturbative study of the theory. For this purpose, we introduce the nonlocally generalized gauge fixing into the SD equation, which is used to define the running coupling constant (this method is applicable only to a gauge theory). Some advantages and the validity of this approach are exemplified in QED 3 . This confirms the slowing down of the rate of decrease of the running coupling and the existence of the nontrivial infrared fixed point (in the normal phase) of QED 3 , claimed recently by Aitchison and Mavromatos, without so many of their approximations. We also argue that the conventional approach is recovered by applying the (inverse) Landau-Khalatnikov transformation to the nonlocal gauge result. copyright 1997 The American Physical Society

On a Kubo-Martin-Schwinger state of the Sine-Gordon system

International Nuclear Information System (INIS)

Peskov, N.V.

1986-01-01

This paper considers the Sine-Gordon equation on a finite interval as a Hamiltonian system. A Gaussian measure is defined on an extension of the phase space. It is shown that the partition funciton Z employed in the statistical mechanics of the solitons is an integral with respect to this measure. An algebra of observables is defined and on it a state is constructed which satisfies the Kubo-Martin-Schwinger condition

Schwinger terms from external field problems

Science.gov (United States)

Ekstrand, Christian

1999-01-01

The current algebra for second quantized chiral fermions in an external eld contains Schwinger terms. These are studied in two di erent ways. Both are non-perturbative and valid for arbitrary odd dimension of the physical space, although explicit expressions are only given for lower dimensions. The thesis is an introductory text to the four appended research papers. In the rst two papers, Schwinger terms are studied by realizing gauge transformations as linear operators acting on sections of the bundle of Fock spaces parametrized byvector potentials. Bosons and fermions are mixed in a Z2-graded fashion. Charged particles are considered in the rst paper and neutral particles in the second. In the the third and the fourth paper, Schwinger terms are identi ed with cocycles obtained from the family index theorem for a manifold with boundary. A generating form for the covariant anomaly and Schwinger term is obtained in the third paper. The rst three papers consider Yang-Mills while the fourth (in cooperation with Jouko Mickelsson) also includes gravitation. Key words: Schwinger terms, external anomaly, Z2-grading, index theory. eld problems, higher dimensions, chiral iii iv Preface This thesis will be about Schwinger terms. It is terms that appear in equal time commutators of currents in quantum eld theory. As a mathematical physicist I nd it hard to write a thesis about this subject. Both the physical and mathematical aspects should preferably be covered. Ihavedecided to focus on some of the mathematical tools that the Schwinger term and the closely related chiral anomaly have in common. This is part of what I have learned during the years 1994{1999 as a graduate student attheRoyal Institute of Technology. The following conventions and assumptions will be made throughout the thesis: All manifolds are assumed to be second countable and Hausdor . They are assumed to be paracompact whenever a partition of unity argument is needed. In nite-dimensional manifolds are also

Comparison of Schwinger and Kohn variational phase shift calculations

International Nuclear Information System (INIS)

Callaway, I.

1980-01-01

Numerical calculations of the l = 0 phase shift for an attractive Yukawa potential are reported using Schwinger and Kohn (type) variational methods. Accurate values can be obtained from both procedures, but when the same basis set of short range functions is used, the Kohn procedure gives superior results. (orig.)

An Etude in non-linear Dyson-Schwinger Equations

International Nuclear Information System (INIS)

Kreimer, Dirk; Yeats, Karen

2006-01-01

We show how to use the Hopf algebra structure of quantum field theory to derive nonperturbative results for the short-distance singular sector of a renormalizable quantum field theory in a simple but generic example. We discuss renormalized Green functions G R (α,L) in such circumstances which depend on a single scale L=lnq 2 /μ 2 and start from an expansion in the scale G R (α,L)=1+-bar k γ k (α)L k . We derive recursion relations between the γ k which make full use of the renormalization group. We then show how to determine the Green function by the use of a Mellin transform on suitable integral kernels. We exhibit our approach in an example for which we find a functional equation relating weak and strong coupling expansions

Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory

International Nuclear Information System (INIS)

Hebenstreit, F.; Alkofer, R.; Gies, H.

2010-01-01

The nonperturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields E-vector(x-vector,t). Based on the Dirac-Heisenberg-Wigner formalism, we derive a system of partial differential equations of infinite order for the 16 irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field E(t)=E 0 and the Sauter-type electric field E(t)=E 0 sech 2 (t/τ). These analytic solutions translate into corresponding expressions within the Dirac-Heisenberg-Wigner formalism and allow to discuss the effect of higher derivatives. We observe that spatial field variations typically exert a strong influence on the components of the Wigner function for large momenta or for late times.

Schwinger variational calculation of ionization of hydrogen atoms for ...

Indian Academy of Sciences (India)

Schwinger variational calculation of ionization of hydrogen atoms for large momentum transfers. K CHAKRABARTI. Department of Mathematics, Scottish Church College, 1 & 3 Urquhart Square,. Kolkata 700 006, India. MS received 7 July 2001; revised 10 October 2001. Abstract. Schwinger variational principle is used here ...

Nonperturbative confinement in quantum chromodynamics : I. Study of an approximate equation of Mandelstam

NARCIS (Netherlands)

Atkinson, D.; Drohm, J. K.; Johnson, P. W.; Stam, K.

1981-01-01

An approximated form of the Dyson–Schwinger equation for the gluon propagator in quarkless QCD is subjected to nonlinear functional and numerical analysis. It is found that solutions exist, and that these have a double pole at the origin of the square of the propagator momentum, together with an

The geometric Schwinger model on the torus. Pt. 1

International Nuclear Information System (INIS)

Joos, H.

1990-01-01

The author analyzes the Euclidean version of the geometric Schwinger model on the torus. After the calculation of the zero mode wave functions associated with the different topological sectors, which can be expressed by θ functions defined on the two-dimensional torus, he determines the regularized effective action and discusses the propagator related to it. Finally he studies applications to the standard questions like the particle spectrum, the screening of the static potential, and the appearance of the anomaly. (HSI)

The Schwinger Model on the torus

International Nuclear Information System (INIS)

Azakov, S.

1996-08-01

The classical and quantum aspects of the Schwinger model on the torus are considered. First we find explicitly all zero modes of the Dirac operator in the topological sectors with nontrivial Chern index and its spectrum. In the second part we determine the regularized effective action and discuss the propagators related to it. Finally we calculate the gauge invariant averages of the fermion bilinears and correlation functions of currents and densities. We show that in the infinite volume limit the well-known result for the chiral condensate can be obtained and the clustering property can be established. (author). 23 refs

Equivalence of Dirac quantization and Schwinger's action principle quantization

International Nuclear Information System (INIS)

Das, A.; Scherer, W.

1987-01-01

We show that the method of Dirac quantization is equivalent to Schwinger's action principle quantization. The relation between the Lagrange undetermined multipliers in Schwinger's method and Dirac's constraint bracket matrix is established and it is explicitly shown that the two methods yield identical (anti)commutators. This is demonstrated in the non-trivial example of supersymmetric quantum mechanics in superspace. (orig.)

Are Crab nanoshots Schwinger sparks?

Energy Technology Data Exchange (ETDEWEB)

Stebbins, Albert [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Yoo, Hojin [Univ. of Wisconsin, Madison, WI (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)

2015-05-21

The highest brightness temperature ever observed are from "nanoshots" from the Crab pulsar which we argue could be the signature of bursts of vacuum e^± pair production. If so this would be the first time the astronomical Schwinger effect has been observed. These "Schwinger sparks" would be an intermittent but extremely powerful, ~10³ L_⊙, 10 PeV e^± accelerator in the heart of the Crab. These nanosecond duration sparks are generated in a volume less than 1 m³ and the existence of such sparks has implications for the small scale structure of the magnetic field of young pulsars such as the Crab. As a result, this mechanism may also play a role in producing other enigmatic bright short radio transients such as fast radio bursts.

Leading-order calculation of hadronic contributions to the Muon g-2 using the Dyson-Schwinger approach

Science.gov (United States)

Goecke, Tobias; Fischer, Christian S.; Williams, Richard

2011-10-01

We present a calculation of the hadronic vacuum polarisation (HVP) tensor within the framework of Dyson-Schwinger equations. To this end we use a well-established phenomenological model for the quark-gluon interaction with parameters fixed to reproduce hadronic observables. From the HVP tensor we compute both the Adler function and the HVP contribution to the anomalous magnetic moment of the muon, aμ. We find aμHVP = 6760 ×10-11 which deviates about two percent from the value extracted from experiment. Additionally, we make comparison with a recent lattice determination of aμHVP and find good agreement within our approach. We also discuss the implications of our result for a corresponding calculation of the hadronic light-by-light scattering contribution to aμ.

Leading-order calculation of hadronic contributions to the Muon g-2 using the Dyson-Schwinger approach

International Nuclear Information System (INIS)

Goecke, Tobias; Fischer, Christian S.; Williams, Richard

2011-01-01

We present a calculation of the hadronic vacuum polarisation (HVP) tensor within the framework of Dyson-Schwinger equations. To this end we use a well-established phenomenological model for the quark-gluon interaction with parameters fixed to reproduce hadronic observables. From the HVP tensor we compute both the Adler function and the HVP contribution to the anomalous magnetic moment of the muon, a μ . We find a μ HVP =6760x10 -11 which deviates about two percent from the value extracted from experiment. Additionally, we make comparison with a recent lattice determination of a μ HVP and find good agreement within our approach. We also discuss the implications of our result for a corresponding calculation of the hadronic light-by-light scattering contribution to a μ .

Effective field equations for expectation values

International Nuclear Information System (INIS)

Jordan, R.D.

1986-01-01

We discuss functional methods which allow calculation of expectation values, rather than the usual in-out amplitudes, from a path integral. The technique, based on Schwinger's idea of summing over paths which go from the past to the future and then back to the past, provides effective field equations satisfied by the expectation value of the field. These equations are shown to be real and causal for a general theory up to two-loop order, and unitarity is checked to this order. These methods are applied to a simple quantum-mechanical example to illustrate the differences between the new formalism and the standard theory. When applied to the gravitational field, the new effective field equations should be useful for studies of quantum cosmology

Schwinger mechanism in linear covariant gauges

Science.gov (United States)

Aguilar, A. C.; Binosi, D.; Papavassiliou, J.

2017-02-01

In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modeled by means of certain physically motivated Ansätze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ansätze are compatible with the existence of nontrivial solutions. When such Ansätze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic "zero crossing," while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.

Schwinger variational principle applied to molecular photoionization

International Nuclear Information System (INIS)

Smith, M.E.

1985-01-01

A method based upon the Schwinger variational principle was developed to study molecular photoionization and electron-molecule scattering. Exact static-exchange solutions to the equations for the continuum orbitals are obtained within the Hartree-Fock approximation; and from these cross sections and angular distributions are derived for both of the above processes. This method was applied to photoionization of the valence levels of three different systems. The first application of this method is a study of the photoionization of the valence levels of NO. Next, vibrationally resolved branching ratios and vibrational state-specific asymmetry parameters for photoionization of the 5sigma level of CO are presented. Finally, a study of the photoionization of the 5sigma level of CO absorbed on a nickel surface is reported. Approximating this system by the linear triatomic molecule NiCO leads to cross sections and angular distributions which are in good agreement with experimental data

Perturbation theory for continuous stochastic equations

International Nuclear Information System (INIS)

Chechetkin, V.R.; Lutovinov, V.S.

1987-01-01

The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)

Leading-order calculation of hadronic contributions to the Muon g-2 using the Dyson-Schwinger approach

Energy Technology Data Exchange (ETDEWEB)

Goecke, Tobias [Institut fuer Theoretische Physik, Universitaet Giessen, 35392 Giessen (Germany); Fischer, Christian S., E-mail: christian.fischer@theo.physik.uni-giessen.de [Institut fuer Theoretische Physik, Universitaet Giessen, 35392 Giessen (Germany); Gesellschaft fuer Schwerionenforschung mbH, Planckstr. 1, D-64291 Darmstadt (Germany); Williams, Richard [Dept. Fisica Teorica I, Universidad Complutense, 28040 Madrid (Spain)

2011-10-13

We present a calculation of the hadronic vacuum polarisation (HVP) tensor within the framework of Dyson-Schwinger equations. To this end we use a well-established phenomenological model for the quark-gluon interaction with parameters fixed to reproduce hadronic observables. From the HVP tensor we compute both the Adler function and the HVP contribution to the anomalous magnetic moment of the muon, a{sub {mu}}. We find a{sub {mu}}{sup HVP}=6760x10{sup -11} which deviates about two percent from the value extracted from experiment. Additionally, we make comparison with a recent lattice determination of a{sub {mu}}{sup HVP} and find good agreement within our approach. We also discuss the implications of our result for a corresponding calculation of the hadronic light-by-light scattering contribution to a{sub {mu}.}

Schwinger-Keldysh propagators from AdS/CFT correspondence

International Nuclear Information System (INIS)

Herzog, C.P.; Son, D.T.

2003-01-01

We demonstrate how to compute real-time Green's functions for a class of finite temperature field theories from their AdS gravity duals. In particular, we reproduce the two-by-two Schwinger-Keldysh matrix propagator from a gravity calculation. Our methods should work also for computing higher point lorentzian signature correlators. We elucidate the boundary condition subtleties which hampered previous efforts to build a lorentzian-signature AdS/CFT correspondence. For two-point correlators, our construction is automatically equivalent to the previously formulated prescription for the retarded propagator. (author)

New solution for the Schwinger model

International Nuclear Information System (INIS)

Baaquie, B.E.

1980-08-01

We solve the Schwinger model exactly using the path integral. The fermion sector is solved using the axial current anomaly. We then study the Wilson loop integral for the interacting theory, and discuss the Wilson criterion for confinement. (author)

A generalized Schwinger boson mapping with a physical subspace

International Nuclear Information System (INIS)

Scholtz, F.G.; Geyer, H.B.

1988-01-01

We investigate the existence of a physical subspace for generalized Schwinger boson mappings of SO(2n+1) contains SO(2n) in view of previous observations by Marshalek and the recent construction of such a mapping and subspace for SO(8) by Kaup. It is shown that Kaup's construction can be attributed to the existence of a unique SO(8) automorphism. We proceed to construct a generalized Schwinger-type mapping for SO(2n+1) contains SO(2n) which, in contrast to a similar attempt by Yamamura and Nishiyama, indeed has a corresponding physical subspace. This new mapping includes in the special case of SO(8) the mapping by Kaup which is equivalent to the one given by Yamamura and Nishiyama for n=4. Nevertheless, we indicate the limitations of the generalized Schwinger mapping regarding its applicability to situations where one seeks to establish a direct link between phenomenological boson models and an underlying fermion microscopy. (orig.)

Self-consistence equations for extended Feynman rules in quantum chromodynamics

International Nuclear Information System (INIS)

Wielenberg, A.

2005-01-01

In this thesis improved solutions for Green's functions are obtained. First the for this thesis essential techniques and concepts of QCD as euclidean field theory are presented. After a discussion of the foundations of the extended approach for the Feynman rules of QCD with a systematic approach for the 4-gluon vertex a modified renormalization scheme for the extended approach is developed. Thereafter the resummation of the Dyson-Schwinger equations (DSE) by the appropriately modified Bethe-Salpeter equation is discussed. Then the leading divergences for the 1-loop graphs of the resummed DSE are determined. Thereafter the equation-of-motion condensate is defined as result of an operator-product expansion. Then the self-consistency equations for the extended approaches are defined and numerically solved. (HSI)

Delta and Omega electromagnetic form factors in a Dyson-Schwinger/Bethe-Salpeter approach

Energy Technology Data Exchange (ETDEWEB)

Diana Nicmorus, Gernot Eichmann, Reinhard Alkofer

2010-12-01

We investigate the electromagnetic form factors of the Delta and the Omega baryons within the Poincare-covariant framework of Dyson-Schwinger and Bethe-Salpeter equations. The three-quark core contributions of the form factors are evaluated by employing a quark-diquark approximation. We use a consistent setup for the quark-gluon dressing, the quark-quark bound-state kernel and the quark-photon interaction. Our predictions for the multipole form factors are compatible with available experimental data and quark-model estimates. The current-quark mass evolution of the static electromagnetic properties agrees with results provided by lattice calculations.

Overview on the anomaly and Schwinger term in two dimensional QED

International Nuclear Information System (INIS)

Adam, C.; Bertlmann, R.A.; Hofer, P.

1993-01-01

The axial anomaly of two-dimensional QED is computed in different ways (perturbative, via dispersion integrals, path integral and index theorem) and their relation is discussed as well as the relation between anomaly, Schwinger term and the Dirac vacuum. Some features of the special case of massless fermions (Schwinger model) and some methods of exactly solving it are demonstrated. (authors)

Schwinger-Keldysh diagrammatics for primordial perturbations

Science.gov (United States)

Chen, Xingang; Wang, Yi; Xianyu, Zhong-Zhi

2017-12-01

We present a systematic introduction to the diagrammatic method for practical calculations in inflationary cosmology, based on Schwinger-Keldysh path integral formalism. We show in particular that the diagrammatic rules can be derived directly from a classical Lagrangian even in the presence of derivative couplings. Furthermore, we use a quasi-single-field inflation model as an example to show how this formalism, combined with the trick of mixed propagator, can significantly simplify the calculation of some in-in correlation functions. The resulting bispectrum includes the lighter scalar case (mcase (m>3H/2) that has not been explicitly computed for this model. The latter provides a concrete example of quantum primordial standard clocks, in which the clock signals can be observably large.

Fermion structures of state vectors of the Schwinger model with multi-fermions

International Nuclear Information System (INIS)

Nakawaki, Yuji

1983-01-01

Coulomb-gauge Schwinger model with multi-fermions is formulated consistently in a box [-L, L] by introducing true dynamical degrees of freedom of electromagnetic fields, namely zero-mode part A 1 sup((0)) of A 1 and its canonical conjugate momentum π 1 sup((0)). State vectors are constructed of free massless fermion operators and zero-mode operators A 1 sup((0)) and π 1 sup((0)) and it is clarified how and why multifermion condensations become degenerate ground states and chiral invariance is spontaneously broken. It is also examined that physical space of covariant gauge Schwinger model is isomorphic to that of Coulomb-gauge Schwinger model. (author)

Determination of covariant Schwinger terms in anomalous gauge theories

International Nuclear Information System (INIS)

Kelnhofer, G.

1991-01-01

A functional integral method is used to determine equal time commutators between the covariant currents and the covariant Gauss-law operators in theories which are affected by an anomaly. By using a differential geometrical setup we show how the derivation of consistent- and covariant Schwinger terms can be understood on an equal footing. We find a modified consistency condition for the covariant anomaly. As a by-product the Bardeen-Zumino functional, which relates consistent and covariant anomalies, can be interpreted as connection on a certain line bundle over all gauge potentials. Finally the commutator anomalies are calculated for the two- and four dimensional case. (Author) 13 refs

Determination of covariant Schwinger terms in anomalous gauge theories

International Nuclear Information System (INIS)

Kelnhofer, G.

1991-01-01

A functional integral method is used to determine equal time commutators between the covariant currents and the covariant Gauss-law operators in theories which are affected by an anomaly. By using a differential geometrical setup we show how the derivation of consistent- and covariant Schwinger terms can be understood on an equal footing. We find a modified consistency condition for the covariant anomaly. As a by-product the Bardeen-Zumino functional, which relates consistent and covariant anomalies, can be interpreted as connection on a certain line bundle over all gauge potentials. Finally the covariant commutator anomalies are calculated for the two- and four dimensional case. (orig.)

The Jordan-Schwinger realization of two-parametric quantum group Slq,s(2)

International Nuclear Information System (INIS)

Jing Sicong.

1991-10-01

In order to construct the Jordan-Schwinger realization for two-parametric quantum group Sl q,s (2), two independent q, s-deformed harmonic oscillators are defined in this paper and the Heisenberg commutation relations of the q, s-deformed oscillator are also derived by Schwinger's contraction procedure. (author). 11 refs

Julian Schwinger the physicist, the teacher, and the man

CERN Document Server

1996-01-01

In the post-quantum-mechanics era, few physicists, if any, have matched Julian Schwinger in contributions to and influence on the development of physics. A deep and provocative thinker, Schwinger left his indelible mark on all areas of theoretical physics; an eloquent lecturer and immensely successful mentor, he was gentle, intensely private, and known for being "modest about everything except his physics". This book is a collection of talks in memory of him by some of his contemporaries and his former students: A Klein, F Dyson, B DeWitt, W Kohn, D Saxon, P C Martin, K Johnson, S Deser, R Fin

Green's functions for off-shell electromagnetism and spacelike correlations

International Nuclear Information System (INIS)

Land, M.C.; Horwitz, L.P.

1991-01-01

The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and proper time τ. The Maxwell theory is contained in this theory; integration of the field equations over τ restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, the authors study the Green's functions for the five dimensional hyperbolic field equations for both signatures ± [corresponding to O(4, 1) or O(3, 2) symmetry of the field equations] of the proper time derivative. The classification of the Green's functions follows that of the four-dimensional theory for massive fields, for which the mass squared may be positive or negative, respectively. The Green's function for the five-dimensional field are then given by the Fourier transform over the mass parameter. They derive the Green's functions corresponding to the principal part Δ P and the homogeneous function Δ t ; all of the Green's functions can be expressed in terms of these, as for the usual field equations with definite mass. In the O(3, 2) case, the principal part function has support for x 2 ≥ τ 2 , corresponding to spacelike propagation, as well as along the light cone X 2 = 0 (for τ = 0). There can be no transmission of information in spacelike directions, with this propagator, since the Maxwell field, obtained by integration over τ, does not contain this component of the support. Measurements are characterized by such an integration. The spacelike field therefore can dynamically establish spacelike correlations

The inverse problem for Schwinger pair production

Directory of Open Access Journals (Sweden)

F. Hebenstreit

2016-02-01

Full Text Available The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

Schwinger Model Mass Anomalous Dimension

CERN Document Server

Keegan, Liam

2016-06-20

The mass anomalous dimension for several gauge theories with an infrared fixed point has recently been determined using the mode number of the Dirac operator. In order to better understand the sources of systematic error in this method, we apply it to a simpler model, the massive Schwinger model with two flavours of fermions, where analytical results are available for comparison with the lattice data.

Equilibrium and nonequilibrium many-body perturbation theory: a unified framework based on the Martin-Schwinger hierarchy

International Nuclear Information System (INIS)

Van Leeuwen, Robert; Stefanucci, Gianluca

2013-01-01

We present a unified framework for equilibrium and nonequilibrium many-body perturbation theory. The most general nonequilibrium many-body theory valid for general initial states is based on a time-contour originally introduced by Konstantinov and Perel'. The various other well-known formalisms of Keldysh, Matsubara and the zero-temperature formalism are then derived as special cases that arise under different assumptions. We further present a single simple proof of Wick's theorem that is at the same time valid in all these flavors of many-body theory. It arises simply as a solution of the equations of the Martin-Schwinger hierarchy for the noninteracting many-particle Green's function with appropriate boundary conditions. We further discuss a generalized Wick theorem for general initial states on the Keldysh contour and derive how the formalisms based on the Keldysh and Konstantinov-Perel'-contours are related for the case of general initial states.

From Euclidean to Minkowski space with the Cauchy-Riemann equations

International Nuclear Information System (INIS)

Gimeno-Segovia, Mercedes; Llanes-Estrada, Felipe J.

2008-01-01

We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from Green's functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy-Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation. (orig.)

Excitation functions of parameters in Erlang distribution, Schwinger mechanism, and Tsallis statistics in RHIC BES program

International Nuclear Information System (INIS)

Gao, Li-Na; Liu, Fu-Hu; Lacey, Roy A.

2016-01-01

Experimental results of the transverse-momentum distributions of φ mesons and Ω hyperons produced in gold-gold (Au-Au) collisions with different centrality intervals, measured by the STAR Collaboration at different energies (7.7, 11.5, 19.6, 27, and 39 GeV) in the beam energy scan (BES) program at the relativistic heavy-ion collider (RHIC), are approximately described by the single Erlang distribution and the two-component Schwinger mechanism. Moreover, the STAR experimental transverse-momentum distributions of negatively charged particles, produced in Au-Au collisions at RHIC BES energies, are approximately described by the two-component Erlang distribution and the single Tsallis statistics. The excitation functions of free parameters are obtained from the fit to the experimental data. A weak softest point in the string tension in Ω hyperon spectra is observed at 7.7 GeV. (orig.)

Gravity Before Einstein and Schwinger Before Gravity

Science.gov (United States)

Trimble, Virginia L.

2012-05-01

Julian Schwinger was a child prodigy, and Albert Einstein distinctly not; Schwinger had something like 73 graduate students, and Einstein very few. But both thought gravity was important. They were not, of course, the first, nor is the disagreement on how one should think about gravity that is being highlighted here the first such dispute. The talk will explore, first, several of the earlier dichotomies: was gravity capable of action at a distance (Newton), or was a transmitting ether required (many others). Did it act on everything or only on solids (an odd idea of the Herschels that fed into their ideas of solar structure and sunspots)? Did gravitational information require time for its transmission? Is the exponent of r precisely 2, or 2 plus a smidgeon (a suggestion by Simon Newcomb among others)? And so forth. Second, I will try to say something about Scwinger's lesser known early work and how it might have prefigured his "source theory," beginning with "On the Interaction of Several Electrons (the unpublished, 1934 "zeroth paper," whose title somewhat reminds one of "On the Dynamics of an Asteroid," through his days at Berkeley with Oppenheimer, Gerjuoy, and others, to his application of ideas from nuclear physics to radar and of radar engineering techniques to problems in nuclear physics. And folks who think good jobs are difficult to come by now might want to contemplate the couple of years Schwinger spent teaching elementary physics at Purdue before moving on to the MIT Rad Lab for war work.

Functional equations with causal operators

CERN Document Server

Corduneanu, C

2003-01-01

Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.

The Boltzmann-Langevin Equation derived from the real-time path formalism

International Nuclear Information System (INIS)

Suraud, E.; Reinhard, P.G.

1991-01-01

We derive the Boltzmann-Langevin equation using Green's functions techniques in the real-time path formalism. We start from the Martin-Schwinger hierarchy and close it approximately at the two-body level. A careful discussion of the initial conditions for the free two-body Green's function provides the flexibility to recover the discarded correlations as fluctuations leading to the Langevin force. The derivation is generalized to the T-matrix approach which allows to prove that one can use the same effective interaction in the mean-field as well as in the collision term and Langevin force

Simple form for the Gaussian equations in curved space

International Nuclear Information System (INIS)

Mazzitelli, F.D.; Paz, J.P.

1988-01-01

We show that the variational Gaussian equations for λphi 4 theory in an arbitrary background gravitational field admit a simple form, which allows the use of a Schwinger-DeWitt-type expansion in order to renormalize them

Low-momentum ghost dressing function and the gluon mass

International Nuclear Information System (INIS)

Boucaud, Ph.; Leroy, J. P.; Le Yaouanc, A.; Micheli, J.; Pene, O.; Gomez, M. E.; Rodriguez-Quintero, J.

2010-01-01

We study the low-momentum ghost propagator Dyson-Schwinger equation in the Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. Then, regular Dyson-Schwinger equation solutions (the zero-momentum ghost dressing function not diverging) appear to emerge, and we show the ghost propagator to be described by an asymptotic expression reliable up to the order O(q 2 ). That expression, depending on the gluon mass and the zero-momentum Taylor-scheme effective charge, is proven to fit pretty well some low-momentum ghost propagator data [I. L. Bogolubsky, E. M. Ilgenfritz, M. Muller-Preussker, and A. Sternbeck, Phys. Lett. B 676, 69 (2009); Proc. Sci., LAT2007 (2007) 290] from big-volume lattice simulations where the so-called ''simulated annealing algorithm'' is applied to fix the Landau gauge.

DeWitt-Schwinger renormalization and vacuum polarization in d dimensions

International Nuclear Information System (INIS)

Thompson, R. T.; Lemos, Jose P. S.

2009-01-01

Calculation of the vacuum polarization, 2 (x)>, and expectation value of the stress tensor, μν (x)>, has seen a recent resurgence, notably for black hole spacetimes. To date, most calculations of this type have been done only in four dimensions. Extending these calculations to d dimensions includes d-dimensional renormalization. Typically, the renormalizing terms are found from Christensen's covariant point splitting method for the DeWitt-Schwinger expansion. However, some manipulation is required to put the correct terms into a form that is compatible with problems of the vacuum polarization type. Here, after a review of the current state of affairs for 2 (x)> and μν (x)> calculations and a thorough introduction to the method of calculating 2 (x)>, a compact expression for the DeWitt-Schwinger renormalization terms suitable for use in even-dimensional spacetimes is derived. This formula should be useful for calculations of 2 (x)> and μν (x)> in even dimensions, and the renormalization terms are shown explicitly for four and six dimensions. Furthermore, use of the finite terms of the DeWitt-Schwinger expansion as an approximation to 2 (x)> for certain spacetimes is discussed, with application to four and five dimensions.

Physical interpretation of Schwinger's formula for effective actions

International Nuclear Information System (INIS)

Albuquerque, L.C. de; Farina, C.; Rabello, Silvio J.; Vaidya, Arvind N.

1994-01-01

We show explicitly that Schwinger's formula for one-loop effective actions corresponds to the summation of energies associated with the zero-point oscillations of the fields. We begin with a formal proof, and after that we confirm it using a regularization prescription. (author)

Aspects of the functional renormalisation group

International Nuclear Information System (INIS)

Pawlowski, Jan M.

2007-01-01

We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being NPI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson-Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation

Non-relativistic and relativistic quantum kinetic equations in nuclear physics

International Nuclear Information System (INIS)

Botermans, W.M.M.

1989-01-01

In this thesis an attempt is made to draw up a quantummechanical tranport equation for the explicit calculation oof collision processes between two (heavy) ions, by making proper approaches of the exact equations (non-rel.: N-particles Schroedinger equation; rel.: Euler-Lagrange field equations.). An important starting point in the drag-up of the theory is the behaviour of nuclear matter in equilibrium which is determined by individual as well as collective effects. The central point in this theory is the effective interaction between two nucleons both surrounded by other nucleons. In the derivation of the tranport equations use is made of the green's function formalism as developed by Schwinger and Keldys. For the Green's function kinematic equations are drawn up and are solved by choosing a proper factorization of three- and four-particle Green's functions in terms of one- and two-particle Green's functions. The necessary boundary condition is obtained by explicitly making use of Boltzmann's assumption that colliding particles are statistically uncorrelated. Finally a transport equation is obtained in which the mean field as well as the nucleon-nucleon collisions are given by the same (medium dependent) interaction. This interaction is the non-equilibrium extension of the interaction as given in the Brueckner theory of nuclear matter. Together, kinetic equation and interaction, form a self-consistent set of equations for the case of a non-relativistic as well as for the case of a relativistic starting point. (H.W.) 148 refs.; 6 figs.; 411 schemes

Fermion current algebras and Schwinger terms in (3+1)-dimensions

International Nuclear Information System (INIS)

Langmann, E.

1994-01-01

We discuss the restricted linear group in infinite dimensions modeled by the Schatten class of rank 2p=4 which contains the (3+1)-dimensional analogs of the loop groups and is closely related to Yang-Mills theory with fermions in (3+1)-dimensions. We give an alternative to the construction of the ''highest weight'' representation of this group found by Mickelsson and Rajeev. Our approach is close to quantum field theory, with the elements of this group regarded as Bogoliubov transformations for fermions in an external Yang-Mills field. Though these cannot be unitarily implemented in the physically relevant representation of the fermion field algebra, we argue that they can be implemented by sesquilinear forms, and that there is a (regularized) product of forms providing an appropriate group structure. On the Lie algebra level, this gives an explicit, non-perturbative construction of fermion current algebras in (3+1) space-time dimensions which explicitly shows that the ''wave function renormalization'' required for a consistent definition of the currents and their Lie bracket naturally leads to the Schwinger term identical with the Mickelsson-Rajeev cocycle. Though the explicit form of the Schwinger term is given only for the case p=2, our arguments apply also to the restricted linear groups modeled by Schatten classes of rank 2p=6, 8, .. corresponding to current algebras in (d+1)-dimensions, d=5, 7, .. (orig.)

Massive Schwinger model at finite θ

Science.gov (United States)

Azcoiti, Vicente; Follana, Eduardo; Royo-Amondarain, Eduardo; Di Carlo, Giuseppe; Vaquero Avilés-Casco, Alejandro

2018-01-01

Using the approach developed by V. Azcoiti et al. [Phys. Lett. B 563, 117 (2003), 10.1016/S0370-2693(03)00601-4], we are able to reconstruct the behavior of the massive one-flavor Schwinger model with a θ term and a quantized topological charge. We calculate the full dependence of the order parameter with θ . Our results at θ =π are compatible with Coleman's conjecture on the phase diagram of this model.

On current superalgebras and super-schwinger terms

International Nuclear Information System (INIS)

Grosse, H.; Langmann, E.

1990-01-01

We present a general construction of current superalgebras within the framework of quasi-free second quantization of bosons and fermions. Mathematically speaking, we give projective representations of certain Lie superalgebras realized as bounded operators on Z 2 -graded Hilbert spaces and, more generally, on Grassmann algebra-modules. The super-Schwinger terms occuring correspond to Z 2 -graded two-cocycles. (Authors) 11 refs

Schwinger pair creation of Kaluza-Klein particles: Pair creation without tunneling

International Nuclear Information System (INIS)

Friedmann, Tamar; Verlinde, Herman

2005-01-01

We study Schwinger pair creation of charged Kaluza-Klein (KK) particles from a static KK electric field. We find that the gravitational backreaction of the electric field on the geometry--which is incorporated via the electric KK-Melvin solution--prevents the electrostatic potential from overcoming the rest mass of the KK particles, thus impeding the tunneling mechanism which is often thought of as responsible for the pair creation. However, we find that pair creation still occurs with a finite rate formally similar to the classic Schwinger result, but via an apparently different mechanism, involving a combination of the Unruh effect and vacuum polarization due to the E-field

The Schwinger term and the Berry phase in simple models

International Nuclear Information System (INIS)

Grosse, H.

1989-01-01

We discuss quantization of fermions interacting with external fields and observe the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations. Implementability of gauge and axial gauge transformations leads to generators which fulfill an algebra of charges with Schwinger term. This term can be written as a cocycle and leads to the boson-fermion correspondence. During an adiabatic transport along closed loops in a parameter space we may pick up a nonintegrable phase factor, usually called the Berry phase. We study the occurrence of such a topological phase in a model and give the parallel transport for density matrices. After second quantization one may pick up both a Berry phase and a Schwinger term. 13 refs. (Author)

Infra-red ghost contribution to the gluon Green's functions

International Nuclear Information System (INIS)

Paccanoni, F.

1985-01-01

The Schwinger-Dyson equations for the ghost propagator and the ghost-ghost-gluon vertex function are studied in the Landau gauge. A confining infra-red singularity is assumed for the gluon propagator and a suitable approximation is devised for the solution of the integral equations. It is found that the bare values of the ghost propagator and coupling cannot be a consistent solution of either equation. It is determined a possible behaviour of the correction factor for the ghost propagator in the small-momentum limit and discussed the consistency of the approximation schemes for the gluon propagator that neglet Faddeev-Popov ghost

Yet another Monte Carlo study of the Schwinger model

International Nuclear Information System (INIS)

Sogo, K.; Kimura, N.

1986-01-01

Some methodological improvements are introduced in the quantum Monte Carlo simulation of the 1 + 1 dimensional quantum electrodynamics (the Schwinger model). Properties at finite temperatures are investigated, concentrating on the existence of the chirality transition and of the deconfinement transition. (author)

Yet another Monte Carlo study of the Schwinger model

International Nuclear Information System (INIS)

Sogo, K.; Kimura, N.

1986-03-01

Some methodological improvements are introduced in the quantum Monte Carlo simulation of the 1 + 1 dimensional quantum electrodynamics (the Schwinger model). Properties at finite temperatures are investigated, concentrating on the existence of the chirality transition and of the deconfinement transition. (author)

Lyapunov functionals and stability of stochastic functional differential equations

CERN Document Server

Shaikhet, Leonid

2013-01-01

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...

Siegel's chiral boson and the chiral Schwinger model

International Nuclear Information System (INIS)

Berger, T.

1992-01-01

In this paper Siegel's proposal for a Lagrangian formulation of a chiral boson is analyzed by applying recent results on 2d chiral quantum gravity. A model is derived whose solution consists of a massive scalar and two massless chiral scalars. Therefore it is a minimally bosonized two-fermion chiral Schwinger model

Chiral Schwinger model and lattice fermionic regularizations

International Nuclear Information System (INIS)

Kieu, T.D.; Sen, D.; Xue, S.

1988-01-01

The chiral Schwinger model is studied on the lattice with use of Wilson fermions. The arbitrary mass term for the gauge boson is shown to originate from the arbitrariness of the Wilson parameter, which is required to avoid the doubling phenomenon on the lattice. The necessity for such a term is thus demonstrated in contrast to the mere admissibility as indicated by previous continuum calculations

Stress-tensor commutators and Schwinger terms in singleton theories

International Nuclear Information System (INIS)

Bergshoeff, E.; Sezgin, E.; Tanii, Y.

1989-06-01

We compute the commutators of the regularized quantum stress-tensor of singleton theories formulated on the boundary of a (p + 2)-dimensional anti de Sitter space (AdS p+2 ). (These are superconformal field theories on S p x S 1 ). We find that the algebra is not closed except in the case of AdS 3 . It does contain, however, the finite dimensional AdS p+2 algebra SO(p + 1,2). We also find divergent, field dependent as well as field independent Schwinger terms (i.e. the central extensions), which, however, do not lead to anomalies in the algebra of the AdS charges. We also give a simple derivation of the two-point functions for bosonic and fermionic singletons. (author). 15 refs

Functional equation for the Mordell-Tornheim multiple zeta-function

OpenAIRE

Okamoto, Takuya; Onozuka, Tomokazu

2016-01-01

We show a relation between the Mordell-Tornheim multiple zeta-function and the confluent hypergeometric function, and using it, we give the functional equation for the Mordell-Tornheim multiple zeta-function. In the double case, the functional equation includes the known functional equation for the Euler-Zagier double zeta-function.

To semi-centenary anniversary of discovering the Schwinger scattering and starting the first works on neutron polarizability

International Nuclear Information System (INIS)

Alexandrov, Yu.A.

2006-01-01

The theory of neutron Schwinger scattering was proposed and developed by Schwinger in 1948, but despite multiple efforts, the experimental discovery of this phenomenon was made eight years later. Currently, Schwinger scattering should be accounted for in many precise neutron experiments, for example, while studying the electromagnetic interaction of neutrons with nuclei. By means of Schwinger scattering it is possible to measure the degree of polarization of the initial beam even at particle energies of 1 GeV order. The concept of neutron polarizability was introduced as additional natural phenomenon indicating the nucleon space structure after the first Hofstadter's experiments (1953-1954). The neutron polarizability was detected in a small-angle neutron scattering experiment in 1957. However, the serious contradiction between the results obtained in megaelectronvolt and kiloelectronvolt neutron energy ranges was explained only in 2001. It is also shown that existent small-angle neutron experiments at megaelectronvolt energy by heavy nuclei do not confirm the idea of (n+3)-dimensional gravity

Solution of the scattering T matrix equation in discrete complex momentum space

International Nuclear Information System (INIS)

Rawitscher, G.H.; Delic, G.

1984-01-01

The scattering solution to the Lippmann-Schwinger equation is expanded into a set of spherical Bessel functions of complex wave numbers, K/sub j/, with j = 1,2 , . . . , M. The value of each K/sub j/ is determined from the condition that the spherical Bessel function smoothly matches onto an asymptotically outgoing spherical Hankel (or Coulomb) function of the correct physical wave number at a matching point R. The spherical Bessel functions thus determined are Sturmian functions, and they form a complete set in the interval 0 to R. The coefficients of the expansion of the scattering function are determined by matrix inversion of a linear set of algebraic equations, which are equivalent to the solution of the T-matrix equation in complex momentum space. In view of the presence of a matching radius, no singularities are encountered for the Green's functions, and the inclusion of Coulomb potentials offers no computational difficulties. Three numerical examples are performed in order to illustrate the convergence of the elastic scattering matrix S with M. One of these consists of a set of coupled equations which describe the breakup of a deuteron as it scatters from the nucleus on 58 Ni. A value of M of 15 or less is found sufficient to reproduce the exact S matrix element to an accuracy of four figures after the decimal point

The convergence radius of the chiral expansion in the Dyson-Schwinger approach

International Nuclear Information System (INIS)

Meissner, T.

1994-01-01

We determine the convergence radius m conv or the expansion in the current quark mass using the Dyson-Schwinger (DS) equation of QCD in the rainbow approximation. Within a Gaussian form for the gluon propagator D μ ν(p) ∼ δμνχ 2 e - Δ /p 2 we find that m conv increases with decreasing width Δ and increasing strength χ 2 . For those values of χ 2 and Δ, which provide the best known description of low energy hadronic phenomena, m conv lies around 2Λ QCD , which is big enough, that the chiral expansion in the strange sector converges. Our analysis also explains the rather low value of m conv ∼ 50...80 MeV in the Nambu-Jona-Lasinio model, which as itself can be regarded as a special case of the rainbow DS models, where the gluon propagator is a constant in momentum space

Microscopy of bosonic models using Schwinger and Holstein - Primakoff bosonization techniques

International Nuclear Information System (INIS)

Pinto, M.E.B.

1988-01-01

Two kinds of bosonic expansions for the SU(2) case, one being finite (Schwinger) and the other being infinite (Holstein-Primakoff) are analysed. The existence of a transformation connecting them was discussed. Utilizing the two methods, the Two Level Model hamiltonian into the many boson space is mapped. Considering systems composed by 4, 6 and 14 particles, calculations for the eigenenergies within the ''vibrational limit'' of the model were performed. The results show that the Schwinger mapping is exact. Approximated bosonic images with the Holstein-Primakoff mapping are obtained. Indeed, the anharmonicities observed in the region between the ideal '' spherical limit'' and the ''transitional point'', were well described by the approximation containing up to quartic terms on the bosonic operators. (author) [pt

Functional equations and Green's functions for augmented scalar fields

International Nuclear Information System (INIS)

Klauder, J.R.

1977-01-01

Certain noncanonical self-coupled scalar quantum field theories, previously formulated by means of functional integration, are herein recast into the form of functional differential equations for the Green's functional. From these expressions the set of coupled equations relating the Green's functions is obtained. The new equations are compared with those of the conventional formulation, and are proposed as alternatives, especially for nonrenormalizable models when the conventional equations fail

Lorentz Invariant Spectrum of Minimal Chiral Schwinger Model

Science.gov (United States)

Kim, Yong-Wan; Kim, Seung-Kook; Kim, Won-Tae; Park, Young-Jai; Kim, Kee Yong; Kim, Yongduk

We study the Lorentz transformation of the minimal chiral Schwinger model in terms of the alternative action. We automatically obtain a chiral constraint, which is equivalent to the frame constraint introduced by McCabe, in order to solve the frame problem in phase space. As a result we obtain the Lorentz invariant spectrum in any moving frame by choosing a frame parameter.

The geometric phase and the Schwinger term in some models

International Nuclear Information System (INIS)

Grosse, H.; Langmann, E.

1991-01-01

We discuss quantization of fermions interacting with external fields and observe the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations. Implementability of gauge and axial gauge transformations leads to generators which fulfill an algebra of charges with Schwinger term. This term can be written as a cocycle and leads to the boson-fermion correspondence. Transport of a quantum mechanical system along a closed loop of parameter space may yield a geometric mechanical system along a closed loop of parameter space may yield a geometric phase. We discuss models for which nonintegrable phase factors are obtained from the adiabatic parallel transport. After second quantization one obtains, in addition, a Schwinger term. Depending on the type of transformation a subtle relationship between these two obstructions can occur. We indicate finally how we may transport density matrices along closed loops in parameter space. (authors)

On the operator Schwinger term in zero mass photon QED

International Nuclear Information System (INIS)

Bordes, G.

1977-01-01

The matrix element of the e.m. current commutator between the vacuum and a two-photon state is computed directly without introducing a mass for the photon. The result is zero and then seems confirm the absence of an operator Schwinger term in quantum electrodynamics

Electromagnetic Radiation : Variational Methods, Waveguides and Accelerators Including seminal papers of Julian Schwinger

CERN Document Server

Milton, Kimball A

2006-01-01

This is a graduate level textbook on the theory of electromagnetic radiation and its application to waveguides, transmission lines, accelerator physics and synchrotron radiation. It has grown out of lectures and manuscripts by Julian Schwinger prepared during the war at MIT's Radiation Laboratory, updated with material developed by Schwinger at UCLA in the 1970s and 1980s, and by Milton at the University of Oklahoma since 1994. The book includes a great number of straightforward and challenging exercises and problems. It is addressed to students in physics, electrical engineering, and applied mathematics seeking a thorough introduction to electromagnetism with emphasis on radiation theory and its applications.

New Bessel-type function associated with SU(3) representation

International Nuclear Information System (INIS)

Tanimura, N.; Tanimura, O.

1990-01-01

A new set of functions that are given by the coefficients of the character expansion of the single-link action in the SU(3) lattice-gauge theory is studied. The function is specified by the indices λ and μ of the SU(3) representation of the Young tableau. From the Schwinger-Dyson variational method the recursion relations among the functions are derived. By combining the recursion relation and the relation of the differentiation, the linear differential equation of the sixth order for the function is derived. The properties of the function are discussed in detail in comparison with the functions in the SU(2) group

Perturbative versus Schwinger-propagator method for the calculation of amplitudes in a magnetic field

International Nuclear Information System (INIS)

Nieves, Jose F.; Pal, Palash B.

2006-01-01

We consider the calculation of amplitudes for processes that take place in a constant background magnetic field, first using the standard method for the calculation of an amplitude in an external field, and second utilizing the Schwinger propagator for charged particles in a magnetic field. We show that there are processes for which the Schwinger-propagator method does not yield the total amplitude. We explain why the two methods yield equivalent results in some cases and indicate when we can expect the equivalence to hold. We show these results in fairly general terms and illustrate them with specific examples as well

QCD Green's Functions and Phases of Strongly-Interacting Matter

Directory of Open Access Journals (Sweden)

Schaefer B.J.

2011-04-01

Full Text Available After presenting a brief summary of functional approaches to QCD at vanishing temperatures and densities the application of QCD Green's functions at non-vanishing temperature and vanishing density is discussed. It is pointed out in which way the infrared behavior of the gluon propagator reflects the (de-confinement transition. Numerical results for the quark propagator are given thereby verifying the relation between (de--confinement and dynamical chiral symmetry breaking (restoration. Last but not least some results of Dyson-Schwinger equations for the color-superconducting phase at large densities are shown.

IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation

International Nuclear Information System (INIS)

Boucaud, Ph.; Leroy, J.P.; Yaouanc, A. Le; Micheli, J.; Pene, O.; RodrIguez-Quintero, J.

2008-01-01

We solve numerically the Schwinger-Dyson ghost equation in the Landau gauge for a given, finite at k = 0 gluon propagator (i.e. the infrared exponent of its dressing function, α gluon , is 1) and under the usual assumption of constancy of the ghost-gluon vertex ; we show that there exist two possible types of ghost dressing function solutions, as we have previously inferred from analytical considerations: one which is singular at zero momentum (the infrared exponent of its dressing function, α ghost , (We shall use α G and α F as shorthands for α gluon and α ghost respectively; let us recall that we denote the gluon by a G and the ghost by a F, for ''fantome''.) is gluon +2α ghost = 0 and has therefore α ghost = -1/2, and another one which is finite at the origin with α ghost = 0 and violates the relation. It is most important that the type of solution which is realized depends on the value of the coupling constant. There are regular ones - α F = 0 - for any coupling below some value, while there is only one singular solution - α F <0 -, obtained for a single critical value of the coupling. For all momenta k <.5 GeV where they can be trusted, our lattice data exclude neatly the singular one, and agree very well with the regular solution we obtain at a coupling constant compatible with the bare lattice value.

Dirac equation of spin particles and tunneling radiation from a Kinnersly black hole

Energy Technology Data Exchange (ETDEWEB)

Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Feng, Zhong-Wen [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Li, Hui-Ling [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Shenyang Normal University, College of Physics Science and Technology, Shenyang (China)

2017-04-15

In curved space-time, the Hamilton-Jacobi equation is a semi-classical particle equation of motion, which plays an important role in the research of black hole physics. In this paper, starting from the Dirac equation of spin 1/2 fermions and the Rarita-Schwinger equation of spin 3/2 fermions, respectively, we derive a Hamilton-Jacobi equation for the non-stationary spherically symmetric gravitational field background. Furthermore, the quantum tunneling of a charged spherically symmetric Kinnersly black hole is investigated by using the Hamilton-Jacobi equation. The result shows that the Hamilton-Jacobi equation is helpful to understand the thermodynamic properties and the radiation characteristics of a black hole. (orig.)

Developments in functional equations and related topics

CERN Document Server

Ciepliński, Krzysztof; Rassias, Themistocles

2017-01-01

This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

Julian Schwinger — Personal Recollections

Science.gov (United States)

Martin, Paul C.

We're gathered here today to salute Julian Schwinger, a towering figure of the golden age of physics — and a kind and gentle human being. Even at our best universities, people with Julian's talent and his passion for discovery and perfection are rare — so rare that neither they nor the rest of us know how to take best advantage of their genius. The failure to find a happier solution to this dilemma in recent years has concerned many of us. It should not becloud the fact that over their lifetimes, few physicists, if any, have surmounted this impedance mismatch more effectively than Julian, conveying not only knowledge but lofty values and aspirations directly and indirectly to thousands of physicists…

Nonequilibrium dynamics of moving mirrors in quantum fields: Influence functional and the Langevin equation

International Nuclear Information System (INIS)

Wu, C.-H.; Lee, D.-S.

2005-01-01

We employ the Schwinger-Keldysh formalism to study the nonequilibrium dynamics of the mirror with perfect reflection moving in a quantum field. In the case where the mirror undergoes the small displacement, the coarse-grained effective action is obtained by integrating out the quantum field with the method of influence functional. The semiclassical Langevin equation is derived, and is found to involve two levels of backreaction effects on the dynamics of mirrors: radiation reaction induced by the motion of the mirror and backreaction dissipation arising from fluctuations in quantum field via a fluctuation-dissipation relation. Although the corresponding theorem of fluctuation and dissipation for the case with the small mirror's displacement is of model independence, the study from the first principles derivation shows that the theorem is also independent of the regulators introduced to deal with short-distance divergences from the quantum field. Thus, when the method of regularization is introduced to compute the dissipation and fluctuation effects, this theorem must be fulfilled as the results are obtained by taking the short-distance limit in the end of calculations. The backreaction effects from vacuum fluctuations on moving mirrors are found to be hardly detected while those effects from thermal fluctuations may be detectable

Schwinger terms of the super-Virasoro algebra in (1,0) superspace

International Nuclear Information System (INIS)

Lee, J.; Louis, J.; Ovrut, B.A.

1988-01-01

We calculate the Schwinger terms of the super-Virasoro algebra for the heterotic string, and the associated anomalous seagull terms, directly from the Lorentz and super-Weyl anomalies using the (1,0) superspace formalism. The various supercurrents in (1,0) superspace are also discussed

Light propagation in finite-sized photonic crystals: multiple scattering using an electric field integral equation

DEFF Research Database (Denmark)

Kristensen, Philip Trøst; Lodahl, Peter; Mørk, Jesper

2010-01-01

We present an accurate, stable, and efficient solution to the Lippmann–Schwinger equation for electromagnetic scattering in two dimensions. The method is well suited for multiple scattering problems and may be applied to problems with scatterers of arbitrary shape or non-homogenous background mat...

Advanced functional evolution equations and inclusions

CERN Document Server

Benchohra, Mouffak

2015-01-01

This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

Canonical variables and Heisenberg equations of motion for the spin-3/2 field in the presence of interactions

International Nuclear Information System (INIS)

Nagpal, A.K.

1978-01-01

Contrary to the prevalent belief, it is shown here that for the spin-3/2 Rarita-Schwinger field in the presence of a fully quantized interaction, the (anti) commutation relations are compatible with the Heisenberg equations of motion. The latter are indeed the same as the Lagrangian equations of motion. Further, it is shown that the validity of the Heisenberg equations of motion does not depend upon the choice of the canonical variables

Towards loop quantum supergravity (LQSG): I. Rarita–Schwinger sector

International Nuclear Information System (INIS)

Bodendorfer, N; Thiemann, T; Thurn, A

2013-01-01

In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is Poisson-commuting, which implies that loop quantum gravity quantization methods apply. We also provided the coupling to standard matter. In this paper, we extend our methods to derive a connection formulation of a large class of Lorentzian signature supergravity theories, in particular 11 D SUGRA and 4 D, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formulation in the time gauge which yields a Spin(D) theory, a major challenge is to extend the internal gauge group to Spin(D + 1) in the presence of the Rarita–Schwinger field. This is non-trivial because SUSY typically requires the Rarita–Schwinger field to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana representations of the Clifford algebra are not available in the same spacetime dimension for both Lorentzian and Euclidean signatures. We resolve the arising tension and provide a background-independent representation of the non-trivial Dirac antibracket *-algebra for the Majorana field which significantly differs from the analogous construction for Dirac fields already available in the literature. (paper)

Exact solution of matricial Φ23 quantum field theory

Science.gov (United States)

Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar

2017-12-01

We apply a recently developed method to exactly solve the Φ3 matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large- N limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

The exact solution of self-consistent equations in the scanning near-field optic microscopy problem

DEFF Research Database (Denmark)

Lozovski, Valeri; Bozhevolnyi, Sergey I.

1999-01-01

The macroscopic approach that allows one to obtain an exact solution of the self-consistent equation of the Lippmann-Schwinger type is developed. The main idea of our method consist in usage of diagram technque for exact summation of the infinite series corresponding to the iteration procedure fo...

Path integral measure and the fermion-boson equivalence in the Schwinger model

International Nuclear Information System (INIS)

Maiella, G.

1980-02-01

I perform a change of field variables in the Schwinger model using the non-invariance of path integral measure under γ 5 transformations. The known equivalence of the model with a bosonic field theory and the Kogut-Susskind dipole mechanism is then derived. (author)

Comparing Erlang Distribution and Schwinger Mechanism on Transverse Momentum Spectra in High Energy Collisions

Directory of Open Access Journals (Sweden)

Li-Na Gao

2016-01-01

Full Text Available We study the transverse momentum spectra of J/ψ and Υ mesons by using two methods: the two-component Erlang distribution and the two-component Schwinger mechanism. The results obtained by the two methods are compared and found to be in agreement with the experimental data of proton-proton (pp, proton-lead (p-Pb, and lead-lead (Pb-Pb collisions measured by the LHCb and ALICE Collaborations at the large hadron collider (LHC. The related parameters such as the mean transverse momentum contributed by each parton in the first (second component in the two-component Erlang distribution and the string tension between two partons in the first (second component in the two-component Schwinger mechanism are extracted.

Solving polynomial differential equations by transforming them to linear functional-differential equations

OpenAIRE

Nahay, John Michael

2008-01-01

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

On one approximation in quantum chromodynamics

International Nuclear Information System (INIS)

Alekseev, A.I.; Bajkov, V.A.; Boos, Eh.Eh.

1982-01-01

Form of a complete fermion propagator near the mass shell is investigated. Considered is a nodel of quantum chromodynamics (MQC) where in the fermion section the Block-Nordsic approximation has been made, i. e. u-numbers are substituted for ν matrices. The model was investigated by means of the Schwinger-Dyson equation for a quark propagator in the infrared region. The Schwinger-Dyson equation was managed to reduce to a differential equation which is easily solved. At that, the Green function is suitable to represent as integral transformation

Simple functional-differential equations for the bound-state wave-function components

International Nuclear Information System (INIS)

Kamuntavicius, G.P.

1986-01-01

The author presents a new method of a direct derivation of differential equations for the wave-function components of identical-particles systems. The method generates in a simple manner all the possible variants of these equations. In some cases they are the differential equations of Faddeev or Yakubovskii. It is shown that the case of the bound states allows to formulate very simple equations for the components which are equivalent to the Schroedinger equation for the complete wave function. The components with a minimal antisymmetry are defined and the corresponding equations are derived. (Auth.)

Schwinger effect and negative differential conductivity in holographic models

Directory of Open Access Journals (Sweden)

Shankhadeep Chakrabortty

2015-01-01

Full Text Available The consequences of the Schwinger effect for conductivity are computed for strong coupling systems using holography. The one-loop diagram on the flavor brane introduces an O(λNc imaginary part in the effective action for a Maxwell flavor gauge field. This in turn introduces a real conductivity in an otherwise insulating phase of the boundary theory. Moreover, in certain regions of parameter space the differential conductivity is negative. This is computed in the context of the Sakai–Sugimoto model.

Spectral representation of the particle production out of equilibrium—Schwinger mechanism in pulsed electric fields

International Nuclear Information System (INIS)

Fukushima, Kenji

2014-01-01

We develop a formalism to describe the particle production out of equilibrium in terms of dynamical spectral functions, i.e. Wigner transformed Pauli–Jordan's and Hadamard's functions. We take an explicit example of a spatially homogeneous scalar theory under pulsed electric fields and investigate the time evolution of the spectral functions. In the out-state we find an oscillatory peak in Hadamard's function as a result of the mixing between positive- and negative-energy waves. The strength of this peak is of the linear order of the Bogoliubov mixing coefficient, whereas the peak corresponding to the Schwinger mechanism is of the quadratic order. Between the in- and the out-states we observe a continuous flow of the spectral peaks together with two transient oscillatory peaks. We also discuss the medium effect at finite temperature and density. We emphasize that the entire structure of the spectral functions conveys rich information on real-time dynamics including the particle production. (paper)

Functional Fourier transforms and the loop equation

International Nuclear Information System (INIS)

Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.

1986-01-01

The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables

Schwinger's quantum action principle from Dirac’s formulation through Feynman’s path integrals, the Schwinger-Keldysh method, quantum field theory, to source theory

CERN Document Server

Milton, Kimball A

2015-01-01

Starting from the earlier notions of stationary action principles, these tutorial notes shows how Schwinger’s Quantum Action Principle descended from Dirac’s formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. Part I brings out in more detail the connection between the two formulations, and applications are discussed. Then, the Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.

Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

Science.gov (United States)

Göschl, Daniel

2018-03-01

We discuss simulation strategies for the massless lattice Schwinger model with a topological term and finite chemical potential. The simulation is done in a dual representation where the complex action problem is solved and the partition function is a sum over fermion loops, fermion dimers and plaquette-occupation numbers. We explore strategies to update the fermion loops coupled to the gauge degrees of freedom and check our results with conventional simulations (without topological term and at zero chemical potential), as well as with exact summation on small volumes. Some physical implications of the results are discussed.

Relativistic three-dimensional Lippmann-Schwinger cross sections for space radiation applications

Science.gov (United States)

Werneth, C. M.; Xu, X.; Norman, R. B.; Maung, K. M.

2017-12-01

Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world's best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic three-dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scattering Theory (MST) that uses 5 parameterizations-3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations-predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame (TLab) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which TLab > 220MeV /n .

On a functional equation related to the intermediate long wave equation

International Nuclear Information System (INIS)

Hone, A N W; Novikov, V S

2004-01-01

We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

Extended Hamiltonian formalism of the pure space-like axial gauge Schwinger model

International Nuclear Information System (INIS)

Nakawaki, Yuji; Mccartor, Gary

2001-01-01

We demonstrate that pure space-like axial gauge quantizations of gauge fields can be constructed in ways that are free from infrared divergences. To do so, we must extend the Hamiltonian formalism to include residual gauge fields. We construct an operator solution and an extended Hamiltonian of the pure space-like axial gauge Schwinger model. We begin by constructing an axial gauge formation in auxiliary coordinates, x μ =(x + , x - ), where x + =x 0 sinθ + x 1 cosθ, x - =x 0 cosθ - x 1 sinθ, and we take A=A 0 cosθ + A 1 sin θ=0 as the gauge fixing condition. In the region 0 - as the evolution parameter and construct a traditional canonical formulation of the temporal gauge Schwinger model in which residual gauge fields dependent only on x + are static canonical variables. Then we extrapolate the temporal gauge operator solution into the axial region, π / 4 + is taken as the evolution parameter. In the axial region we find that we have to take the representation of the residual gauge fields realizing the Mandelstam-Leibbrandt prescription in order for the infrared divergences resulting from (∂) -1 to be canceled by corresponding ones resulting from the inverse of the hyperbolic Laplace operator. We overcome the difficulty of constructing the Hamiltonian for the residual gauge fields by employing McCartor and Robertson's method, which gives us a term integrated over x - =constant. Finally, by taking the limit θ→π / 2 - 0, we obtain an operator solution and the Hamiltonian of the axial gauge (Coulomb gauge) Schwinger model in ordinary coordinates. That solution includes auxiliary fields, and the representation space is of indefinite metric, providing further evidence that 'physical' gauges are no more physical than 'unphysical' gauges. (author)

Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal modes

DEFF Research Database (Denmark)

de Lasson, Jakob Rosenkrantz; Mørk, Jesper; Kristensen, Philip Trøst

2013-01-01

We present a numerical formalism for solving the Lippmann–Schwinger equation for the electric field in three dimensions. The formalism may be applied to scatterers of different shapes and embedded in different background media, and we develop it in detail for the specific case of spherical scatte...

Glueball properties from the Bethe-Salpeter equation

International Nuclear Information System (INIS)

Kellermann, Christian

2012-01-01

For over thirty years bound states of gluons are an outstanding problem of both theoretical and experimental physics. Being predicted by Quantum-Chromodynamics their experimental confirmation is one of the foremost goals of large experimental facilities currently under construction like FAIR in Darmstadt. This thesis presents a novel approach to the theoretical determination of physical properties of bound states of two gluons, called glueballs. It uses the consistent combination of Schwinger-Dyson equations for gluons and ghosts and appropriate Bethe-Salpeter equations describing their corresponding bound-states. A rigorous derivation of both sets of equations, starting from an 2PI effective action is given as well as a general determination of appropriate decompositions of Bethe-Salpeter amplitudes to a given set of quantum numbers of a glueball. As an application example bound state masses of glueballs in a simple truncation scheme are calculated. (orig.)

The generalized Schwinger-DeWitt technique and the unique effective action in quantum gravity

International Nuclear Information System (INIS)

Barvinsky, A.O.; Vilkovisky, G.A.

1983-01-01

We consider the one-loop approximation to the recently proposed unique effective action in gauge theory. The Schwinger-DeWitt technique is generalized and applied to the computation of the unique gravitational counterterms. The issue of asymptotic freedom is reexamined. (orig.)

Legendre-tau approximations for functional differential equations

Science.gov (United States)

Ito, K.; Teglas, R.

1986-01-01

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

The Hadamard construction of Green's functions on a curved space-time: physics and explicit rigorous results

International Nuclear Information System (INIS)

John, R.W.

1987-01-01

First, in connection with their construction due to Hadamard, the mathematical and physical meaning of covariant Green's functions in relativistic gravitational fields - according to Einstein: on curved space-time - is discussed. Then, in the case of a general static spherically symmetric space-time the construction equations for a scalar Green's function are cast into symmetry-adapted form providing a convenient starting point for an explicit calculation of the Hadamard building elements. In applying the obtained basic scheme to a special one-parameter family of model metrics one succeeds in advancing to the explicit exact calculation of tail-term coefficients of a massless Green's function which are simultaneously coefficients in the Schwinger-De Witt expansion of the Feynman propagator for the corresponding massive Klein-Gordon equation on curved space-time. (author)

{theta}-vacua in the light-front quantized Schwinger model

Energy Technology Data Exchange (ETDEWEB)

Srivastava, Prem P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

1996-09-01

The light-front quantization of the bosonized Schwinger model is discussed in the continuum formulation. The proposal, successfully used earlier for describing the spontaneous symmetry breaking on the light-front, of separating first the scalar field into the dynamical condensate and the fluctuation fields before employing the standard Dirac method works here as well. Some topics on the front form theory are summarized in the Appendices and attention is drawn to the fact that the theory quantized, at x{sup +} seems already to carry information on equal x{sup -} commutators as well. (author). 21 refs.

θ-vacua in the light-front quantized Schwinger model

International Nuclear Information System (INIS)

Srivastava, Prem P.

1996-09-01

The light-front quantization of the bosonized Schwinger model is discussed in the continuum formulation. The proposal, successfully used earlier for describing the spontaneous symmetry breaking on the light-front, of separating first the scalar field into the dynamical condensate and the fluctuation fields before employing the standard Dirac method works here as well. Some topics on the front form theory are summarized in the Appendices and attention is drawn to the fact that the theory quantized, at x + seems already to carry information on equal x - commutators as well. (author). 21 refs

Critical behavior of the Schwinger model with Wilson fermions

International Nuclear Information System (INIS)

Azcoiti, V.; Laliena, V.

1995-09-01

A detailed analysis, in the framework of the MFA approach, of the critical behaviour of the lattice Schwinger model with Wilson fermions on lattices up to 24 2 , through the study of the Lee-Yang zeros and the specific heat, is presented. Compelling evidence is found for a critical line ending at k= 0.25 at large β. Finite size scaling analysis on lattices 8 2 , 12 2 , 16 2 , 20 2 and 24 2 indicates a continuous transition. The hyper scaling relation is verified in the explored β region

Linear measure functional differential equations with infinite delay

OpenAIRE

Monteiro, G. (Giselle Antunes); Slavík, A.

2014-01-01

We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.

Relativistic wave equations without the Velo-Zwanziger pathology

International Nuclear Information System (INIS)

Khalil, M.A.K.

1976-06-01

For particles described by relativistic wave equations of the form: (-iGAMMA x delta + m) psi(x) = 0 interacting with an external field B(x) it is known that the ''noncausal'' propagation characteristics are not present when (1) GAMMA 0 is diagonalizable and (2) B(x) = -eGAMMA/sub mu/A/sup mu/(x) (Amar--Dozzio). The ''noncausality''difficulties arise for the Rarita--Schwinger spin 3 / 2 equation, with nondiagonalizable GAMMA 0 , in minimal coupling (i.e., B(x) = -eGAMMA x A(x)) and the PDK spin 1 equation, with diagonalizable GAMMA 0 , in a quadrupole coupling (Velo--Zwanziger) where either (1) or (2) of the Amar--Dozzio (sufficient) conditions are violated. Some sufficient conditions are derived and explored where the Velo--Zwanziger ''noncausality'' pathology can be avoided, even though one, or the other, or both of the conditions (1) and (2) are violated. Examples with both reducible and irreducible wave equations are included

A novel method to solve functional differential equations

International Nuclear Information System (INIS)

Tapia, V.

1990-01-01

A method to solve differential equations containing the variational operator as the derivation operation is presented. They are called variational differential equations (VDE). The solution to a VDE should be a function containing the derivatives, with respect to the base space coordinates, of the fields up to a generic order s: a s-th-order function. The variational operator doubles the order of the function on which it acts. Therefore, in order to make compatible the orders of the different terms appearing in a VDE, the solution should be a function containing the derivatives of the fields at all orders. But this takes us again back to the functional methods. In order to avoid this, one must restrict the considerations, in the case of second-order VDEs, to the space of s-th-order functions on which the variational operator acts transitively. These functions have been characterized for a one-dimensional base space for the first- and second-order cases. These functions turn out to be polynomial in the highest-order derivatives of the fields with functions of the lower-order derivatives as coefficients. Then VDEs reduce to a system of coupled partial differential equations for the coefficients above mentioned. The importance of the method lies on the fact that the solutions to VDEs are in a one-to-one correspondence with the solutions of functional differential equations. The previous method finds direct applications in quantum field theory, where the Schroedinger equation plays a central role. Since the Schroedinger equation is reduced to a system of coupled partial differential equations, this provides a nonperturbative scheme for quantum field theory. As an example, the massless scalar field is considered

QCD bound states and their response to extremes of temperature and density

International Nuclear Information System (INIS)

Maris, P.

1998-01-01

We describe the application of Dyson-Schwinger equations to the calculation of hadron observable. The studies at zero temperature (T) and quark chemical potential (μ) provide a springboard for the extension to finite-(T, μ). Our exemplars highlight that much of hadronic physics can be understood as simply a manifestation of the nonperturbative, momentum-dependent dressing of the elementary Schwinger functions in QCD

Control functions in nonseparable simultaneous equations models

OpenAIRE

Blundell, R.; Matzkin, R. L.

2014-01-01

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has thus far been unknown. In this paper, we define a new property of functions called control function ...

Prospects of 'Topologically unquenched QCD' from a study of the analogous importance sampling method in the massive Schwinger model

International Nuclear Information System (INIS)

Duerr, S.

2000-01-01

I give a quick summary of my proposal for simulating an improvement on quenched QCD with dynamical fermions which interact with the gluon configuration only via the topological index of the latter. It amounts to include only the topological part of the functional determinant into the measure, thereby absorbing a correction factor into the observable. I discuss the prospects of this concept from a study in the massive N f- flavour Schwinger model, where the correction factor is indeed found to be of order 0(1)

Special solutions of neutral functional differential equations

Directory of Open Access Journals (Sweden)

Győri István

2001-01-01

Full Text Available For a system of nonlinear neutral functional differential equations we prove the existence of an -parameter family of "special solutions" which characterize the asymptotic behavior of all solutions at infinity. For retarded functional differential equations the special solutions used in this paper were introduced by Ryabov.

Some Functional Equations Originating from Number Theory

Indian Academy of Sciences (India)

We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.

Molecular distorted-wave Born approximation for ionization of H2 by electron impact

International Nuclear Information System (INIS)

Liu, Junbo; Liu, Dejun; Zhou, Yajun

2012-01-01

The molecular distorted-wave Born approximation is proposed to study the (e, 2e) reaction for H 2 targets. The wave functions of the incoming and outgoing electrons are obtained by solving the Lippmann-Schwinger equations, and the T-matrix in the Lippmann-Schwinger equations is calculated in a momentum space static-exchange-optical model. Triple differential cross sections are computed for incident energies of 100 and 250 eV in coplanar asymmetric geometry. Comparison of the present calculated results with the available experimental data in the literature reveals that there is good agreement. (paper)

Schwinger variational principle in scattering problems of charged particles on mesic atoms and atoms

International Nuclear Information System (INIS)

Belyaev, V.B.; Zubarev, A.L.; Podkopaev, A.P.

1978-01-01

The Schwinger variational principle is applied to solve the problems of atomic physics. A separable approximation for a Hamiltonian of a bound subsystem is used. The length of e + H-scattering and the elastic p(dμ)-scattering cross section are calculated in the second Born approximation

Resonances, resonance functions and spectral deformations

International Nuclear Information System (INIS)

Balslev, E.

1984-01-01

The present paper is aimed at an analysis of resonances and resonance states from a mathematical point of view. Resonances are characterized as singular points of the analytically continued Lippman-Schwinger equation, as complex eigenvalues of the Hamiltonian with a purely outgoing, exponentially growing eigenfunction, and as poles of the S-matrix. (orig./HSI)

On Kubo-Martin-Schwinger states of classical dynamical systems with the infinite-dimensional phase space

International Nuclear Information System (INIS)

Arsen'ev, A.A.

1979-01-01

Example of a classical dynamical system with the infinite-dimensional phase space, satisfying the analogue of the Kubo-Martin-Schwinger conditions for classical dynamics, is constructed explicitly. Connection between the system constructed and the Fock space dynamics is pointed out

Reduced kinetic equations: An influence functional approach

International Nuclear Information System (INIS)

Wio, H.S.

1985-01-01

The author discusses a scheme for obtaining reduced descriptions of multivariate kinetic equations based on the 'influence functional' method of Feynmann. It is applied to the case of Fokker-Planck equations showing the form that results for the reduced equation. The possibility of Markovian or non-Markovian reduced description is discussed. As a particular example, the reduction of the Kramers equation to the Smoluchwski equation in the limit of high friction is also discussed

Stability analysis of impulsive functional differential equations

CERN Document Server

Stamova, Ivanka

2009-01-01

This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equationsis under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied research

Handbook of functional equations stability theory

CERN Document Server

2014-01-01

This  handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications.                           The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with...

Existence of Mott-Schwinger interaction proved by means of p-/sup 12/C elastic scattering. [450 to 600 keV

Energy Technology Data Exchange (ETDEWEB)

Krause, H H; Arnold, W; Berg, H; Ulbricht, J; Clausnitzer, G [Giessen Univ. (Germany, F.R.). Inst. fuer Kernphysik

1979-01-01

The aim of this work was the unambiguous proof of the existence of the Mott-Schwinger interaction. The analyzing power of the p-/sup 12/C elastic scattering was measured in the energy range from 450 to 600 keV for scattering angles theta/sub Lab/ = 90/sup 0/ and 120/sup 0/ with an overall accuracy up to ..delta..A = 1 x /sup -4/. The data can be described very well with the R-matrix formalism including Mott-Schwinger interaction. Omitting this interaction results in large discrepancies.

On a Functional Equation for the Generating Function of the Logarithmic Series Distribution

OpenAIRE

Panaretos, John

1987-01-01

This note deals with finding the solution of a functional equation, where the function involved has the additional property of being a probability generating function. It turns out that the unique solution of this particular functional equation is the probability generating function of the logarithmic series distribution

General concepts of multichannel collision theory and their translation into the matrix formulation of few-body integral equations

International Nuclear Information System (INIS)

Sandhas, W.

1978-01-01

In the N-body problem mappings between channel states and scattering states are studied. It is shown in particular that the (2sup(N-1)-1) two-fragment MOELLER operators introduced on the whole Hilbert space are sufficient to provide all multi-fragment scattering states. Hence, each of these states is uniquely determined by (2sup(N-1)-1) Lippmann-Schwinger (LS) equations. Rewriting every set of LS equations as one matrix equation, current few-body approaches are incorporated in a rather natural way. The typical uniqueness questions of such coupled systems are discussed, and it is shown that Faddeev-type couplings lead to unique equations for arbitrary N. (author)

General concepts of multichannel collision theory and their translation into the matrix formulation of few-body integral equations

International Nuclear Information System (INIS)

Sandhas, W.

1978-04-01

In the N-body problem mappings between channel states and scattering states are studied. It is shown in particular that the (2sup(N-1)-1) two-fragment Moeller operators introduced on the whole Hilbert space are sufficient to provide all multifragment scattering states. Hence, each of these states is uniquly determined by (2sup(N-1)-1) Lippmann-Schwinger (LS) equations. Rewriting every set of LS equations as one matrix equation, current few-body approaches are incorporated in a rather natural way. The typical uniqueness questions of such coupled systems are discussed, and it si shown that Faddeev-type couplings lead to unique equations for arbitrary N. (orig.) [de

Possibility of experimental detection of the Dirac-Schwinger heavy mass monopoles

Energy Technology Data Exchange (ETDEWEB)

Ginzburg, I F [AN SSSR, Novosibirsk. Inst. Matematiki; Panfil, S L [AN SSSR, Novosibirsk. Inst. Avtomatiki i Ehlektrometrii

1982-12-01

A possibility of the Dirac-Schwinger point heavy-mass monopoles detection in scattering or production of photons at large angles via the monopole loop, is discussed. The monopoles with masses M < or approximately from 50 to 100 GeV may be found in experiments at PETRA and PEP, and monopoles with masses M < or approximately from 2 to 3 TeV may be discovered in future experiments in colliding photon beams of 50-300 GeV energies.

Confined solutions of the Thirring model coupled to a Schwinger field

International Nuclear Information System (INIS)

Hortacsu, M.

1976-08-01

In the study of the confined classical solutions of the bosonized massive Thirring field coupled to a Schwinger field, it is observed that, regardless of their respective magnitudes and signs, the Thirring interaction is dominant over the other one, in determining whether such a solution exists. Confined solutions for the Thirring field are possible if and only if the Thirring coupling is attractive. Solutions are constructed for the Thirring model coupling attractive, repulsive and equal to zero

On Approximate Solutions of Functional Equations in Vector Lattices

Directory of Open Access Journals (Sweden)

Bogdan Batko

2014-01-01

Full Text Available We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra. The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y+F(x+F(y≠0⇒F(x+y=F(x+F(y in Riesz spaces, the Cauchy equation with squares F(x+y2=(F(x+F(y2 in f-algebras, and the quadratic functional equation F(x+y+F(x-y=2F(x+2F(y in Riesz spaces.

Non-Schwinger solution of the two-dimensional massless spinor electrodynamics

International Nuclear Information System (INIS)

Mikhov, S.G.

1981-01-01

In the present paper a regularization procedure is formulated for the current in the two-dimensional massless spinor electrodynamics that is both gauge and γ 5 -gauge invariant. This gives rise to an operator solution of the model that does not involve a massive photon. The latter solution is studied in some detail, and it is shown that although a charge operator exists, it does not define the electric charge of the spinor field. This can be a manifestation of the charge screening mechanism that is present in the Schwinger model [ru

Schwinger mechanism in electromagnetic field in de Sitter spacetime

Directory of Open Access Journals (Sweden)

Bavarsad Ehsan

2018-01-01

Full Text Available We investigate Schwinger scalar pair production in a constant electromagnetic field in de Sitter (dS spacetime. We obtain the pair production rate, which agrees with the Hawking radiation in the limit of zero electric field in dS. The result describes how a cosmic magnetic field affects the pair production rate. In addition, using a numerical method we study the effect of the magnetic field on the induced current. We find that in the strong electromagnetic field the current has a linear response to the electric and magnetic fields, while in the infrared regime, is inversely proportional to the electric field and leads to infrared hyperconductivity.

Heisenberg equations of motion for the spin-3/2 field in the presence of an interaction

International Nuclear Information System (INIS)

Nagpal, A.K.

1977-01-01

The Rarita-Schwinger spin-3/2 field interacting with a Dirac field and a scalar field (external) is found to satisfy the Heisenberg equations of motion, in the weak-field limit. This is analogous to the result, for the case of spin-3/2 field minimally coupled with external electromagnetic field, recently obtained by Mainland and Sudarshan (Phys. Rev. D. 8:1088 (1973)). (author)

On two functional equations originating from number theory

Indian Academy of Sciences (India)

Reducing the functional equations introduced in Proc. Indian Acad. Sci. (Math. Sci.) 113(2) (2003) 91–98 and in Appl. Math. Lett. 21 (2008) 974–977 to equations in complex variables and quaternions, we find general solutions of the equations. We also obtain the stability of the equations.

Numerical approximations of difference functional equations and applications

Directory of Open Access Journals (Sweden)

Zdzisław Kamont

2005-01-01

Full Text Available We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.

The stability of quadratic-reciprocal functional equation

Science.gov (United States)

Song, Aimin; Song, Minwei

2018-04-01

A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

On Some Calculations of Effective Action and Fujikawa Regularized Anomaly in the Chiral Schwinger Model

OpenAIRE

Mehrdad, GOSHTASBPOUR; Center for Theoretical Physics and Mathematics, AEOI:Department of Physics, Shahid Beheshti University

1991-01-01

Extended D^†+D-DD^† Fujikawa regularization of anomaly and a method of integration of fermions for the chiral Schwinger model are criticized. On the basis of the corrected integration method, a new extended version of D^2 is obtained, resulting in the Jackiw-Rajaraman effective action.

Self-consistent assessment of Englert-Schwinger model on atomic properties

Science.gov (United States)

Lehtomäki, Jouko; Lopez-Acevedo, Olga

2017-12-01

Our manuscript investigates a self-consistent solution of the statistical atom model proposed by Berthold-Georg Englert and Julian Schwinger (the ES model) and benchmarks it against atomic Kohn-Sham and two orbital-free models of the Thomas-Fermi-Dirac (TFD)-λvW family. Results show that the ES model generally offers the same accuracy as the well-known TFD-1/5 vW model; however, the ES model corrects the failure in the Pauli potential near-nucleus region. We also point to the inability of describing low-Z atoms as the foremost concern in improving the present model.

Relativistic reconnection in near critical Schwinger field

Science.gov (United States)

Schoeffler, Kevin; Grismayer, Thomas; Fonseca, Ricardo; Silva, Luis; Uzdensky, Dmitri

2017-10-01

Magnetic reconnection in relativistic pair plasma with QED radiation and pair-creation effects in the presence of strong magnetic fields is investigated using 2D particle-in-cell simulations. The simulations are performed with the QED module of the OSIRIS framework that includes photon emission by electrons and positrons and single photon decay into pairs (non-linear Breit-Wheeler). We investigate the effectiveness of reconnection as a pair- and gamma-ray production mechanism across a broad range of reconnecting magnetic fields, including those approaching the critical quantum (Schwinger) field, and we also explore how the radiative cooling and pair-production processes affect reconnection. We find that in the extreme field regime, the magnetic energy is mostly converted into radiation rather than into particle kinetic energy. This study is a first concrete step towards better understanding of magnetic reconnection as a possible mechanism powering gamma-ray flares in magnetar magnetospheres.

Schwinger type processes via branes and their gravity duals

International Nuclear Information System (INIS)

Gorsky, A.S.; Saraikin, K.A.; Selivanov, K.G.

2002-01-01

We consider Schwinger type processes involving the creation of the charge and monopole pairs in the external fields and propose interpretation of these processes via corresponding brane configurations in type IIB string theory. We suggest simple description of some new interesting nonperturbative processes like monopole/dyon transitions in the electric field and W-boson decay in the magnetic field using the brane language. Nonperturbative pair production in the strong coupling regime using the AdS/CFT correspondence is studied. The treatment of the similar processes in the noncommutative theories when noncommutativity is traded for the background fields is presented and the possible role of the critical magnetic field which is S-dual to the critical electric field is discussed

On some functional equations related to Steffensen's inequality

Directory of Open Access Journals (Sweden)

Bogdan Choczewski

2004-05-01

Full Text Available We consider the problem, proposed by the second author (cf. [1] of solving functional equations stemming from the Steffensen integral inequality (S, which is applicable in actuarial problems, cf. [4]. Imposing some regularity conditions we find solutions of two equations in two variables, one with two and another with three unknown functions.

The mass spectrum of the Schwinger model with matrix product states

Energy Technology Data Exchange (ETDEWEB)

Banuls, M.C.; Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Poznan Univ. (Poland). Faculty of Physics; Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Cyprus Univ., Nicosia (Cyprus). Dept. of Physics

2013-07-15

We show the feasibility of tensor network solutions for lattice gauge theories in Hamiltonian formulation by applying matrix product states algorithms to the Schwinger model with zero and non-vanishing fermion mass. We introduce new techniques to compute excitations in a system with open boundary conditions, and to identify the states corresponding to low momentum and different quantum numbers in the continuum. For the ground state and both the vector and scalar mass gaps in the massive case, the MPS technique attains precisions comparable to the best results available from other techniques.

Functional-derivative study of the Hubbard model. III. Fully renormalized Green's function

International Nuclear Information System (INIS)

Arai, T.; Cohen, M.H.

1980-01-01

The functional-derivative method of calculating the Green's function developed earlier for the Hubbard model is generalized and used to obtain a fully renormalized solution. Higher-order functional derivatives operating on the basic Green's functions, G and GAMMA, are all evaluated explicitly, thus making the solution applicable to the narrow-band region as well as the wide-band region. Correction terms Phi generated from functional derivatives of equal-time Green's functions of the type delta/sup n/ /deltaepsilon/sup n/, etc., with n > or = 2. It is found that the Phi's are, in fact, renormalization factors involved in the self-energy Σ and that the structure of the Phi's resembles that of Σ and contains the same renormalization factors Phi. The renormalization factors Phi are shown to satisfy a set of equations and can be evaluated self-consistently. In the presence of the Phi's, all difficulties found in the previous results (papers I and II) are removed, and the energy spectrum ω can now be evaluated for all occupations n. The Schwinger relation is the only basic relation used in generating this fully self-consistent Green's function, and the Baym-Kadanoff continuity condition is automatically satisfied

Modular differential equations for torus one-point functions

International Nuclear Information System (INIS)

Gaberdiel, Matthias R; Lang, Samuel

2009-01-01

It is shown that in a rational conformal field theory every torus one-point function of a given highest weight state satisfies a modular differential equation. We derive and solve these differential equations explicitly for some Virasoro minimal models. In general, however, the resulting amplitudes do not seem to be expressible in terms of standard transcendental functions

Neutral Backward Stochastic Functional Differential Equations and Their Application

OpenAIRE

Wei, Wenning

2013-01-01

In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an application, we discuss the optimal control of neutral stochastic functional differential equations, establish a Pontryagin maximum principle, and give an explicit optimal value for the linear optimal control.

Black hole entropy functions and attractor equations

International Nuclear Information System (INIS)

Lopes Cardoso, Gabriel; Wit, Bernard de; Mahapatra, Swapna

2007-01-01

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N = 2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions

On the existence of solutions for functional differential equations

International Nuclear Information System (INIS)

Walo Omana, R.

1994-12-01

The aim of the paper is to extend the Granas Topological Transversality Method used in boundary value problems for functional differential equations for first and second order, to the case of n-th order functional differential equations. 15 refs

Coulomb singularities in scattering wave functions of spin-orbit-coupled states

International Nuclear Information System (INIS)

Bogdanski, P.; Ouerdane, H.

2011-01-01

We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that Δl= 0, ±2. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum l, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method. We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system.

Integral equations of hadronic correlation functions a functional- bootstrap approach

CERN Document Server

Manesis, E K

1974-01-01

A reasonable 'microscopic' foundation of the Feynman hadron-liquid analogy is offered, based on a class of models for hadron production. In an external field formalism, the equivalence (complementarity) of the exclusive and inclusive descriptions of hadronic reactions is specifically expressed in a functional-bootstrap form, and integral equations between inclusive and exclusive correlation functions are derived. Using the latest CERN-ISR data on the two-pion inclusive correlation function, and assuming rapidity translational invariance for the exclusive one, the simplest integral equation is solved in the 'central region' and an exclusive correlation length in rapidity predicted. An explanation is also offered for the unexpected similarity observed between pi /sup +/ pi /sup -/ and pi /sup -/ pi /sup -/ inclusive correlations. (31 refs).

Squares of White Noise, SL(2,C) and Kubo - Martin -Schwinger States

OpenAIRE

Prokhorenko, D. V.

2007-01-01

We investigate the structure of Kubo - Martin - Schwinger (KMS) states on some extension of the universal enveloping algebra of SL(2,C}. We find that there exists a one-to-one correspondence between the set of all covariant KMS states on this algebra and the set of all probability measures d\\mu on the real half-line, which decrease faster than any inverse polynomial. This problem is connected to the problem of KMS states on square of white noise algebra.

Quasi-Newton methods for parameter estimation in functional differential equations

Science.gov (United States)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

International Nuclear Information System (INIS)

Zhang Liang; Zhang Lifeng; Li Chongyin

2008-01-01

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions

Effects of strain on the Schwinger pair creation in graphene

International Nuclear Information System (INIS)

Fanbanrai, P.; Hutem, A.; Boonchui, S.

2015-01-01

The effects of strain on mechanically deformed graphene are determined by looking at how the strain affects the amplitude of the Schwinger two particle pair state. The influences of the lattice distortions, such as isotropic tensile strain ϵ is , shear strain ϵ ss , uniaxial armchair strain ϵ as , and zigzag strain ϵ zs , on the photon emission spectrum have been analyzed. We find that the intensities of the emission increases or decreases when compared to those of the unstrained graphene, depending on the type of strain applied. Thus the structure of energy band, the frequencies of the photons and the emission spectrum can be controlled by use of the different strains

Determination of quantum defects from the poles of the Schwinger T matrix

International Nuclear Information System (INIS)

Snitchler, G.L.

1987-01-01

Quantum defects are determined for lithium, sodium, potassium, and beryllium by searching for the poles of the Schwinger T matrix along the negative real-energy axis. This method takes advantage of the fundamental ideas of QDT by using a Coulomb Green's function to factor out most of the energy dependence. For the alkali atoms, a single-channel calculation is performed using model potentials to include the effects of core polarization and correlation. Quantum defects accurate to 1% are easily obtained with small grids and small fixed-basis sets for an entire Rydberg series up to principal quantum number, n, as high as 60. A multichannel extension of this method is used to determined neutral-beryllium quantum defects for the 1 P 0 , 3 P 0 , and 3 S Rydberg series. The 1 P 0 and 3 P 0 calculations are performed in a two-channel approximation using 1s 2 2p static-exchange cores. The 3 S calculation includes a third channel with a 1s 2 3s core. Accurate quantum defects are obtained with 4 to 6 basis functions per channel. The energies are variational and the wave functions have the correct asymptotic form enforced by the Coulomb Green's function. Tentative results for Be I 1 P 0 and 3 P 0 resonances below the 1s 2 2p 2 P threshold are presented. This calculation which is performed in a three-channel approximation uses a complex multichannel Coulomb Green's function to search for poles in the fourth quadrant of the complex-energy plane

Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap

International Nuclear Information System (INIS)

Cichy, Krzysztof; Poznan Univ.; Kujawa-Cichy, Agnieszka; Szyniszewski, Marcin; Manchester Univ.

2012-12-01

We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10 -6 %.

Remarks on the stability of some quadratic functional equations

Directory of Open Access Journals (Sweden)

Zygfryd Kominek

2008-01-01

Full Text Available Stability problems concerning the functional equations of the form \\[f(2x+y=4f(x+f(y+f(x+y-f(x-y,\\tag{1}\\] and \\[f(2x+y+f(2x-y=8f(x+2f(y\\tag{2}\\] are investigated. We prove that if the norm of the difference between the LHS and the RHS of one of equations \\((1\\ or \\((2\\, calculated for a function \\(g\\ is say, dominated by a function \\(\\varphi\\ in two variables having some standard properties then there exists a unique solution \\(f\\ of this equation and the norm of the difference between \\(g\\ and \\(f\\ is controlled by a function depending on \\(\\varphi\\.

A systematic approach to sketch Bethe-Salpeter equation

Directory of Open Access Journals (Sweden)

Qin Si-xue

2016-01-01

Full Text Available To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark–anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD’s gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symmetry breaking (DCSB. The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.

Periodic differential equations an introduction to Mathieu, Lamé, and allied functions

CERN Document Server

Arscott, Felix M; Stark, M; Ulam, S

1964-01-01

Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions covers the fundamental problems and techniques of solution of periodic differential equations. This book is composed of 10 chapters that present important equations and the special functions they generate, ranging from Mathieu's equation to the intractable ellipsoidal wave equation.This book starts with a survey of the main problems related to the formation of periodic differential equations. The subsequent chapters deal with the general theory of Mathieu's equation, Mathieu functions of integral order, and

Synchronization with propagation - The functional differential equations

Science.gov (United States)

Rǎsvan, Vladimir

2016-06-01

The structure represented by one or several oscillators couple to a one-dimensional transmission environment (e.g. a vibrating string in the mechanical case or a lossless transmission line in the electrical case) turned to be attractive for the research in the field of complex structures and/or complex behavior. This is due to the fact that such a structure represents some generalization of various interconnection modes with lumped parameters for the oscillators. On the other hand the lossless and distortionless propagation along transmission lines has generated several research in electrical, thermal, hydro and control engineering leading to the association of some functional differential equations to the basic initial boundary value problems. The present research is performed at the crossroad of the aforementioned directions. We shall associate to the starting models some functional differential equations - in most cases of neutral type - and make use of the general theorems for existence and stability of forced oscillations for functional differential equations. The challenges introduced by the analyzed problems for the general theory are emphasized, together with the implication of the results for various applications.

Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap

Energy Technology Data Exchange (ETDEWEB)

Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Kujawa-Cichy, Agnieszka [Poznan Univ. (Poland). Faculty of Physics; Szyniszewski, Marcin [Poznan Univ. (Poland). Faculty of Physics; Manchester Univ. (United Kingdom). NOWNano DTC

2012-12-15

We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10{sup -6} %.

Measure functional differential equations in the space of functions of bounded variation

Czech Academy of Sciences Publication Activity Database

Afonso, S.; Rontó, András

2013-01-01

Roč. 2013, č. 582161 (2013), s. 582161 ISSN 1085-3375 Institutional support: RVO:67985840 Keywords : measure differential equations * functional differential equations Subject RIV: BA - General Mathematics Impact factor: 1.274, year: 2013 http://www.hindawi.com/journals/ aaa /2013/582161/

Exact solutions for nonlinear evolution equations using Exp-function method

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2008-01-01

In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations

Investigation of anomalous Schwinger terms based on the Batalin-Fradkin-Vilkovisky formalism

International Nuclear Information System (INIS)

Fujiwara, T.; Igarashi, Y.; Kubo, J.

1991-01-01

On the basis of the generalized hamiltonian formalism of Batalin, Fradkin and Vilkovisky, we investigate the algebraic structure of the anomalous Schwinger terms that appear in the nilpotency condition and/or the time development of the BRST charge in Yang-Mills theory. These anomalies are shown to satisfy a set of consistency conditions which originate from the (super-)Jacobi identities among (anti-)commutation relations. The consistency conditions are solved in an exhaustive fashion to order h- 2 and our results are independent of a wide class of regularization schemes and gauge choices. (orig.)

Quantum mechanics on Riemannian manifold in Schwinger's quantization approach II

International Nuclear Information System (INIS)

Chepilko, N.M.; Romanenko, A.V.

2001-01-01

The extended Schwinger quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold M is a homogeneous Riemannian space with the given action of an isometry transformation group. Using the identification of M with the quotient space G/H, where H is the isotropy group of an arbitrary fixed point of M, we show that quantum mechanics on G/H possesses a gauge structure, described by a gauge potential that is the connection 1-form of the principal fiber bundle G(G/H, H). The coordinate representation of quantum mechanics and the procedure for selecting the physical sector of the states are developed. (orig.)

Inverse Schroedinger equation and the exact wave function

International Nuclear Information System (INIS)

Nakatsuji, Hiroshi

2002-01-01

Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem

Functional equations in matrix normed spaces

Indian Academy of Sciences (India)

The abstract characterization given for linear spaces of bounded Hilbert space operators in terms of ... effect on operator algebra theory (see [12]). .... of functional equations for the proof of new fixed point theorems with applications. By.

Analytic Solutions of Special Functional Equations

Directory of Open Access Journals (Sweden)

Octav Olteanu

2013-07-01

Full Text Available We recall some of our earlier results on the construction of a mapping defined implicitly, without using the implicit function theorem. All these considerations work in the real case, for functions and operators. Then we consider the complex case, proving the analyticity of the function defined implicitly, under certain hypothesis. Some consequences are given. An approximating formula for the analytic form of the solution is also given. Finally, one illustrates the preceding results by an application to a concrete functional and operatorial equation. Some related examples are given.

Conformable Fractional Bessel Equation and Bessel Functions

OpenAIRE

Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

2015-01-01

In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary solutions. In addition, we present certain property of fractional Bessel functions.

Stability of Functional Differential Equations

CERN Document Server

Lemm, Jeffrey M

1986-01-01

This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.

Green's function method for perturbed Korteweg-de Vries equation

International Nuclear Information System (INIS)

Cai Hao; Huang Nianning

2003-01-01

The x-derivatives of squared Jost solution are the eigenfunctions with the zero eigenvalue of the linearized equation derived from the perturbed Korteweg-de Vries equation. A method similar to Green's function formalism is introduced to show the completeness of the squared Jost solutions in multi-soliton cases. It is not related to Lax equations directly, and thus it is beneficial to deal with the nonlinear equations with complicated Lax pair

Effect of Differential Item Functioning on Test Equating

Science.gov (United States)

Kabasakal, Kübra Atalay; Kelecioglu, Hülya

2015-01-01

This study examines the effect of differential item functioning (DIF) items on test equating through multilevel item response models (MIRMs) and traditional IRMs. The performances of three different equating models were investigated under 24 different simulation conditions, and the variables whose effects were examined included sample size, test…

Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge

International Nuclear Information System (INIS)

Reinhardt, H.; Schleifenbaum, W.

2009-01-01

We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss' law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schroedinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case

Qualitative properties of functional differential equation

Directory of Open Access Journals (Sweden)

Diana Otrocol

2014-10-01

Full Text Available The aim of this paper is to discuss some basic problems (existence and uniqueness, data dependence of the fixed point theory for a functional differential equation with an abstract Volterra operator. In the end an application is given.

Stability of the Exponential Functional Equation in Riesz Algebras

Directory of Open Access Journals (Sweden)

Bogdan Batko

2014-01-01

Full Text Available We deal with the stability of the exponential Cauchy functional equation F(x+y=F(xF(y in the class of functions F:G→L mapping a group (G, + into a Riesz algebra L. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem.

Dynamic equations for gauge-invariant wave functions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.; Solovtsov, I.L.

1984-01-01

The Bethe-Salpeter and quasipotential dynamic equations for wave functions of relative quark motion, have been derived. Wave functions are determined by the gauge invariant method. The V.A. Fock gauge condition is used in the construction. Despite the transl tional noninvariance of the gauge condition the standard separation of variables has been obtained and wave function doesn't contain gauge exponents

Linear measure functional differential equations with infinite delay

Czech Academy of Sciences Publication Activity Database

Monteiro, Giselle Antunes; Slavík, A.

2014-01-01

Roč. 287, 11-12 (2014), s. 1363-1382 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : measure functional differential equations * generalized ordinary differential equations * Kurzweil-Stieltjes integral Subject RIV: BA - General Mathematics Impact factor: 0.683, year: 2014 http://onlinelibrary.wiley.com/doi/10.1002/mana.201300048/abstract

Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Ahmet Bekir

2013-01-01

Full Text Available The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

Thermal evolution of the Schwinger model with matrix product operators

International Nuclear Information System (INIS)

Banuls, M.C.; Cirac, J.I.; Cichy, K.; Jansen, K.; Saito, H.

2015-10-01

We demonstrate the suitability of tensor network techniques for describing the thermal evolution of lattice gauge theories. As a benchmark case, we have studied the temperature dependence of the chiral condensate in the Schwinger model, using matrix product operators to approximate the thermal equilibrium states for finite system sizes with non-zero lattice spacings. We show how these techniques allow for reliable extrapolations in bond dimension, step width, system size and lattice spacing, and for a systematic estimation and control of all error sources involved in the calculation. The reached values of the lattice spacing are small enough to capture the most challenging region of high temperatures and the final results are consistent with the analytical prediction by Sachs and Wipf over a broad temperature range.

Spectator electric fields, de Sitter spacetime, and the Schwinger effect

Science.gov (United States)

Giovannini, Massimo

2018-03-01

During a de Sitter stage of expansion, the spectator fields of different spin are constrained by the critical density bound and by further requirements determined by their specific physical nature. The evolution of spectator electric fields in conformally flat background geometries is occasionally concocted by postulating the existence of ad hoc currents, but this apparently innocuous trick violates the second law of thermodynamics. Such a problem occurs, in particular, for those configurations (customarily employed for the analysis of the Schwinger effect in four-dimensional de Sitter backgrounds) leading to an electric energy density which is practically unaffected by the expansion of the underlying geometry. The obtained results are compared with more mundane situations where Joule heating develops in the early stages of a quasi-de Sitter phase.

Wigner function and Schroedinger equation in phase-space representation

International Nuclear Information System (INIS)

Chruscinski, Dariusz; Mlodawski, Krzysztof

2005-01-01

We discuss a family of quasidistributions (s-ordered Wigner functions of Agarwal and Wolf [Phys. Rev. D 2, 2161 (1970); Phys. Rev. D 2, 2187 (1970); Phys. Rev. D 2, 2206 (1970)]) and its connection to the so-called phase space representation of the Schroedinger equation. It turns out that although Wigner functions satisfy the Schroedinger equation in phase space, they have a completely different interpretation

Special function solutions of the free particle Dirac equation

International Nuclear Information System (INIS)

Strange, P

2012-01-01

The Dirac equation is one of the fundamental equations in physics. Here we present and discuss two novel solutions of the free particle Dirac equation. These solutions have an exact analytical form in terms of Airy or Mathieu functions and exhibit unexpected properties including an enhanced Doppler effect, accelerating wavefronts and solutions with a degree of localization. (paper)

Asymptotic analysis for functional stochastic differential equations

CERN Document Server

Bao, Jianhai; Yuan, Chenggui

2016-01-01

This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity. This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.

Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields

Energy Technology Data Exchange (ETDEWEB)

Schneider, Christian; Schützhold, Ralf [Fakultät für Physik, Universität Duisburg-Essen,Lotharstrasse 1, 47057 Duisburg (Germany)

2016-02-24

Via the world-line instanton method, we study electron-positron pair creation by a strong (but sub-critical) electric field of the profile E/cosh{sup 2} (kx) superimposed by a weaker pulse E{sup ′}/cosh{sup 2} (ωt). If the temporal Keldysh parameter γ{sub ω}=mω/(qE) exceeds a threshold value γ{sub ω}{sup crit} which depends on the spatial Keldysh parameter γ{sub k}=mk/(qE), we find a drastic enhancement of the pair creation probability — reporting on what we believe to be the first analytic non-perturbative result for the interplay between temporal and spatial field dependences E(t,x) in the Sauter-Schwinger effect. Finally, we speculate whether an analogous effect (drastic enhancement of tunneling probability) could occur in other scenarios such as stimulated nuclear decay, for example.

On extension of solutions of a simultaneous system of iterative functional equations

Directory of Open Access Journals (Sweden)

Janusz Matkowski

2009-01-01

Full Text Available Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form \\[ \\varphi(x = h (x, \\varphi[f_1(x],\\ldots,\\varphi[f_m(x],\\] \\[\\varphi(x = H (x, \\varphi[F_1(x],\\ldots,\\varphi[F_m(x],\\] to a global one are presented. Extensions of solutions of functional equations, both in single and in several variables, play important role (cf. for instance [M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers, Warsaw, 1968, M. Kuczma, B. Choczewski, R. Ger, Iterative functional equations, Encyclopedia of Mathematics and Its Applications v. 32, Cambridge, 1990, J. Matkowski, Iteration groups, commuting functions and simultaneous systems of linear functional equations, Opuscula Math. 28 (2008 4, 531-541].

Infrared asymptotics of a gauge-invariant propagator in quantum electrodynamics

International Nuclear Information System (INIS)

Skachkov, N.B.; Shevchenko, O.Yu.; Solovtsov, I.l.

1987-01-01

A new class of gauge-invariant fields is introduced. For the gauge-invariant propagator of a spinor field the analogue of the Dyson-Schwinger equations is derived. With the help of these equations as well as the functional integration method it is shown that the gauge-invariant spinor propagator has a simple pole singularity in the infrared region

Infrared asymptotics of a gauge-invariant propagator in quantum electrodynamics

International Nuclear Information System (INIS)

Skachkov, N.B.; Shevchenko, O.Yu.

1985-01-01

A new class of the gauge-invariant field is introduced. For the gauge-invariant propagator of a spinor field the analog of the Dyson-Schwinger equations is derived. By using these equations as well as the functional integration method it is shown that the gauge-invariant spinor propagator has a simple pole singularity in the infrared region

Predictive equation of state method for heavy materials based on the Dirac equation and density functional theory

Science.gov (United States)

Wills, John M.; Mattsson, Ann E.

2012-02-01

Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Hartman-Wintner growth results for sublinear functional differential equations

Directory of Open Access Journals (Sweden)

John A. D. Appleby

2017-01-01

Full Text Available This article determines the rate of growth to infinity of scalar autonomous nonlinear functional and Volterra differential equations. In these equations, the right-hand side is a positive continuous linear functional of f(x. We assume f grows sublinearly, leading to subexponential growth in the solutions. The main results show that the solution of the functional differential equations are asymptotic to that of an auxiliary autonomous ordinary differential equation with right-hand side proportional to f. This happens provided f grows more slowly than l(x=x/log(x. The linear-logarithmic growth rate is also shown to be critical: if f grows more rapidly than l, the ODE dominates the FDE; if f is asymptotic to a constant multiple of l, the FDE and ODE grow at the same rate, modulo a constant non-unit factor; if f grows more slowly than l, the ODE and FDE grow at exactly the same rate. A partial converse of the last result is also proven. In the case when the growth rate is slower than that of the ODE, sharp bounds on the growth rate are determined. The Volterra and finite memory equations can have differing asymptotic behaviour and we explore the source of these differences.

Exp-function method for solving fractional partial differential equations.

Science.gov (United States)

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

Functional differential equations with unbounded delay in extrapolation spaces

Directory of Open Access Journals (Sweden)

Mostafa Adimy

2014-08-01

Full Text Available We study the existence, regularity and stability of solutions for nonlinear partial neutral functional differential equations with unbounded delay and a Hille-Yosida operator on a Banach space X. We consider two nonlinear perturbations: the first one is a function taking its values in X and the second one is a function belonging to a space larger than X, an extrapolated space. We use the extrapolation techniques to prove the existence and regularity of solutions and we establish a linearization principle for the stability of the equilibria of our equation.

Quarks and gluons in the phase diagram of quantum chromodynamics

Energy Technology Data Exchange (ETDEWEB)

Welzbacher, Christian Andreas

2016-07-14

In this dissertation we study the phase diagram of strongly interacting matter by approaching the theory of quantum chromodynamics in the functional approach of Dyson-Schwinger equations. With these quantum (field) equations of motions we calculate the non-perturbative quark propagator within the Matsubara formalism. We built up on previous works and extend the so-called truncation scheme, which is necessary to render the infinite tower of Dyson-Schwinger equations finite and study phase transitions of chiral symmetry and the confinement/deconfinement transition. In the first part of this thesis we discuss general aspects of quantum chromodynamics and introduce the Dyson-Schwinger equations in general and present the quark Dyson-Schwinger equation together with its counterpart for the gluon. The Bethe-Salpeter equation is introduced which is necessary to perform two-body bound state calculations. A view on the phase diagram of quantum chromodynamics is given, including the discussion of order parameter for chiral symmetry and confinement. Here we also discuss the dependence of the phase structure on the masses of the quarks. In the following we present the truncation and our results for an unquenched N{sub f} = 2+1 calculation and compare it to previous studies. We highlight some complementary details for the quark and gluon propagator and discus the resulting phase diagram, which is in agreement with previous work. Results for an equivalent of the Columbia plot and the critical surface are discussed. A systematically improved truncation, where the charm quark as a dynamical quark flavour is added, will be presented in Ch. 4. An important aspect in this investigation is the proper adjustment of the scales. This is done by matching vacuum properties of the relevant pseudoscalar mesons separately for N{sub f} = 2+1 and N f = 2+1+1 via a solution of the Bethe-Salpeter equation. A comparison of the resulting N{sub f} = 2+1 and N{sub f} = 2+1+1 phase diagram indicates

d'Alembert's other functional equation

DEFF Research Database (Denmark)

Ebanks, Bruce; Stetkaer, Henrik

2015-01-01

Let G be a topological group. We find formulas for the solutions f; g; h is an element of C(G) of the functional equation f(xy) - f (y(-1)x) = g(x)h(y); x; y is an element of G; when G is generated by its squares and its center, as for instance when G is a connected Lie group, and when G is compact...

Best lung function equations for the very elderly selected by survival analysis

DEFF Research Database (Denmark)

Miller, Martin R; Thinggaard, Mikael; Christensen, Kaare

2014-01-01

We evaluated which equations best predicted the lung function of a cohort of nonagenarians based on which best accounted for subsequent survival.In 1998, we measured lung function, grip strength and dementia score (Mini Mental State Examination (MMSE)) in a population-based sample of 2262 Danes...... with a hazard ratio for death of 1, 1.16, 1.32 and 1.60 respectively, compared with equations derived with the inclusion of elderly subjects.We conclude that extrapolating from NHANES III equations to predict lung function in nonagenarians gave better survival predictions from spirometry than when employing...... equations derived using very elderly subjects with possible selection bias. These findings can help inform how future lung function equations for the elderly are derived....

On solvability of some quadratic functional-integral equation in Banach algebra

International Nuclear Information System (INIS)

Darwish, M.A.

2007-08-01

Using the technique of a suitable measure of non-compactness in Banach algebra, we prove an existence theorem for some functional-integral equations which contain, as particular cases, a lot of integral and functional-integral equations that arise in many branches of nonlinear analysis and its applications. Also, the famous Chandrasekhar's integral equation is considered as a special case. (author)

Functional Equations in Fuzzy Banach Spaces

Directory of Open Access Journals (Sweden)

M. Eshaghi Gordji

2012-01-01

generalized Hyers-Ulam stability of the following additive-quadratic functional equation f(x+ky+f(x−ky=f(x+y+f(x−y+(2(k+1/kf(ky−2(k+1f(y for fixed integers k with k≠0,±1 in fuzzy Banach spaces.

Quantization conditions and functional equations in ABJ(M) theories

International Nuclear Information System (INIS)

Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki

2014-12-01

The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case. As a consequence, we find an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants. These functional equations relate the spectral determinants of ABJ theories with consecutive ranks of gauge groups but the same Chern-Simons coupling.

Generating functionals and Lagrangian partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)

2013-08-15

The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.

Green function of the double-fractional Fokker-Planck equation: Path integral and stochastic differential equations

Science.gov (United States)

Kleinert, H.; Zatloukal, V.

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

Multiscale functions, scale dynamics, and applications to partial differential equations

Science.gov (United States)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

Evolution equations for extended dihadron fragmentation functions

International Nuclear Information System (INIS)

Ceccopieri, F.A.; Bacchetta, A.

2007-03-01

We consider dihadron fragmentation functions, describing the fragmentation of a parton in two unpolarized hadrons, and in particular extended dihadron fragmentation functions, explicitly dependent on the invariant mass, M h , of the hadron pair. We first rederive the known results on M h -integrated functions using Jet Calculus techniques, and then we present the evolution equations for extended dihadron fragmentation functions. Our results are relevant for the analysis of experimental measurements of two-particle-inclusive processes at different energies. (orig.)

Medium modifications of mesons. Chiral symmetry restoration, in-medium QCD sum rules for D and ρ mesons, and Bethe-Salpeter equations

Energy Technology Data Exchange (ETDEWEB)

Hilger, Thomas Uwe

2012-04-11

The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D- anti D and B- anti B mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D{sub s} and D{sup *}{sub 0} mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the ρ meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpeter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.

Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

International Nuclear Information System (INIS)

Mota, R D; Xicotencatl, M A; Granados, V D

2004-01-01

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse

Jordan Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

Science.gov (United States)

Mota, R. D.; Xicoténcatl, M. A.; Granados, V. D.

2004-02-01

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.

Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

Energy Technology Data Exchange (ETDEWEB)

Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)

2004-02-20

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.

Distributional Methods for a Class of Functional Equations and Their Stabilities

Institute of Scientific and Technical Information of China (English)

Jae Young CHUNG

2007-01-01

We consider a class of n-dimensional Pompeiu equations and that of Pexider equations and their Hyers-Ulam stability problems in the spaces of Schwartz distributions. First, reducing the given distribution version of functional equations to differential equations we find their solutions. Secondly,using approximate identities we prove the Hyers-Ulam stability of the equations.

Soliton solution for nonlinear partial differential equations by cosine-function method

International Nuclear Information System (INIS)

Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.

2007-01-01

In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations

Application of Exp-function method for (2 + 1)-dimensional nonlinear evolution equations

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2009-01-01

In this paper, the Exp-function method is used to construct solitary and soliton solutions of (2 + 1)-dimensional nonlinear evolution equations. (2 + 1)-dimensional breaking soliton (Calogero) equation, modified Zakharov-Kuznetsov and Konopelchenko-Dubrovsky equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations.

Density induced phase transitions in the Schwinger model. A study with matrix product states

Energy Technology Data Exchange (ETDEWEB)

Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2017-02-15

We numerically study the zero temperature phase structure of the multiflavor Schwinger model at nonzero chemical potential. Using matrix product states, we reproduce analytical results for the phase structure for two flavors in the massless case and extend the computation to the massive case, where no analytical predictions are available. Our calculations allow us to locate phase transitions in the mass-chemical potential plane with great precision and provide a concrete example of tensor networks overcoming the sign problem in a lattice gauge theory calculation.

On the reduction of the multidimensional stationary Schroedinger equation to a first-order equation and its relation to the pseudoanalytic function theory

Energy Technology Data Exchange (ETDEWEB)

Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)

2005-01-28

Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample

Schwinger effect in de Sitter space

Energy Technology Data Exchange (ETDEWEB)

Fröb, Markus B.; Garriga, Jaume [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona (Spain); Kanno, Sugumi [Laboratory for Quantum Gravity and Strings and Astrophysics, Cosmology and Gravity Center, Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7701 (South Africa); Sasaki, Misao; Tanaka, Takahiro [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Soda, Jiro [Department of Physics, Kobe University, Kobe 657-8501 (Japan); Vilenkin, Alexander, E-mail: mfroeb@ffn.ub.edu, E-mail: jaume.garriga@ub.edu, E-mail: sugumi.kanno@uct.ac.za, E-mail: misao@yukawa.kyoto-u.ac.jp, E-mail: jiro@phys.sci.kobe-u.ac.jp, E-mail: tanaka@yukawa.kyoto-u.ac.jp, E-mail: vilenkin@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155 (United States)

2014-04-01

We consider Schwinger pair production in 1+1 dimensional de Sitter space, filled with a constant electric field E. This can be thought of as a model for describing false vacuum decay beyond the semiclassical approximation, where pairs of a quantum field φ of mass m and charge e play the role of vacuum bubbles. We find that the adiabatic ''in'' vacuum associated with the flat chart develops a space-like expectation value for the current J, which manifestly breaks the de Sitter invariance of the background fields. We derive a simple expression for J(E), showing that both ''upward'' and ''downward'' tunneling contribute to the build-up of the current. For heavy fields, with m{sup 2} >> eE,H{sup 2}, the current is exponentially suppressed, in agreement with the results of semiclassical instanton methods. Here, H is the inverse de Sitter radius. On the other hand, light fields with m || H lead to a phenomenon of infrared hyperconductivity, where a very small electric field mH∼

Infrared asymptotic behavior of gauge-invariant propagator in quantum electrodynamics

International Nuclear Information System (INIS)

Skachkov, N.B.; Solovtsov, I.L.; Shevchenko, O.Yu.

1987-01-01

A new class of gauge-invariant fields is introduced. The Dyson-Schwinger equations are obtained for the gauge-invariant generalization of the spinor propagator. On the basis of these equations, and also by means of functional methods, it is shown that the gauge-invariant spinor propagator has a singularity in the form of a simple pole in the infrared region

Nonperturbative Aspects of Axial Vector Vertex

Institute of Scientific and Technical Information of China (English)

ZONG Hong-Shi; CHEN Xiang-Song; WANG Fan; CHANG Chao-Hsi; ZHAO En-Guang

2002-01-01

It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model.Gluon dressing of the axial vector vertex and the quark self-energy functions are described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger Dyson equation in the rainbow approximation,respectively.

A functional-analytic method for the study of difference equations

Directory of Open Access Journals (Sweden)

Siafarikas Panayiotis D

2004-01-01

Full Text Available We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the and spaces, p∈ℕ, . The method will be illustrated by use of two examples concerning a nonlinear ordinary difference equation known as the Putnam equation, and a linear partial difference equation of three variables describing the discrete Newton law of cooling in three dimensions.

The temperature dependence of the chiral condensate in the Schwinger model with Matrix Product States

International Nuclear Information System (INIS)

Saito, H; Jansen, K.; Cichy, K.; Frankfurt Univ.; Poznan Univ.

2014-12-01

We present our recent results for the tensor network (TN) approach to lattice gauge theories. TN methods provide an efficient approximation for quantum many-body states. We employ TN for one dimensional systems, Matrix Product States, to investigate the 1-flavour Schwinger model. In this study, we compute the chiral condensate at finite temperature. From the continuum extrapolation, we obtain the chiral condensate in the high temperature region consistent with the analytical calculation by Sachs and Wipf.

New application of Exp-function method for improved Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Department of Physics, Faculty of Education for Girls, Science Departments, King Khalid University, Bisha (Saudi Arabia)], E-mail: m_abdou_eg@yahoo.com; Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt); Department of Mathematics, Teacher' s College (Bisha), King Khalid University, Bisha, PO Box 551 (Saudi Arabia)], E-mail: asoliman_99@yahoo.com; El-Basyony, S.T. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)

2007-10-01

The Exp-function method is used to obtain generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics with the aid of symbolic computation method, namely, the improved Boussinesq equation. The method is straightforward and concise, and its applications is promising for other nonlinear evolution equations in mathematical physics.

Wave Functions for Time-Dependent Dirac Equation under GUP

Science.gov (United States)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

Exp-function method for solving Fisher's equation

Energy Technology Data Exchange (ETDEWEB)

Zhou, X-W [Department of Mathematics, Kunming Teacher' s College, Kunming, Yunnan 650031 (China)], E-mail: km_xwzhou@163.com

2008-02-15

There are many methods to solve Fisher's equation, but each method can only lead to a special solution. In this paper, a new method, namely the exp-function method, is employed to solve the Fisher's equation. The obtained result includes all solutions in open literature as special cases, and the generalized solution with some free parameters might imply some fascinating meanings hidden in the Fisher's equation.

Functional techniques in quantum field theory and two-dimensional models

International Nuclear Information System (INIS)

Souza, C. Farina de.

1985-03-01

Functional methods applied to Quantum Field Theory are studied. It is shown how to construct the Generating Functional using three of the most important methods existent in the literature, due to Feynman, Symanzik and Schwinger. The Axial Anomaly is discussed in the usual way, and a non perturbative method due to Fujikawa to obtain this anomaly in the path integral formalism is presented. The ''Roskies-Shaposnik-Fujikawa's method'', which makes use of Fujikawa's original idea to solve bidimensional models, is introduced in the Schwinger's model, which, in turn, is applied to obtain the exact solution of the axial model. It is discussed briefly how different regularization procedures can affect the theory in question. (author)

Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function

Science.gov (United States)

Durmus, Aysen

2018-03-01

The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg-Klein-Rees (RKR) results and vibrational energies of NaK, K_2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit D_e=2508cm^{-1}, 254cm^{-1} and 4221cm^{-1}, respectively.

Phase-space analysis of the Schwinger effect in inhomogeneous electromagnetic fields

Science.gov (United States)

Kohlfürst, Christian

2018-05-01

Schwinger pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied. The focus is on the particle phase-space distribution within a high-intensity few-cycle pulse. Accurate numerical solutions of a quantum kinetic theory (DHW formalism) are presented in momentum space and, with the aid of coarse-graining techniques, in a mixed spatial-momentum representation. Additionally, signatures of the carrier-envelope phase as well as spin-field interactions are discussed on the basis of a trajectory-based model taking into account instantaneous pair production and relativistic single-particle dynamics. Although our simple semi-classical single-particle model cannot describe every aspect of the particle production process (quantum interferences), essential features such as spin-field interactions are captured.

The Schwinger Model on S 1: Hamiltonian Formulation, Vacuum and Anomaly

Science.gov (United States)

Stuart, David

2014-12-01

We present a Hamiltonian formulation of the Schwinger model with spatial domain taken to be the circle. It is shown that, in Coulomb gauge, the Hamiltonian is a semi-bounded, self-adjoint operator which is invariant under the group of large gauge transformations. There is a nontrivial action of on fermionic Fock space and its vacuum. This action plays a role analogous to that played by the spectral flow in the infinite Dirac sea formalism. The formulation allows (1) a description of the anomaly and its relation to the group action, and (2) an explicit identification of the vacuum. The anomaly in the chiral conservation law appears as a consequence of insisting upon semi-boundedness and gauge invariance of the quantized Hamiltonian.

Asymptotic expansion of a partition function related to the sinh-model

CERN Document Server

Borot, Gaëtan; Kozlowski, Karol K

2016-01-01

This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integra...

Construction of Green's functions for the Black-Scholes equation

Directory of Open Access Journals (Sweden)

Yuri A. Melnikov

2007-11-01

Full Text Available A technique is proposed for the construction of Green's functions for terminal-boundary value problems of the Black-Scholes equation. The technique permits an application to a variety of problems that vary by boundary conditions imposed. This is possible by extension of an approach that was earlier developed for partial differential equations in applied mechanics. The technique is based on the method of integral Laplace transform and the method of variation of parameters. It provides closed form analytic representations for the constructed Green's functions.

Domains of bosonic functional integrals

International Nuclear Information System (INIS)

Botelho, Luiz C.L.; Para Univ., Belem, PA

1998-07-01

We propose a mathematical framework for bosonic Euclidean quantum field functional integrals based on the theory of integration on the dual algebraic vector space of classical field sources. We present a generalization of the Minlos-Dao Xing theorem and apply it to determine exactly the domain of integration associated to the functional integral representation of the two-dimensional quantum electrodynamics Schwinger generating functional. (author)

A Green function of neutron transport equation

International Nuclear Information System (INIS)

Simovic, R.

1993-01-01

In this paper the angularly dependent Green function of the neutron transport equation is derived analytically and approximately. By applying the analytical FDPN approximation up to eighth order, numerical values of the Green functions are obtained with the accuracy of six significant figures in the whole range of parameter c, angle cosine μ and distances x up to the ten optical lengths from the neutron source. (author)

Lattice Hamiltonian approach to the Schwinger model. Further results from the strong coupling expansion

International Nuclear Information System (INIS)

Szyniszewski, Marcin; Manchester Univ.; Cichy, Krzysztof; Poznan Univ.; Kujawa-Cichy, Agnieszka

2014-10-01

We employ exact diagonalization with strong coupling expansion to the massless and massive Schwinger model. New results are presented for the ground state energy and scalar mass gap in the massless model, which improve the precision to nearly 10 -9 %. We also investigate the chiral condensate and compare our calculations to previous results available in the literature. Oscillations of the chiral condensate which are present while increasing the expansion order are also studied and are shown to be directly linked to the presence of flux loops in the system.

Efficient Estimating Functions for Stochastic Differential Equations

DEFF Research Database (Denmark)

Jakobsen, Nina Munkholt

The overall topic of this thesis is approximate martingale estimating function-based estimationfor solutions of stochastic differential equations, sampled at high frequency. Focuslies on the asymptotic properties of the estimators. The first part of the thesis deals with diffusions observed over...

Solution of the generalized Emden-Fowler equations by the hybrid functions method

International Nuclear Information System (INIS)

Tabrizidooz, H R; Marzban, H R; Razzaghi, M

2009-01-01

In this paper, we present a numerical algorithm for solving the generalized Emden-Fowler equations, which have many applications in mathematical physics and astrophysics. The method is based on hybrid functions approximations. The properties of hybrid functions, which consist of block-pulse functions and Lagrange interpolating polynomials, are presented. These properties are then utilized to reduce the computation of the generalized Emden-Fowler equations to a system of nonlinear equations. The method is easy to implement and yields very accurate results.

Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach

International Nuclear Information System (INIS)

Dai Chaoqing; Zhang Jiefang

2006-01-01

In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.

Ulam-Hyers Stability of Trigonometric Functional Equation with Involution

Directory of Open Access Journals (Sweden)

Jaeyoung Chung

2015-01-01

Full Text Available Let S and G be a commutative semigroup and a commutative group, respectively, C and R+ the sets of complex numbers and nonnegative real numbers, respectively, and σ:S→S or σ:G→G an involution. In this paper, we first investigate general solutions of the functional equation f(x+σy=f(xg(y-g(xf(y for all x,y∈S, where f,g:S→C. We then prove the Hyers-Ulam stability of the functional equation; that is, we study the functional inequality |f(x+σy-f(xg(y+g(xf(y|≤ψ(y for all x,y∈G, where f,g:G→C and ψ:G→R+.

A remark on fractional differential equation involving I-function

Science.gov (United States)

Mishra, Jyoti

2018-02-01

The present paper deals with the solution of the fractional differential equation using the Laplace transform operator and its corresponding properties in the fractional calculus; we derive an exact solution of a complex fractional differential equation involving a special function known as I-function. The analysis of the some fractional integral with two parameters is presented using the suggested Theorem 1. In addition, some very useful corollaries are established and their proofs presented in detail. Some obtained exact solutions are depicted to see the effect of each fractional order. Owing to the wider applicability of the I-function, we can conclude that, the obtained results in our work generalize numerous well-known results obtained by specializing the parameters.

Nonperturbative quantum electrodynamics at T≠0

International Nuclear Information System (INIS)

Pevzner, M.Sh.

1990-01-01

On the base of Schwinger-Dyson equation for the electron temperature Green's function in the nonperturbative QED in the ladder approximation the ordinary differential equation for the function, connected with temperature one has been obtained. The relation, to which the temperature depending electron mass m(T) satisfies, has been found; its low-temperature behaviour has been studied. The phase transition has been shown to take place in the model, that is accompanied by the chiral symmetry restoration. 34 refs

A functional equation for the specular reflection of rays.

Science.gov (United States)

Le Bot, A

2002-10-01

This paper aims to generalize the "radiosity method" when applied to specular reflection. Within the field of thermics, the radiosity method is also called the "standard procedure." The integral equation for incident energy, which is usually derived for diffuse reflection, is replaced by a more appropriate functional equation. The latter is used to solve some specific problems and it is shown that all the classical features of specular reflection, for example, the existence of image sources, are embodied within this equation. This equation can be solved with the ray-tracing technique, despite the implemented mathematics being quite different. Several interesting features of the energy field are presented.

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

Science.gov (United States)

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Modern functional quantum field theory summing Feynman graphs

CERN Document Server

Fried, Herbert M

2013-01-01

A monograph, which can also be used as a textbook for graduate students, this book contains new and novel applications of Schwinger's well-known functional solutions, made possible by the use of Fradkin's little-known functional representations, together with recent research work of the author and his colleagues.

Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

Directory of Open Access Journals (Sweden)

Zakieh Avazzadeh

2014-01-01

Full Text Available We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.

q-Karamata functions and second order q-difference equations

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel; Vítovec, J.

-, č. 24 (2011), s. 1-20 ISSN 1417-3875 Institutional research plan: CEZ:AV0Z10190503 Keywords : regularly varying functions * rapidly varying functions * q-difference equations Subject RIV: BA - General Mathematics Impact factor: 0.557, year: 2011

Reduction of structured population models to threshold-type delay equations and functional differential equations: A case study

Energy Technology Data Exchange (ETDEWEB)

Smith, H.L. (Arizona State Univ., Tempe (United States))

1993-01-01

It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability. 28 refs., 2 figs.

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Science.gov (United States)

Gnoffo, Peter A.

2015-01-01

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Existence families, functional calculi and evolution equations

CERN Document Server

deLaubenfels, Ralph

1994-01-01

This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, ...

The General Analytic Solution of a Functional Equation of Addition Type

OpenAIRE

Braden, H. W.; Buchstaber, V. M.

1995-01-01

The general analytic solution to the functional equation $$ \\phi_1(x+y)= { { \\biggl|\\matrix{\\phi_2(x)&\\phi_2(y)\\cr\\phi_3(x)&\\phi_3(y)\\cr}\\biggr|} \\over { \\biggl|\\matrix{\\phi_4(x)&\\phi_4(y)\\cr\\phi_5(x)&\\phi_5(y)\\cr}\\biggr|} } $$ is characterised. Up to the action of the symmetry group, this is described in terms of Weierstrass elliptic functions. We illustrate our theory by applying it to the classical addition theorems of the Jacobi elliptic functions and the functional equations $$ \\phi_1(x+...

Preequilibrium decay models and the quantum Green function method

International Nuclear Information System (INIS)

Zhivopistsev, F.A.; Rzhevskij, E.S.; Gosudarstvennyj Komitet po Ispol'zovaniyu Atomnoj Ehnergii SSSR, Moscow. Inst. Teoreticheskoj i Ehksperimental'noj Fiziki)

1977-01-01

The nuclear process mechanism and preequilibrium decay involving complex particles are expounded on the basis of the Green function formalism without the weak interaction assumptions. The Green function method is generalized to a general nuclear reaction: A+α → B+β+γ+...rho, where A is the target nucleus, α is a complex particle in the initial state, B is the final nucleus, and β, γ, ... rho are nuclear fragments in the final state. The relationship between the generalized Green function and Ssub(fi)-matrix is established. The resultant equations account for: 1) direct and quasi-direct processes responsible for the angular distribution asymmetry of the preequilibrium component; 2) the appearance of addends corresponding to the excitation of complex states of final nucleus; and 3) the relationship between the preequilibrium decay model and the general models of nuclear reaction theories (Lippman-Schwinger formalism). The formulation of preequilibrium emission via the S(T) matrix allows to account for all the differential terms in succession important to an investigation of the angular distribution assymetry of emitted particles

Complex Kohn variational principle for the solution of Lippmann-Schwinger equations

International Nuclear Information System (INIS)

Adhikari, S.K.

1992-07-01

A recently proposed version of the Kohn variational principle for the t matrix incorporating the correct boundary condition is applied for the first time to the study of nucleon-nucleon scattering. Analytic expressions can be obtained for all the integrals in the method for a wide class of potentials and for a suitable choice of trial functions. Closed-form analytic expressions for these integrals are given for Yakawa and exponential potentials. Calculations with two commonly used S-wave nucleon-nucleon potentials show that the method may converge faster than other solution schemes not only for the phase-shifts but also for the off-shell t matrix elements if the freedom in the choice of the trial function is exploited. (author)

Method of construction of the Riemann function for a second-order hyperbolic equation

Science.gov (United States)

Aksenov, A. V.

2017-12-01

A linear hyperbolic equation of the second order in two independent variables is considered. The Riemann function of the adjoint equation is shown to be invariant with respect to the fundamental solutions transformation group. Symmetries and symmetries of fundamental solutions of the Euler-Poisson-Darboux equation are found. The Riemann function is constructed with the aid of fundamental solutions symmetries. Examples of the application of the algorithm for constructing Riemann function are given.

Conditions for the existence of control functions in nonseparable simultaneous equations models

OpenAIRE

Blundell, Richard; Matzkin, Rosa L.

2010-01-01

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has thus far been unknown. In this note, we define a new property of functions called control function s...

Solving Kepler's equation using implicit functions

Science.gov (United States)

Mortari, Daniele; Elipe, Antonio

2014-01-01

A new approach to solve Kepler's equation based on the use of implicit functions is proposed here. First, new upper and lower bounds are derived for two ranges of mean anomaly. These upper and lower bounds initialize a two-step procedure involving the solution of two implicit functions. These two implicit functions, which are non-rational (polynomial) Bézier functions, can be linear or quadratic, depending on the derivatives of the initial bound values. These are new initial bounds that have been compared and proven more accurate than Serafin's bounds. The procedure reaches machine error accuracy with no more that one quadratic and one linear iterations, experienced in the "tough range", where the eccentricity is close to one and the mean anomaly to zero. The proposed method is particularly suitable for space-based applications with limited computational capability.

Iterative method of the parameter variation for solution of nonlinear functional equations

International Nuclear Information System (INIS)

Davidenko, D.F.

1975-01-01

The iteration method of parameter variation is used for solving nonlinear functional equations in Banach spaces. The authors consider some methods for numerical integration of ordinary first-order differential equations and construct the relevant iteration methods of parameter variation, both one- and multifactor. They also discuss problems of mathematical substantiation of the method, study the conditions and rate of convergence, estimate the error. The paper considers the application of the method to specific functional equations

Differential functional von Foerster equations with renewal

Directory of Open Access Journals (Sweden)

H.Leszczyński

2008-06-01

Full Text Available Natural iterative methods converge to the exact solution of a differential-functional von Foerster-type equation which describes a single population dependent on its past time and state densities as well as on its total size. On the lateral boundary we impose a renewal condition.

A Hamiltonian functional for the linearized Einstein vacuum field equations

International Nuclear Information System (INIS)

Rosas-RodrIguez, R

2005-01-01

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained

Lyapunov functionals and stability of stochastic difference equations

CERN Document Server

Shaikhet, Leonid

2011-01-01

This book offers a general method of Lyapunov functional construction which lets researchers analyze the degree to which the stability properties of differential equations are preserved in their difference analogues. Includes examples from physical systems.

Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

Directory of Open Access Journals (Sweden)

Bapurao C. Dhage

2015-01-01

Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

OSCILLATION BEHAVIOR OF SOLUTIONS FOR EVEN ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

T.Candan

2006-01-01

Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.

The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations

International Nuclear Information System (INIS)

Liu Chunping; Liu Xiaoping

2004-01-01

First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions

Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method

International Nuclear Information System (INIS)

Ebaid, A.

2007-01-01

Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV-mKdV equation are chosen to illustrate the effectiveness of the method

Numerical solution of the potential problem by integral equations without Green's functions

International Nuclear Information System (INIS)

De Mey, G.

1977-01-01

An integral equation technique will be presented to solve Laplace's equation in a two-dimensional area S. The Green's function has been replaced by a particular solution of Laplace equation in order to establish the integral equation. It is shown that accurate results can be obtained provided the pivotal elimination method is used to solve the linear algebraic set

BSDES IN GAMES, COUPLED WITH THE VALUE FUNCTIONS.ASSOCIATED NONLOCAL BELLMAN-ISAACS EQUATIONS

Institute of Scientific and Technical Information of China (English)

Tao HAO; Juan LI

2017-01-01

We establish a new type of backward stochastic differential equations (BSDEs) connected with stochastic differential games (SDGs),namely,BSDEs strongly coupled with the lower and the upper value functions of SDGs,where the lower and the upper value functions are defined through this BSDE.The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method.We also show that the lower and the upper value functions satisfy the dynamic programming principle.Moreover,we study the associated Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs) equations,which are nonlocal,and strongly coupled with the lower and the upper value functions.Using a new method,we characterize the pair (W,U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation.Furthermore,the game has a value under the Isaacs' condition.

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

Science.gov (United States)

Sels, Dries; Brosens, Fons

2013-10-01

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

Yang-Mills theory in Coulomb gauge; Yang-Mills-theorie in Coulombeichung

Energy Technology Data Exchange (ETDEWEB)

Feuchter, C.

2006-07-01

In this thesis we study the Yang-Mills vacuum structure by using the functional Schroedinger picture in Coulomb gauge. In particular we discuss the scenario of colour confinement, which was originally formulated by Gribov. After a short introduction, we recall some basic aspects of Yang-Mills theories, its canonical quantization in the Weyl gauge and the functional Schroedinger picture. We then consider the minimal Coulomb gauge and the Gribov problem of the gauge theory. The gauge fixing of the Coulomb gauge is done by using the Faddeev-Popov method, which enables the resolution of the Gauss law - the constraint on physical states. In the third chapter, we variationally solve the stationary Yang-Mills Schroedinger equation in Coulomb gauge for the vacuum state. Therefor we use a vacuum wave functional, which is strongly peaked at the Gribov horizon. The vacuum energy functional is calculated and minimized resulting in a set of coupled Schwinger-Dyson equations for the gluon energy, the ghost and Coulomb form factors and the curvature in gauge orbit space. Using the angular approximation these integral equations have been solved analytically in both the infrared and the ultraviolet regime. The asymptotic analytic solutions in the infrared and ultraviolet regime are reasonably well reproduced by the full numerical solutions of the coupled Schwinger-Dyson equations. In the fourth chapter, we investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. (orig.)

States, ideals and automorphisms of the algebra of test functions for quantum fields

International Nuclear Information System (INIS)

Yngvason, J.

1984-01-01

I report on two subjects: 1. Construction of positive, linear functionals on Borcher's tensor algebra satisfying parts of the linear Wightman conditions, and 2. a criterion for the existence of Euclidean invariant integral representations for Schwinger functionals. (orig./HSI)

Momentum-space representation of Green's functions with modified dispersion on ultrastatic space-time

International Nuclear Information System (INIS)

Rinaldi, Massimiliano

2007-01-01

We consider Green's functions associated to a scalar field propagating on a curved, ultrastatic background, in the presence of modified dispersion relations. The usual proper-time DeWitt-Schwinger procedure to obtain a series representation of Green's functions is doomed to failure because of higher order spatial derivatives in the Klein-Gordon operator. We show how to overcome this difficulty by considering a preferred frame, associated to a unit timelike vector. With respect to this frame, we can express Green's functions as an integral over all frequencies of a space-dependent function. The latter can be expanded in momentum space, as a series with geometric coefficients similar to the DeWitt-Schwinger ones. By integrating over all frequencies, we finally find the expansion of Green's function up to four derivatives of the metric tensor. The relation with the proper-time formalism is also discussed

Evaluation of time correlation functions from a generalized Enskog equation

Energy Technology Data Exchange (ETDEWEB)

Yip, S.; Alley, W.E.; Alder, B.J.

1982-01-01

Numerical results for the density and current correlation functions in dense hard-shape fluids are obtained from a kinetic equation which is the extension of the linearized Enskog equation to finite wavelengths in order to demonstrate the convergence of the method of solution. Comparison is made to a previously proposed approximate solution.

Evaluation of time correlation functions from a generalized Enskog equation

International Nuclear Information System (INIS)

Yip, S.; Alley, W.E.; Alder, B.J.

1982-01-01

Numerical results for the density and current correlation functions in dense hard-shape fluids are obtained from a kinetic equation which is the extension of the linearized Enskog equation to finite wavelengths in order to demonstrate the convergence of the method of solution. Comparison is made to a previously proposed approximate solution

Dynamical breakdown of chiral symmetry and abnormal perturbation expansion

International Nuclear Information System (INIS)

Ebert, D.; Pervushin, V.N.

1976-01-01

Dynamical breakdown of γ 5 -symmetry is studied in the Abelian gauge theory of massless ''quarks'' interacting with massless vector ''gluons''. For this purpose the path-integral approach with bilocal fields as dynamical variables is used. The classical field equation defined by the stationary point of the generating functional turns out to be identical with the Schwinger-Dyson equation for the quark propagator. After a short discussion of the possible solutions of this equation an abnormal perturbation theory has been worked out

Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

Directory of Open Access Journals (Sweden)

Elmira Ashpazzadeh

2018-04-01

Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

Directory of Open Access Journals (Sweden)

Yusuf Pandir

2013-01-01

Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

A continuum order parameter for deconfinement

International Nuclear Information System (INIS)

Roberts, C.D.

1997-01-01

Dyson-Schwinger equations are presented as a non-perturbative tool for the study and modeling of QCD at finite-T. An order parameter for deconfinement, applicable for both light and heavy quarks, is introduced. In a simple Dyson-Schwinger equation model of two-flavor QCD, coincident, 2nd-order chiral symmetry restoration and deconfinement transitions occur at T ∼ 150 MeV, with the same critical exponent, Β ∼ 0.33

A functional-analytic method for the study of difference equations

Directory of Open Access Journals (Sweden)

Panayiotis D. Siafarikas

2004-07-01

Full Text Available We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the ℓp1 and ℓp2 spaces, p∈ℕ, p≥1. The method will be illustrated by use of two examples concerning a nonlinear ordinary difference equation known as the Putnam equation, and a linear partial difference equation of three variables describing the discrete Newton law of cooling in three dimensions.

AN ENERGY FUNCTION APPROACH FOR FINDING ROOTS OF CHARACTERISTIC EQUATION

OpenAIRE

Deepak Mishra; Prem K. Kalra

2011-01-01

In this paper, an energy function approach for finding roots of a characteristic equation has been proposed. Finding the roots of a characteristics equation is considered as an optimization problem. We demonstrated that this problem can be solved with the application of feedback type neural network. The proposed approach is fast and robust against variation of parameter.

Application of the Exp-function method to the equal-width wave equation

International Nuclear Information System (INIS)

Biazar, J; Ayati, Z

2008-01-01

In this paper, the Exp-function method is used to find an exact solution of the equal-width wave (EW) equation. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving the EW equation.

A Generalized Halanay Inequality for Stability of Nonlinear Neutral Functional Differential Equations

Directory of Open Access Journals (Sweden)

Wansheng Wang

2010-01-01

Full Text Available This paper is devoted to generalize Halanay's inequality which plays an important rule in study of stability of differential equations. By applying the generalized Halanay inequality, the stability results of nonlinear neutral functional differential equations (NFDEs and nonlinear neutral delay integrodifferential equations (NDIDEs are obtained.

On two functional equations originating from number theory

Indian Academy of Sciences (India)

On two functional equations originating from number theory. JAEYOUNG CHUNG1 and JEONGWOOK CHANG2,∗. 1Department of Mathematics, Kunsan National University, Kunsan, 573-701, Korea. 2Department of Mathematics Education, Dankook University, Yongin 448-701, Korea. *Corresponding author. E-mail: ...

Quantum gravitational corrections to the functional Schroedinger equation

International Nuclear Information System (INIS)

Kiefer, C.; Singh, T.P.

1990-10-01

We derive corrections to the Schroedinger equation which arise from the quantization of the gravitational field. This is achieved through an expansion of the full functional Wheeler-DeWitt equation with respect to powers of the Planck mass. We demonstrate that the corrections terms are independent of the factor ordering which is chosen for the gravitational kinetic term. Although the corrections are numerically extremely tiny, we show how they lead, at least in principle, to shift in the spectral lines of hydrogen type atoms. We discuss the significance of these corrections for quantum field theory near the Planck scale. (author). 35 refs

Infrared behaviour, sources and the Schwinger action principle

International Nuclear Information System (INIS)

Burgess, M.

1994-05-01

An action principle technique is used to explore some issues concerning the infra-red problem in the effective action for gauge field theories. The relationship between the renormalization group and other non-perturbative resummation schemes is demonstrated by means of a source theory. It is shown that the use of vertex renormalization conditions and other resummation methods (large N expansion) can lead to erroneous conclusions about the phase transitions in the gauge theory, since it corresponds to only a partial resummation of the scalar self-energies at the expense of the gauge sector. The renormalization group as well as the ansatz of non-local sources can be derived from an associated operator problem for the field couplings by use of the Schwinger action principle. This method generalizes to curved spacetime and non-equilibrium models in a straightforward way. Some examples are computed to lowest order and the conclusion is drawn that none of the approximation schemes are able to extract true non-perturbative information from field theory. Only results which rely on the particular recursive structure of the perturbation series are accessible and the main purpose of the investigation is to determine legal ways of regulating the theory in the infrared. 35 refs

Hamiltonian approach to the lattice massive Schwinger model

International Nuclear Information System (INIS)

Sidorov, A.V.; Zastavenko, L.G.

1996-01-01

The authors consider the limit e 2 /m 2 much-lt 1 of the lattice massive Schwinger model, i.e., the lattice massive QED in two space-time dimensions, up to lowest order in the effective coupling constant e 2 /m 2 . Here, m is the fermion mass parameter and e is the electron charge. They compare their lattice QED model with the analogous continuous space and lattice space models, (CSM and LSM), which do not take account of the zero momentum mode, z.m.m., of the vector potential. The difference is that (due to extra z.m.m. degree of freedom) to every eigenstate of the CSM and LSM there corresponds a family of eigenstates of the authors lattice QED with the parameter λ. They restrict their consideration to small values of the parameter λ. Then, the energies of the particle states of their lattice QED and LSM do coincide (in their approximation). In the infinite periodicity length limit the Hamiltonian of the authors lattice QED (as well as the Hamiltonian of the LSM) possesses two different Hilbert spaces of eigenfunctions. Thus, in this limit the authors lattice QED model (as well as LSM) describes something like two connected, but different, worlds

Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator

International Nuclear Information System (INIS)

Decanini, Yves; Folacci, Antoine

2006-01-01

Having in mind applications to gravitational wave theory (in connection with the radiation reaction problem), stochastic semiclassical gravity (in connection with the regularization of the noise kernel) and quantum field theory in higher-dimensional curved spacetime (in connection with the Hadamard regularization of the stress-energy tensor), we improve the DeWitt-Schwinger and Hadamard representations of the Feynman propagator of a massive scalar field theory defined on an arbitrary gravitational background by deriving higher-order terms for the covariant Taylor series expansions of the geometrical coefficients--i.e., the DeWitt and Hadamard coefficients--that define them

System of delay difference equations with continuous time with lag function between two known functions

Directory of Open Access Journals (Sweden)

Hajnalka Péics

2016-08-01

Full Text Available The asymptotic behavior of solutions of the system of difference equations with continuous time and lag function between two known real functions is studied. The cases when the lag function is between two linear delay functions, between two power delay functions and between two constant delay functions are observed and illustrated by examples. The asymptotic estimates of solutions of the considered system are obtained.

Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

Directory of Open Access Journals (Sweden)

Taher S. Hassan

2016-01-01

Full Text Available We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t≔ri(tϕαixi-1Δ(t,  i=1,…,n-1,   with  x0=x,  ϕβ(u≔uβsgn⁡u, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.

WWNPQFT-2013 - Abstracts

International Nuclear Information System (INIS)

Cessac, B.; Bianchi, E.; Bellon, M.; Fried, H.; Krajewski, T.; Schubert, C.; Barre, J.; Hofmann, R.; Muller, B.; Raffaelli, B.

2014-01-01

The object of this Workshop is to consolidate and publicize new efforts in non perturbative-like Field Theories, relying in Functional Methods, Renormalization Group, and Dyson-Schwinger Equations. A presentation deals with effective vertices and photon-photon scattering in SU(2) Yang-Mills thermodynamics. This document gathers the abstracts of the presentations

Modulating functions method for parameters estimation in the fifth order KdV equation

KAUST Repository

Asiri, Sharefa M.

2017-07-25

In this work, the modulating functions method is proposed for estimating coefficients in higher-order nonlinear partial differential equation which is the fifth order Kortewegde Vries (KdV) equation. The proposed method transforms the problem into a system of linear algebraic equations of the unknowns. The statistical properties of the modulating functions solution are described in this paper. In addition, guidelines for choosing the number of modulating functions, which is an important design parameter, are provided. The effectiveness and robustness of the proposed method are shown through numerical simulations in both noise-free and noisy cases.

Existence Results for Some Nonlinear Functional-Integral Equations in Banach Algebra with Applications

Directory of Open Access Journals (Sweden)

Lakshmi Narayan Mishra

2016-04-01

Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.

Nonlinear differential equations with exact solutions expressed via the Weierstrass function

NARCIS (Netherlands)

Kudryashov, NA

2004-01-01

A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear

Counting master integrals. Integration by parts vs. functional equations

International Nuclear Information System (INIS)

Kniehl, Bernd A.; Tarasov, Oleg V.

2016-01-01

We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.

Some functional solutions of the Yang-Baxter equation

International Nuclear Information System (INIS)

Stoyanov, D.Ts.

1994-09-01

A general functional definition of the infinite dimensional quantum R-matrix satisfying the Yang-Baxter equation is given. A procedure for extracting a finite dimensional R-matrix from the general definition is demonstrated in a particular case when the group SU(2) takes place. (author). 6 refs

Fixed Points and Fuzzy Stability of Functional Equations Related to Inner Product

Directory of Open Access Journals (Sweden)

Hassan Azadi Kenary

2012-04-01

Full Text Available In , Th.M. Rassias introduced the following equality sum_{i,j=1}^m |x_i - x_j |^2 = 2m sum_{i=1}^m|x_i|^2, qquad sum_{i=1}^m x_i =0 for a fixed integer $m ge 3$. Let $V, W$ be real vector spaces. It is shown that if a mapping $f : V ightarrow W$ satisfies sum_{i,j=1}^m f(x_i - x_j = 2m sum_{i=1}^m f(x_i for all $x_1, ldots, x_{m} in V$ with $sum_{i=1}^m x_i =0$, then the mapping $f : V ightarrow W$ is realized as the sum of an additive mapping and a quadratic mapping. From the above equality we can define the functional equation f(x-y +f(2x+y + f(x+2y= 3f(x+ 3f(y + 3f(x+y , which is called a {it quadratic functional equation}. Every solution of the quadratic functional equation is said to be a {it quadratic mapping}. Using fixed point theorem we prove the Hyers-Ulam stability of the functional equation ( in fuzzy Banach spaces.

Uniformly constructing combinatorial solutions, combining a rational function with hyperbolic or trigonometric functions, for the (2+1) dimensional Broer-Kaup-Kupershmidt equation

International Nuclear Information System (INIS)

Liu Qing; Wang Zihua

2010-01-01

According to two dependent rational solutions to a generalized Riccati equation together with the equation itself, a rational-exponent solution to a nonlinear partial differential equation can be constructed. By selecting different parameter values in the rational-exponent solution, many families of combinatorial solutions combined with a rational function such as hyperbolic functions or trigonometric functions, are rapidly derived. This method is applied to the Whitham-Broer-Kaup equation and a series of combinatorial solutions are obtained, showing that this method is a more concise and efficient approach and can uniformly construct many types of combined solutions to nonlinear partial differential equations.

A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method

Directory of Open Access Journals (Sweden)

Changqing Yang

2012-01-01

Full Text Available A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Exp-function method for constructing exact solutions of Sharma-Tasso-Olver equation

International Nuclear Information System (INIS)

Erbas, Baris; Yusufoglu, Elcin

2009-01-01

In this paper we use the Exp-function method for the analytic treatment of Sharma-Tasso-Olver equation. New solitonary solutions are formally derived. Change of parameters, which drastically changes the characteristics of the equations, is examined. It is shown that the Exp-function method provides a powerful mathematical tool for solving high-dimensional nonlinear evolutions in mathematical physics. The proposed schemes are reliable and manageable.

ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS

Directory of Open Access Journals (Sweden)

Giorgio Gubbiotti

2016-06-01

Full Text Available In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries.

The Green functions in curved spacetime

International Nuclear Information System (INIS)

Buchbinder, I.L.; Kirillova, E.N.; Odinstov, S.D.

1987-01-01

The theory of a free scalar field with conformal coupling in curved spacetime with some special metrics is considered. The integral representations for the green function G-tilde in the form of integrals with Schwinger-De Witt kernel over contours in the complex plane of proper time are obtained. It is shown how the transitions from a unique Green function in Euclidean space to different Green functions in Minkowski space and vice versa can be carried out. (author)

Equation satisfied by electron-electron mutual Coulomb repulsion energy density functional

OpenAIRE

Joubert, Daniel P.

2011-01-01

The electron-electron mutual Coulomb repulsion energy density functional satisfies an equation that links functionals and functional derivatives at N-electron and (N-1)-electron densities for densities determined from the same adiabatic scaled external potential for the N-electron system.

Exponential stability in a scalar functional differential equation

Directory of Open Access Journals (Sweden)

Pituk Mihály

2006-01-01

Full Text Available We establish a criterion for the global exponential stability of the zero solution of the scalar retarded functional differential equation whose linear part generates a monotone semiflow on the phase space with respect to the exponential ordering, and the nonlinearity has at most linear growth.

Zeta functional equation on Jordan algebras of type II

International Nuclear Information System (INIS)

Kayoya, J.B.

2003-10-01

Using the Jordan algebras method, specially the properties of Peirce decomposition and the Frobenius transformation, we compute the coefficients of the zeta functional equation, in the case of Jordan algebras of Type II. As particular cases of our result, we can cite the case of V M (n, R) studied by Gelbart and Godement-Jacquet, and the case of V Herm(3, O s ) studied by Muro. Let us also mention, that recently, Bopp and Rubenthaler have obtained a more general result on the zeta functional equation by using methods based on the algebraic properties of regular graded algebras which are in one to one correspondence with simple Jordan algebras. The method used in this paper is a direct application of specific properties of Jordan algebras of Type H. (author)

String beta function equations from c=1 matrix model

CERN Document Server

Dhar, A; Wadia, S R; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R

1995-01-01

We derive the \\sigma-model tachyon \\beta-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the c=1 matrix model. The tachyon \\beta-function equation is satisfied by a \\underbar{nonlocal} and \\underbar{nonlinear} combination of the (massless) scalar field of the matrix model. We discuss the possibility of describing the `discrete states' as well as other possible gravitational and higher tensor backgrounds of 2-dimensional string theory within the c=1 matrix model. We also comment on the realization of the W-infinity symmetry of the matrix model in the string theory. The present work reinforces the viewpoint that a nonlocal (and nonlinear) transform is required to extract the space-time physics of 2-dimensional string theory from the c=1 matrix model.

On the zero-crossing of the three-gluon Green's function from lattice simulations

Energy Technology Data Exchange (ETDEWEB)

Athenodorou, Andreas [Univ. of Cyprus, Nicosia, Cyprus; Boucaud, Philippe [Univ. Paris-Sud, Orsay (France); de Soto, Feliciano [Univ. Pablo de Olavide, 41013 Sevilla; Spain; Univ. of Granada (Spain); Rodriguez-Quintero, Jose [Universidad de Huelva, 21071 Huelva; Spain; Univ. of Granada (Spain); Zafeiropoulos, Savvas [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States); Heidelberg Univ. (Germany). Inst. for Theoretische Physik

2018-04-01

We report on some efforts recently made in order to gain a better understanding of some IR properties of the 3-point gluon Green’s function by exploiting results from large-volume quenched lattice simulations. These lattice results have been obtained by using both tree-level Symanzik and the standard Wilson action, in the aim of assessing the possible impact of effects presumably resulting from a particular choice for the discretization of the action. The main resulting feature is the existence of a negative log-aritmic divergence at zero-momentum, which pulls the 3-gluon form factors down at low momenta and, consequently, yields a zero-crossing at a given deep IR momentum. The results can be correctly explained by analyzing the relevant Dyson-Schwinger equations and appropriate truncation schemes.

Reduction of the Breit Coulomb equation to an equivalent Schroedinger equation, and investigation of the behavior of the wave function near the origin

International Nuclear Information System (INIS)

Malenfant, J.

1988-01-01

The Breit equation for two equal-mass spin-1/2 particles interacting through an attractive Coulomb potential is separated into its angular and radial parts, obtaining coupled sets of first-order differential equations for the radial wave functions. The radial equations for the 1 J/sub J/, 3 J/sub J/, and 3 P 0 states are further reduced to a single, one-dimensional Schroedinger equation with a relatively simple effective potential. No approximations, other than the initial one of an instantaneous Coulomb interaction, are made in deriving this equation; it accounts for all relativistic effects, as well as for mixing between different components of the wave function. Approximate solutions are derived for this Schroedinger equation, which gives the correct O(α 4 ) term for the 1 1 S 0 energy and for the n 1 J/sub J/ energies, for J>0. The radial equations for the 3 (J +- 1)/sub J/ states are reduced to two second-order coupled equations. At small r, the Breit Coulomb wave functions behave as r/sup ν//sup -1/, where ν is either √J(J+1)+1-α 2 /4 or √J(J+1)-α 2 /4 . The 1 S 0 and 3 P 0 wave functions therefore diverge at the origin as r/sup //sup √//sup 1-//sup α//sup <2//4 -1$. This divergence of the J = 0 states, however, does not occur when the spin-spin interaction, -(α/r)αxα, is added to the Coulomb potential

The convergence of the order sequence and the solution function sequence on fractional partial differential equation

Science.gov (United States)

Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.

2018-03-01

One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).

The application of He's exp-function method to a nonlinear differential-difference equation

International Nuclear Information System (INIS)

Dai Chaoqing; Cen Xu; Wu Shengsheng

2009-01-01

This paper applies He's exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear partial differential equations (NPDEs) or coupled nonlinear partial differential equations (CNPDEs), to a nonlinear differential-difference equation, and some new travelling wave solutions are obtained.

Jacobian elliptic function expansion solutions of nonlinear stochastic equations

International Nuclear Information System (INIS)

Wei Caimin; Xia Zunquan; Tian Naishuo

2005-01-01

Jacobian elliptic function expansion method is extended and applied to construct the exact solutions of the nonlinear Wick-type stochastic partial differential equations (SPDEs) and some new exact solutions are obtained via this method and Hermite transformation

Hyperbolic white noise functional solutions of Wick-type stochastic compound KdV-Burgers equations

International Nuclear Information System (INIS)

Han Xiu; Xie Yingchao

2009-01-01

Variable coefficient and Wick-type stochastic compound KdV-Burgers equations are investigated. By using white noise analysis, Hermite transform and the hyperbolic function method, we obtain a number of Wick versions of hyperbolic white noise functional solutions and hyperbolic function solutions for Wick-type stochastic and variable coefficient compound KdV-Burgers equations, respectively.

Iohexol clearance is superior to creatinine-based renal function estimating equations in detecting short-term renal function decline in chronic heart failure.

Science.gov (United States)

Cvan Trobec, Katja; Kerec Kos, Mojca; von Haehling, Stephan; Anker, Stefan D; Macdougall, Iain C; Ponikowski, Piotr; Lainscak, Mitja

2015-12-01

To compare the performance of iohexol plasma clearance and creatinine-based renal function estimating equations in monitoring longitudinal renal function changes in chronic heart failure (CHF) patients, and to assess the effects of body composition on the equation performance. Iohexol plasma clearance was measured in 43 CHF patients at baseline and after at least 6 months. Simultaneously, renal function was estimated with five creatinine-based equations (four- and six-variable Modification of Diet in Renal Disease, Cockcroft-Gault, Cockcroft-Gault adjusted for lean body mass, Chronic Kidney Disease Epidemiology Collaboration equation) and body composition was assessed using bioimpedance and dual-energy x-ray absorptiometry. Over a median follow-up of 7.5 months (range 6-17 months), iohexol clearance significantly declined (52.8 vs 44.4 mL/[min ×1.73 m2], P=0.001). This decline was significantly higher in patients receiving mineralocorticoid receptor antagonists at baseline (mean decline -22% of baseline value vs -3%, P=0.037). Mean serum creatinine concentration did not change significantly during follow-up and no creatinine-based renal function estimating equation was able to detect the significant longitudinal decline of renal function determined by iohexol clearance. After accounting for body composition, the accuracy of the equations improved, but not their ability to detect renal function decline. Renal function measured with iohexol plasma clearance showed relevant decline in CHF patients, particularly in those treated with mineralocorticoid receptor antagonists. None of the equations for renal function estimation was able to detect these changes. ClinicalTrials.gov registration number: NCT01829880.

A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation

International Nuclear Information System (INIS)

Ma Wenxiu; Lee, J.-H.

2009-01-01

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanh-function type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type methods. Its key point is to search for rational solutions to variable-coefficient ordinary differential equations transformed from given partial differential equations. As an application, the construction problem of exact solutions to the 3+1 dimensional Jimbo-Miwa equation is treated, together with a Baecklund transformation.

Parametrically Excited Oscillations of Second-Order Functional Differential Equations and Application to Duffing Equations with Time Delay Feedback

Directory of Open Access Journals (Sweden)

Mervan Pašić

2014-01-01

Full Text Available We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.

Bifurcation to a chiral-symmetry-breaking state in continuum quantum electrodynamics

International Nuclear Information System (INIS)

Rembiesa, P.

1990-01-01

Dyson-Schwinger equations for a fermion propagator in the Landau gauge are studied in the approximation of a small-momentum-transfer vertex function. There exists a critical value of the coupling constant above which the ordinary solution bifurcates to another, chiral-symmetry-breaking solution. The new solution does not require either infrared or ultraviolet momentum cutoffs

Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra

Directory of Open Access Journals (Sweden)

Zhaolin Jiang

2014-01-01

Full Text Available The skew-circulant matrix has been used in solving ordinary differential equations. We prove that the set of skew-circulants with complex entries has an idempotent basis. On that basis, a skew-cyclic group of automorphisms and functional equations on the skew-circulant algebra is introduced. And different operators on linear vector space that are isomorphic to the algebra of n×n complex skew-circulant matrices are displayed in this paper.

Contractivity and Exponential Stability of Solutions to Nonlinear Neutral Functional Differential Equations in Banach Spaces

Institute of Scientific and Technical Information of China (English)

Wan-sheng WANG; Shou-fu LI; Run-sheng YANG

2012-01-01

A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.

The Green Function cellular method and its relation to multiple scattering theory

International Nuclear Information System (INIS)

Butler, W.H.; Zhang, X.G.; Gonis, A.

1992-01-01

This paper investigates techniques for solving the wave equation which are based on the idea of obtaining exact local solutions within each potential cell, which are then joined to form a global solution. The authors derive full potential multiple scattering theory (MST) from the Lippmann-Schwinger equation and show that it as well as a closely related cellular method are techniques of this type. This cellular method appears to have all of the advantages of MST and the added advantage of having a secular matrix with only nearest neighbor interactions. Since this cellular method is easily linearized one can rigorously reduce electronic structure calculation to the problem of solving a nearest neighbor tight-binding problem

Iohexol clearance is superior to creatinine-based renal function estimating equations in detecting short-term renal function decline in chronic heart failure

Science.gov (United States)

Cvan Trobec, Katja; Kerec Kos, Mojca; von Haehling, Stephan; Anker, Stefan D.; Macdougall, Iain C.; Ponikowski, Piotr; Lainscak, Mitja

2015-01-01

Aim To compare the performance of iohexol plasma clearance and creatinine-based renal function estimating equations in monitoring longitudinal renal function changes in chronic heart failure (CHF) patients, and to assess the effects of body composition on the equation performance. Methods Iohexol plasma clearance was measured in 43 CHF patients at baseline and after at least 6 months. Simultaneously, renal function was estimated with five creatinine-based equations (four- and six-variable Modification of Diet in Renal Disease, Cockcroft-Gault, Cockcroft-Gault adjusted for lean body mass, Chronic Kidney Disease Epidemiology Collaboration equation) and body composition was assessed using bioimpedance and dual-energy x-ray absorptiometry. Results Over a median follow-up of 7.5 months (range 6-17 months), iohexol clearance significantly declined (52.8 vs 44.4 mL/[min ×1.73 m2], P = 0.001). This decline was significantly higher in patients receiving mineralocorticoid receptor antagonists at baseline (mean decline -22% of baseline value vs -3%, P = 0.037). Mean serum creatinine concentration did not change significantly during follow-up and no creatinine-based renal function estimating equation was able to detect the significant longitudinal decline of renal function determined by iohexol clearance. After accounting for body composition, the accuracy of the equations improved, but not their ability to detect renal function decline. Conclusions Renal function measured with iohexol plasma clearance showed relevant decline in CHF patients, particularly in those treated with mineralocorticoid receptor antagonists. None of the equations for renal function estimation was able to detect these changes. ClinicalTrials.gov registration number NCT01829880 PMID:26718759

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

Science.gov (United States)

Colmenares, Pedro J.

2018-05-01

This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

Functionals Hartree-Fock equations in the Schrodinger representation of quantum field theory

International Nuclear Information System (INIS)

Gamboa, J.

1989-08-01

Hartree-Fock equations for a scalar field theory in the Schrodinger representation are derived. It is shown that renormalization of the total energy in the functional Schrodinger equation is enterely contained in the eigenvalues of the Hartree-Fock hamiltonian. (A.C.A.S.) [pt

Path integral solutions of the master equation. [Lagrangian function, Ehrenfest-type theorem, Cauchy method, inverse functions

Energy Technology Data Exchange (ETDEWEB)

Etim, E; Basili, C [Rome Univ. (Italy). Ist. di Matematica

1978-08-21

The lagrangian in the path integral solution of the master equation of a stationary Markov process is derived by application of the Ehrenfest-type theorem of quantum mechanics and the Cauchy method of finding inverse functions. Applied to the non-linear Fokker-Planck equation the authors reproduce the result obtained by integrating over Fourier series coefficients and by other methods.

Application of Exp-function method to potential Kadomtsev-Petviashvili equation

International Nuclear Information System (INIS)

Xian Daquan; Dai Zhengde

2009-01-01

Exact periodic kink-wave solution, periodic soliton and doubly periodic solutions for the potential Kadomtsev-Petviashvii (PKP) equation are obtained using Exp-function method with the help of Maple computation.

Low energy elastic scattering of positrons by CO: An application of continued fractions and Schwinger variational iterative methods

Energy Technology Data Exchange (ETDEWEB)

Arretche, F. [Departamento de Fisica, Universidade Federal de Santa Catarina, 88040-900, Florianopolis, Santa Catarina (Brazil)], E-mail: farretche@hotmail.com; Mazon, K.T.; Michelin, S.E. [Departamento de Fisica, Universidade Federal de Santa Catarina, 88040-900, Florianopolis, Santa Catarina (Brazil); Fujimoto, M.M. [Departamento de Fisica, Universidade Federal do Parana, 81531-990, Curitiba, Parana (Brazil); Iga, I.; Lee, M.-T. [Departamento de Quimica, Universidade Federal de Sao Carlos, 13565-905, Sao Paulo (Brazil)

2008-02-15

Iterative Schwinger variational methods and the method of continued fractions, widely used for electron-molecule scattering, are applied for the first time to investigate positron-molecule interactions. Specifically, integral and differential cross sections for elastic positron scattering by CO in the (0.5-20) eV energy range are calculated and reported. In our calculation, a static plus correlation-polarization potential is used to represent the collisional dynamics. Our calculated results are in general agreement with the theoretical and experimental data available in the literature.

Periodic solutions of first-order functional differential equations in population dynamics

CERN Document Server

Padhi, Seshadev; Srinivasu, P D N

2014-01-01

This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, a...

Green functions in Bianci-type spaces

International Nuclear Information System (INIS)

Bukhbinder, I.L.; Kirillova, E.N.

1988-01-01

The theory of free scalar field with conformal connection in distorted space - time with Bianci 1 type metrics is considered. The presentation of the Green functions G-tilde approximately in in in the form of integral from the Schwinger - De Witt kernel over the contour in the plane of complex values of eigentime is obtained. The way, in which the transfer from the Green function in space with Euclidean signature to the Green functions in space with Minkowski signature and vice versa is realized, has been shown

Evolution equation for the shape function in the parton model approach to inclusive B decays

International Nuclear Information System (INIS)

Baek, Seungwon; Lee, Kangyoung

2005-01-01

We derive an evolution equation for the shape function of the b quark in an analogous way to the Altarelli-Parisi equation by incorporating the perturbative QCD correction to the inclusive semileptonic decays of the B meson. Since the parton picture works well for inclusive B decays due to the heavy mass of the b quark, the scaling feature manifests and the decay rate may be expressed by a single structure function describing the light-cone distribution of the b quark apart from the kinematic factor. The evolution equation introduces a q 2 dependence of the shape function and violates the scaling properties. We solve the evolution equation and discuss the phenomenological implication.

Solution of the chemical master equation by radial basis functions approximation with interface tracking

NARCIS (Netherlands)

Kryven, I.; Röblitz, S; Schütte, C.

2015-01-01

Background: The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents

Quantum kinetic field theory in curved spacetime: Covariant Wigner function and Liouville-Vlasov equations

International Nuclear Information System (INIS)

Calzetta, E.; Habib, S.; Hu, B.L.

1988-01-01

We consider quantum fields in an external potential and show how, by using the Fourier transform on propagators, one can obtain the mass-shell constraint conditions and the Liouville-Vlasov equation for the Wigner distribution function. We then consider the Hadamard function G 1 (x 1 ,x 2 ) of a real, free, scalar field in curved space. We postulate a form for the Fourier transform F/sup (//sup Q//sup )/(X,k) of the propagator with respect to the difference variable x = x 1 -x 2 on a Riemann normal coordinate centered at Q. We show that F/sup (//sup Q//sup )/ is the result of applying a certain Q-dependent operator on a covariant Wigner function F. We derive from the wave equations for G 1 a covariant equation for the distribution function and show its consistency. We seek solutions to the set of Liouville-Vlasov equations for the vacuum and nonvacuum cases up to the third adiabatic order. Finally we apply this method to calculate the Hadamard function in the Einstein universe. We show that the covariant Wigner function can incorporate certain relevant global properties of the background spacetime. Covariant Wigner functions and Liouville-Vlasov equations are also derived for free fermions in curved spacetime. The method presented here can serve as a basis for constructing quantum kinetic theories in curved spacetime or for near-uniform systems under quasiequilibrium conditions. It can also be useful to the development of a transport theory of quantum fields for the investigation of grand unification and post-Planckian quantum processes in the early Universe

Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay

Directory of Open Access Journals (Sweden)

Hassane Bouzahir

2007-02-01

Full Text Available We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the nonlinear semigroup.

Numerical solution of neutral functional-differential equations with proportional delays

Directory of Open Access Journals (Sweden)

Mehmet Giyas Sakar

2017-07-01

Full Text Available In this paper, homotopy analysis method is improved with optimal determination of auxiliary parameter by use of residual error function for solving neutral functional-differential equations (NFDEs with proportional delays. Convergence analysis and error estimate of method are given. Some numerical examples are solved and comparisons are made with the existing results. The numerical results show that the homotopy analysis method with residual error function is very effective and simple.

Green's functions of the induction equation on regions with boundary. 1

International Nuclear Information System (INIS)

Braeuer, H.J.; Raedler, K.H.

1986-01-01

The evolution of a magnetic field is considered which pervades an electrically conducting fluid and its non-conducting surroundings under the influence of electromotive forces due to internal motion and other causes. The governing equations - among which the induction equation of magnetohydrodynamics is the most prominent - pose an initial value problem for the magnetic flux density. Properties of this initial value problem and of the solving Green's function are reviewed and a general construction principle for the Green's function is given. Detailed treatment of cases where the fluid occupies a sphere or an evenly bounded half-space are presented in two subsequent papers. (author)

Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces

Institute of Scientific and Technical Information of China (English)

LI Shoufu

2005-01-01

A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.

Modulating functions method for parameters estimation in the fifth order KdV equation

KAUST Repository

Asiri, Sharefa M.; Liu, Da-Yan; Laleg-Kirati, Taous-Meriem

2017-01-01

In this work, the modulating functions method is proposed for estimating coefficients in higher-order nonlinear partial differential equation which is the fifth order Kortewegde Vries (KdV) equation. The proposed method transforms the problem into a

General Large Deviations and Functional Iterated Logarithm Law for Multivalued Stochastic Differential Equations

OpenAIRE

Ren, Jiagang; Wu, Jing; Zhang, Hua

2015-01-01

In this paper, we prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations. As an application, we derive a functional iterated logarithm law for the solutions of multivalued stochastic differential equations.

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

Science.gov (United States)

Baumeister, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

Science.gov (United States)

Baumeiste, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Multi-point boundary value problems for linear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

2017-01-01

Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional-differential equations * functional-differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076. xml

Multi-point boundary value problems for linear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

2017-01-01

Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional- differential equations * functional- differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076.xml

Green`s function of Maxwell`s equations and corresponding implications for iterative methods

Energy Technology Data Exchange (ETDEWEB)

Singer, B.S. [Macquarie Univ., Sydney (Australia); Fainberg, E.B. [Inst. of Physics of the Earth, Moscow (Russian Federation)

1996-12-31

Energy conservation law imposes constraints on the norm and direction of the Hilbert space vector representing a solution of Maxwell`s equations. In this paper, we derive these constrains and discuss the corresponding implications for the Green`s function of Maxwell`s equations in a dissipative medium. It is shown that Maxwell`s equations can be reduced to an integral equation with a contracting kernel. The equation can be solved using simple iterations. Software based on this algorithm have successfully been applied to a wide range of problems dealing with high contrast models. The matrix corresponding to the integral equation has a well defined spectrum. The equation can be symmetrized and solved using different approaches, for instance one of the conjugate gradient methods.

Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

Science.gov (United States)

Azadbakht, F. Teimoury; Boroun, G. R.

2018-02-01

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions δ FS(x,Q2)=F[partial δ FS0(x), δ FS0(x)] and {δ G}(x,Q2)=G[partial δ G0(x), δ G0(x)]. We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC'08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.

A Generalized Analytic Operator-Valued Function Space Integral and a Related Integral Equation

International Nuclear Information System (INIS)

Chang, K.S.; Kim, B.S.; Park, C.H.; Ryu, K.S.

2003-01-01

We introduce a generalized Wiener measure associated with a Gaussian Markov process and define a generalized analytic operator-valued function space integral as a bounded linear operator from L p into L p-ci r cumflexprime (1< p ≤ 2) by the analytic continuation of the generalized Wiener integral. We prove the existence of the integral for certain functionals which involve some Borel measures. Also we show that the generalized analytic operator-valued function space integral satisfies an integral equation related to the generalized Schroedinger equation. The resulting theorems extend the theory of operator-valued function space integrals substantially and previous theorems about these integrals are generalized by our results

On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind

Directory of Open Access Journals (Sweden)

Dinesh Kumar

2015-01-01

Full Text Available We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably new results.

Controllability for Semilinear Functional and Neutral Functional Evolution Equations with Infinite Delay in Frechet Spaces

International Nuclear Information System (INIS)

Agarwal, Ravi P.; Baghli, Selma; Benchohra, Mouffak

2009-01-01

The controllability of mild solutions defined on the semi-infinite positive real interval for two classes of first order semilinear functional and neutral functional differential evolution equations with infinite delay is studied in this paper. Our results are obtained using a recent nonlinear alternative due to Avramescu for sum of compact and contraction operators in Frechet spaces, combined with the semigroup theory

Functional differential equation approach to the large N expansion and mean field perturbation theory

International Nuclear Information System (INIS)

Bender, C.M.; Cooper, F.

1985-01-01

An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi

About sign-constancy of Green's functions for impulsive second order delay equations

Directory of Open Access Journals (Sweden)

Alexander Domoshnitsky

2014-01-01

Full Text Available We consider the following second order differential equation with delay \\[\\begin{cases} (Lx(t\\equiv{x''(t+\\sum_{j=1}^p {b_{j}(tx(t-\\theta_{j}(t}}=f(t, \\quad t\\in[0,\\omega],\\\\ x(t_j=\\gamma_{j}x(t_j-0, x'(t_j=\\delta_{j}x'(t_j-0, \\quad j=1,2,\\ldots,r. \\end{cases}\\] In this paper we find necessary and sufficient conditions of positivity of Green's functions for this impulsive equation coupled with one or two-point boundary conditions in the form of theorems about differential inequalities. By choosing the test function in these theorems, we obtain simple sufficient conditions. For example, the inequality \\(\\sum_{i=1}^p{b_i(t\\left(\\frac{1}{4}+r\\right}\\lt \\frac{2}{\\omega^2}\\ is a basic one, implying negativity of Green's function of two-point problem for this impulsive equation in the case \\(0\\lt \\gamma_i\\leq{1}\\, \\(0\\lt \\delta_i\\leq{1}\\ for \\(i=1,\\ldots ,p\\.

New exact solutions of coupled Boussinesq–Burgers equations by Exp-function method

Directory of Open Access Journals (Sweden)

L.K. Ravi

2017-03-01

Full Text Available In the present paper, we build the new analytical exact solutions of a nonlinear differential equation, specifically, coupled Boussinesq–Burgers equations by means of Exp-function method. Then, we analyze the results by plotting the three dimensional soliton graphs for each case, which exhibit the simplicity and effectiveness of the proposed method. The primary purpose of this paper is to employ a new approach, which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq–Burgers equations.

The Landau-Lifshitz equation describes the Ising spin correlation function in the free-fermion model

CERN Document Server

Rutkevich, S B

1998-01-01

We consider time and space dependence of the Ising spin correlation function in a continuous one-dimensional free-fermion model. By the Ising spin we imply the 'sign' variable, which takes alternating +-1 values in adjacent domains bounded by domain walls (fermionic world paths). The two-point correlation function is expressed in terms of the solution of the Cauchy problem for a nonlinear partial differential equation, which is proved to be equivalent to the exactly solvable Landau-Lifshitz equation. A new zero-curvature representation for this equation is presented. In turn, the initial condition for the Cauchy problem is given by the solution of a nonlinear ordinary differential equation, which has also been derived. In the Ising limit the above-mentioned partial and ordinary differential equations reduce to the sine-Gordon and Painleve III equations, respectively. (author)

Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations

KAUST Repository

Asiri, Sharefa M.

2016-10-20

In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.

Discriminants and functional equations for polynomials orthogonal on the unit circle

International Nuclear Information System (INIS)

Ismail, M.E.H.; Witte, N.S.

2000-01-01

We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and q-difference equations for these polynomials. A general functional equation is found which allows one to relate the zeros of the orthogonal polynomials to the stationary values of an explicit quasi-energy and implies recurrences on the orthogonal polynomial coefficients. We also evaluate the discriminants and quantized discriminants of polynomials orthogonal on the unit circle

Block-pulse functions approach to numerical solution of Abel’s integral equation

Directory of Open Access Journals (Sweden)

Monireh Nosrati Sahlan

2015-12-01

Full Text Available This study aims to present a computational method for solving Abel’s integral equation of the second kind. The introduced method is based on the use of Block-pulse functions (BPFs via collocation method. Abel’s integral equations as singular Volterra integral equations are hard and heavy in computation, but because of the properties of BPFs, as is reported in examples, this method is more efficient and more accurate than some other methods for solving this class of integral equations. On the other hand, the benefit of this method is low cost of computing operations. The applied method transforms the singular integral equation into triangular linear algebraic system that can be solved easily. An error analysis is worked out and applications are demonstrated through illustrative examples.

On nonnegative solutions of second order linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander; Vodstrčil, Petr

2004-01-01

Roč. 32, č. 1 (2004), s. 59-88 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z1019905 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics

A bijection for tri-cellular maps

DEFF Research Database (Denmark)

Han, Hillary Siwei; Reidys, Christian

2013-01-01

In this paper we give a bijective proof for a relation between unicellular, bicellular and tricellular maps. These maps represent cell-complexes of orientable surfaces having one, two or three boundary components. The relation can formally be obtained using matrix theory \\cite{Dyson} employing...... the Schwinger-Dyson equation \\cite{Schwinger}. In this paper we present a bijective proof of the corresponding coefficient equation. Our result is a bijection that transforms a unicellular map of genus $g$ into unicellular, bicellular or tricellular maps of strictly lower genera. The bijection employs edge...

Generalization of the linear algebraic method to three dimensions

International Nuclear Information System (INIS)

Lynch, D.L.; Schneider, B.I.

1991-01-01

We present a numerical method for the solution of the Lippmann-Schwinger equation for electron-molecule collisions. By performing a three-dimensional numerical quadrature, this approach avoids both a basis-set representation of the wave function and a partial-wave expansion of the scattering potential. The resulting linear equations, analogous in form to the one-dimensional linear algebraic method, are solved with the direct iteration-variation method. Several numerical examples are presented. The prospect for using this numerical quadrature scheme for electron-polyatomic molecules is discussed

The bound state problem and quark confinement

International Nuclear Information System (INIS)

Chaichian, M.; Demichev, A.P.; Nelipa, N.F.

1980-01-01

A quantum field-theoretic model in which quark is confined is considered. System of equations for the Green functions of colour singlet and octet bound states is obtained. The method is based on the nonperturbative Schwinger-Dyson equations with the use of Slavnov-Taylor identities. It is shown that in the framework of the model if there exist singlet, then also exist octet bound states of the quark-antiquark system. Thus in general, confinement of free quarks does not mean absence of their coloured bound states. (author)

Oscillation of certain higher-order neutral partial functional differential equations.

Science.gov (United States)

Li, Wei Nian; Sheng, Weihong

2016-01-01

In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.

On Delay-Independent Criteria for Oscillation of Higher-Order Functional Differential Equations

Directory of Open Access Journals (Sweden)

Yuangong Sun

2011-01-01

Full Text Available We investigate the oscillation of the following higher-order functional differential equation: x(n(t+q(t|x(t-τ|λ-1x(t-τ=e(t, where q(t and e(t are continuous functions on [t0,∞, 1>λ>0 and τ≠0 are constants. Unlike most of delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the case τ>0 and the case τ<0 under the assumption that the potentials q(t and e(t change signs on [t0,∞.

STABILITY OF A FUNCTIONAL EQUATION IN COMPLEX BANACH SPACES

Directory of Open Access Journals (Sweden)

PRATAP MONDAL

2016-12-01

Full Text Available Using fixed point technique, in the present paper , we wish to examine gen- eralization of the Hyers-Ulam-Rassias stability theorem for the functional equations f ( 2 x + i y + f ( x + 2 i y = 4 f ( x + i y + f ( x + f ( y (0.1 and f ( 2 x + i y .

Positron scattering by molecules: implementation of the C-tilde-functional

International Nuclear Information System (INIS)

Silva Lino, Jorge Luiz da

1995-01-01

In this work, we present a formulation called the C-Functional to study collisions of low-energy positron by molecules. This formalism is based on the Schwinger Multichannel Method for positrons which although being a quite general method (it is applicable to polyatomic molecules and include polarization and multichannel coupling) is limited to the use of trial wavefunctions consisting only of square integrable basis functions (Gaussian Cartesian Function). In principle this is not a problem, considering that the Schwinger type of methods require a good description of the scattering wavefunction only in the region where the potential is non-zero. However, there exist some situations (long range potentials) where the SMC has consequences. The C-functional (CF) consists in writing the wavefunctions as a sum of a plane-wave plus a combination of trial functions (where the combination is variationally determined). The basic difference between the 2 cases (SMC and CF) is the presence in the CF amplitude of the First (FBA) and Second Born terms. Aiming the preservation of important features of the SMG, we have developed general codes (applicable to polyatomic targets) to evaluate these terms. To illustrate the CF method we show elastic cross sections ti He and H 2 . (author)

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

Science.gov (United States)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

Two-dimensional massless quantum electrodynamics in the Landau-gauge formalism and the Higgs mechanism. [Schwinger model

Energy Technology Data Exchange (ETDEWEB)

Ito, K R [Kyoto Univ. (Japan). Research Inst. for Mathematical Sciences

1975-03-01

The Schwinger model is considered in the Landau-gauge formalism of quantum electrodynamics. This model can be solved exactly on the assumption of no radiative corrections to the anomaly. It is found that the photon obtains a non-zero mass through the Higgs mechanism. In this case, the would-be Nambu-Goldstone boson is an associated boson which is constructed from a pair of two-component massless fermions. This would-be Nambu-Goldstone boson appears as a result of the spontaneous breaking of the gauge invariance of the first kind, and it becomes unphysical through the Higgs mechanism. However, as all the fermions themselves decouple from photons, they cannot appear as real particles in our world.

Superposition of elliptic functions as solutions for a large number of nonlinear equations

International Nuclear Information System (INIS)

Khare, Avinash; Saxena, Avadh

2014-01-01

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ 4 , the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn 2 (x, m), it also admits solutions in terms of dn 2 (x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations

Functional differential equations for the q-Fourier transform of q-Gaussians

International Nuclear Information System (INIS)

Umarov, S; Queiros, S M Duarte

2010-01-01

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 ≤ q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Functional differential equations for the q-Fourier transform of q-Gaussians

Energy Technology Data Exchange (ETDEWEB)

Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: sdqueiro@gmail.co [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)

2010-02-05

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 <= q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

Directory of Open Access Journals (Sweden)

T. E. Govindan

2011-01-01

Full Text Available This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.

Functional analysis in the study of differential and integral equations

International Nuclear Information System (INIS)

Sell, G.R.

1976-01-01

This paper illustrates the use of functional analysis in the study of differential equations. Our particular starting point, the theory of flows or dynamical systems, originated with the work of H. Poincare, who is the founder of the qualitative theory of ordinary differential equations. In the qualitative theory one tries to describe the behaviour of a solution, or a collection of solutions, without ''solving'' the differential equation. As a starting point one assumes the existence, and sometimes the uniqueness, of solutions and then one tries to describe the asymptotic behaviour, as time t→+infinity, of these solutions. We compare the notion of a flow with that of a C 0 -group of bounded linear operators on a Banach space. We shall show how the concept C 0 -group, or more generally a C 0 -semigroup, can be used to study the behaviour of solutions of certain differential and integral equations. Our main objective is to show how the concept of a C 0 -group and especially the notion of weak-compactness can be used to prove the existence of an invariant measure for a flow on a compact Hausdorff space. Applications to the theory of ordinary differential equations are included. (author)

The fractional coupled KdV equations: Exact solutions and white noise functional approach

International Nuclear Information System (INIS)

Ghany, Hossam A.; El Bab, A. S. Okb; Zabel, A. M.; Hyder, Abd-Allah

2013-01-01

Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types. (general)

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

Science.gov (United States)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

A toy model for higher spin Dirac operators

International Nuclear Information System (INIS)

Eelbode, D.; Van de Voorde, L.

2010-01-01

This paper deals with the higher spin Dirac operator Q 2,1 acting on functions taking values in an irreducible representation space for so(m) with highest weight (5/2, 3/2, 1/2,..., 1/2). . This operator acts as a toy model for generalizations of the classical Rarita-Schwinger equations in Clifford analysis. Polynomial null solutions for this operator are studied in particular.

Vacuum polarization and dynamical chiral symmetry breaking in quantum electrodynamics

International Nuclear Information System (INIS)

Gusynin, V.P.

1989-01-01

The Schwinger-Dyson equation in the ladder approximation is considered for the fermion mass function taking into account the vacuum polarization effects. It is shown that even in the 'zero-charge' situation there exists, at rather large coupling constant (α>α c >0), a solution with spontaneously broken chiral symmetry. The existence of the local limit in the model concerned is discussed. 30 refs.; 1 fig

Infrared slavery and quark confinement

CERN Document Server

Alabiso, C

1976-01-01

The question is considered of whether the so-called infrared slavery mechanism as, e.g., being manifest in non-Abelian gauge theories, necessarily confines quarks. Making a specific ansatz for the long- range forces, the Schwinger-Dyson equation is solved for the quark Green function. Besides having a confining solution, it appears that quarks may by-pass the long-range forces and be produced. (20 refs).

Infrared slavery and quark confinement

International Nuclear Information System (INIS)

Alabiso, C.; Schierholz, G.

1976-01-01

The question of whether the so-called infrared slavery mechanism as, e.g., being manifest in non-Abelian gauge theories, necessarily confines quarks is posed. Making a specific ansatz for the long-range forces, the Schwinger-Dyson equation is solved for the quark Green function. Besides having a confining solution, it appears that quarks may by-pass the long-range forces and be produced. (Auth.)

Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion

Science.gov (United States)

Shimizu, Yuya; Kuramashi, Yoshinobu

2018-02-01

We have made a detailed study of the phase structure for the lattice Schwinger model with one flavor of Wilson fermion on the (m ,g ) plane. For numerical investigation, we develop a decorated tensor renormalization method for lattice gauge theories with fermions incorporating the Grassmann tensor renormalization. Our algorithm manifestly preserves rotation and reflection symmetries. We find not only a parity-broken phase but also a Berezinskii-Kosterlitz-Thouless (BKT) transition by evaluating the central charge and an expectation value of a projection operator into the parity-odd subspace. The BKT phase boundaries converge into the degenerated doubler pole (m ,g )=(-2 ,0 ), while the parity-breaking transition line ends at the physical pole (m ,g )=(0 ,0 ). In addition, our analysis of scaling dimensions indicates that a conformal field theory with SU(2) symmetry arises on the line of m =-2 .

Integration Processes of Delay Differential Equation Based on Modified Laguerre Functions

Directory of Open Access Journals (Sweden)

Yeguo Sun

2012-01-01

Full Text Available We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for refinement of modified Laguerre-Radau interpolations. Lastly, numerical results demonstrate the spectral accuracy of the proposed method and coincide well with analysis.

Stochastic wave-function unravelling of the generalized Lindblad equation using correlated states

International Nuclear Information System (INIS)

Moodley, Mervlyn; Nsio Nzundu, T; Paul, S

2012-01-01

We perform a stochastic wave-function unravelling of the generalized Lindblad master equation using correlated states, a combination of the system state vectors and the environment population. The time-convolutionless projection operator method using correlated projection superoperators is applied to a two-state system, a qubit, that is coupled to an environment consisting of two energy bands which are both populated. These results are compared to the data obtained from Monte Carlo wave-function simulations based on the unravelling of the master equation. We also show a typical quantum trajectory and the average time evolution of the state vector on the Bloch sphere. (paper)

TWIN POSITIVE PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

In this paper, the author studies a class of nonlinear functional differential equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of twin positive periodic solutions.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

International Nuclear Information System (INIS)

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-01

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations

Fixed Point Methods in the Stability of the Cauchy Functional Equations

Directory of Open Access Journals (Sweden)

Z. Dehvari

2013-03-01

Full Text Available By using the fixed point methods, we prove some generalized Hyers-Ulam stability of homomorphisms for Cauchy and CauchyJensen functional equations on the product algebras and on the triple systems.

Mittag-Leffler functions as solutions of relaxation-oscillation and diffusion-wave fractional order equation

International Nuclear Information System (INIS)

Sandev, D. Trivche

2010-01-01

The fractional calculus basis, Mittag-Leffler functions, various relaxation-oscillation and diffusion-wave fractional order equation and systems of fractional order equations are considered in this thesis. To solve these fractional order equations analytical methods, such as the Laplace transform method and method of separation of variables are employed. Some applications of the fractional calculus are considered, particularly physical system with anomalous diffusive behavior. (Author)

An existence theorem for a type of functional differential equation with infinite delay

NARCIS (Netherlands)

Izsak, F.

We prove an existence theorem for a functional differential equation with infinite delay using the Schauder fixpoint theorem. We extend a result in [19] applying the fixed point procedure in an appropriate function space.

QCD propagators and vertices from lattice QCD (in memory of Michael Müller-Preußker

Directory of Open Access Journals (Sweden)

Sternbeck André

2017-01-01

Full Text Available We review lattice calculations of the elementary Greens functions of QCD with a special emphasis on the Landau gauge. These lattice results have been of interest to continuum approaches to QCD over the past 20 years. They are used as reference for Dyson-Schwinger- and functional renormalization group equation calculations as well as for hadronic bound state equations. The lattice provides low-energy data for propagators and three-point vertices in Landau gauge at zero and finite temperature even including dynamical fermions. We summarize Michael Müller-Preußker’s important contributions to this field and put them into the perspective of his other research interests.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

Science.gov (United States)

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

The extended hyperbolic function method and exact solutions of the long-short wave resonance equations

International Nuclear Information System (INIS)

Shang Yadong

2008-01-01

The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

Full Text Available In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE through substitution is converted into a nonlinear ordinary differential equation (NODE. The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM, homotopy perturbation method (HPM, and optimal homotopy asymptotic method (OHAM, show that the suggested scheme is fairly accurate and viable for solving such problems.

Two-body Dirac equation and its wave function at the origin

International Nuclear Information System (INIS)

Ito, Hitoshi

1998-01-01

We propose a relativistic bound state equation for the Dirac particles interacting through an Abelian gauge field. It reduces to the (one body) Dirac equation in the infinite limit of one of the masses and is invariant under the PCT transformation. This invariance is a consequence of a modification of the Stueckelberg-Feynman boundary condition for propagation of the negative-energy two-body states, by which the some effect of the crossed diagram is taken in the lowest ladder equation. We can correct back the modification in perturbative calculations of the weak-coupling theory by adding a counter correction term in the interaction kernel. The equation can be used for the phenomenology of the heavy flavored mesons. We get good behavior of the wave function at the origin (WFO), with which the annihilation amplitude of the pseudoscalar meson becomes finite. Some comments are mentioned for the application in the heavy quark effective theory. The talk was based on a preprint

Gluon structure function of a color dipole in the light-cone limit of lattice QCD

International Nuclear Information System (INIS)

Gruenewald, D.; Ilgenfritz, E.-M.; Pirner, H. J.

2009-01-01

We calculate the gluon structure function of a color dipole in near-light-cone SU(2) lattice QCD as a function of x B . The quark and antiquark are external nondynamical degrees of freedom which act as sources of the gluon string configuration defining the dipole. We compute the color dipole matrix element of transversal chromo-electric and chromo-magnetic field operators separated along a direction close to the light cone, the Fourier transform of which is the gluon structure function. As vacuum state in the pure glue sector, we use a variational ground state of the near-light-cone Hamiltonian. We derive a recursion relation for the gluon structure function on the lattice similar to the perturbative Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation. It depends on the number of transversal links assembling the Schwinger string of the dipole. Fixing the mean momentum fraction of the gluons to the 'experimental value' in a proton, we compare our gluon structure function for a dipole state with four links with the next-to-leading-order MRST 2002 and the CTEQ AB-0 parametrizations at Q 2 =1.5 GeV 2 . Within the systematic uncertainty we find rather good agreement. We also discuss the low x B behavior of the gluon structure function in our model calculation.

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

2000-01-01

We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

equate: An R Package for Observed-Score Linking and Equating

Directory of Open Access Journals (Sweden)

Anthony D. Albano

2016-10-01

Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.

Thermodynamical and Green function many-body Wick theorems

International Nuclear Information System (INIS)

Westwanski, B.

1987-01-01

The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)

Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations

KAUST Repository

Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem

2016-01-01

In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear

Scattering theory methods for bound state problems

International Nuclear Information System (INIS)

Raphael, R.B.; Tobocman, W.

1978-01-01

For the analysis of the properties of a bound state system one may use in place of the Schroedinger equation the Lippmann-Schwinger (LS) equation for the wave function or the LS equation for the reactance operator. Use of the LS equation for the reactance operator constrains the solution to have correct asymptotic behaviour, so this approach would appear to be desirable when the bound state wave function is to be used to calculate particle transfer form factors. The Schroedinger equation based N-level analysis of the s-wave bound states of a square well is compared to the ones based on the LS equation. It is found that the LS equation methods work better than the Schroedinger equation method. The method that uses the LS equation for the wave function gives the best results for the wave functions while the method that uses the LS equation for the reactance operator gives the best results for the binding energies. The accuracy of the reactance operator based method is remarkably insensitive to changes in the oscillator constant used for the harmonic oscillator function basis set. It is also remarkably insensitive to the number of nodes in the bound state wave function. (Auth.)

Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions

Science.gov (United States)

Ishizaki, Akihito; Tanimura, Yoshitaka

2008-05-01

Based on the influence functional formalism, we have derived a nonperturbative equation of motion for a reduced system coupled to a harmonic bath with colored noise in which the system-bath coupling operator does not necessarily commute with the system Hamiltonian. The resultant expression coincides with the time-convolutionless quantum master equation derived from the second-order perturbative approximation, which is also equivalent to a generalized Redfield equation. This agreement occurs because, in the nonperturbative case, the relaxation operators arise from the higher-order system-bath interaction that can be incorporated into the reduced density matrix as the influence operator; while the second-order interaction remains as a relaxation operator in the equation of motion. While the equation describes the exact dynamics of the density matrix beyond weak system-bath interactions, it does not have the capability to calculate nonlinear response functions appropriately. This is because the equation cannot describe memory effects which straddle the external system interactions due to the reduced description of the bath. To illustrate this point, we have calculated the third-order two-dimensional (2D) spectra for a two-level system from the present approach and the hierarchically coupled equations approach that can handle quantal system-bath coherence thanks to its hierarchical formalism. The numerical demonstration clearly indicates the lack of the system-bath correlation in the present formalism as fast dephasing profiles of the 2D spectra.

Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

Science.gov (United States)

Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

2013-06-01

In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient

International Nuclear Information System (INIS)

Cao Rui; Zhang Jian

2013-01-01

In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions. (general)

Stability of Jensen functional equation in intuitionistic fuzzy normed space

International Nuclear Information System (INIS)

Mohiuddine, S.A.

2009-01-01

In this paper, we determine some stability results concerning the Jensen functional equation 2f((x+y)/2)=f(x)+f(y) in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the Jensen mappings and prove that the existence of a solution for any approximately Jensen mapping implies the completeness of IFNS.

Enhanced finite difference scheme for the neutron diffusion equation using the importance function

International Nuclear Information System (INIS)

Vagheian, Mehran; Vosoughi, Naser; Gharib, Morteza

2016-01-01

Highlights: • An enhanced finite difference scheme for the neutron diffusion equation is proposed. • A seven-step algorithm is considered based on the importance function. • Mesh points are distributed through entire reactor core with respect to the importance function. • The results all proved that the proposed algorithm is highly efficient. - Abstract: Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient.

How to use the cosmological Schwinger principle for energy flux, entropy, and 'atoms of space-time' to create a thermodynamic space-time and multiverse

International Nuclear Information System (INIS)

Beckwith, Andrew

2011-01-01

We make explicit an idea by Padmanabhan in DICE 2010, as to finding 'atoms of space-time' permitting a thermodynamic treatment of emergent structure similar to Gibbs treatment of statistical physics. That is, an ensemble of gravitons is used to give an 'atom' of space-time congruent with relic GW. The idea is to reduce the number of independent variables to get a simple emergent space-time structure of entropy. An electric field, based upon the cosmological Schwinger principle, is linked to relic heat flux, with entropy production tied in with candidates as to inflaton potentials. The effective electric field links with the Schwinger 1951s result of an E field leading to pairs of e + e - charges nucleated in space-time volume V · t. Note that in most inflationary models, the assumption is for a magnetic field, not an electric field. An electric field permits a kink-anti-kink construction of an emergent structure, which includes Glinka's recent pioneering approach to a Multiverse. Also an E field allows for an emergent relic particle frequency range between one and 100 GHz. The novel contribution is a relic E field, instead of a B field, in relic space-time 'atom' formation and vacuum nucleation of the same.

Communication: An exact bound on the bridge function in integral equation theories.

Science.gov (United States)

Kast, Stefan M; Tomazic, Daniel

2012-11-07

We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.

Geometric description of a discrete power function associated with the sixth Painlevé equation.

Science.gov (United States)

Joshi, Nalini; Kajiwara, Kenji; Masuda, Tetsu; Nakazono, Nobutaka; Shi, Yang

2017-11-01

In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with [Formula: see text] symmetry. By constructing the action of [Formula: see text] as a subgroup of [Formula: see text], i.e. the symmetry group of P VI , we show how to relate [Formula: see text] to the symmetry group of the lattice. Moreover, by using translations in [Formula: see text], we explain the odd-even structure appearing in previously known explicit formulae in terms of the τ function.

Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painleve equations

International Nuclear Information System (INIS)

Dzhamay, Anton

2009-01-01

We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painleve equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D Arinkin and A Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.

Playing with Quantum Toys: Julian Schwinger's Measurement Algebra and the Material Culture of Quantum Mechanics Pedagogy at Harvard in the 1960s

Science.gov (United States)

Gauvin, Jean-François

2018-03-01

In the early 1960s, a PhD student in physics, Costas Papaliolios, designed a simple—and playful—system of Polaroid polarizer filters with a specific goal in mind: explaining the core principles behind Julian Schwinger's quantum mechanical measurement algebra, developed at Harvard in the late 1940s and based on the Stern-Gerlach experiment confirming the quantization of electron spin. Papaliolios dubbed his invention "quantum toys." This article looks at the origins and function of this amusing pedagogical device, which landed half a century later in the Collection of Historical Scientific Instruments at Harvard University. Rendering the abstract tangible was one of Papaliolios's demonstration tactics in reforming basic teaching of quantum mechanics. This article contends that Papaliolios's motivation in creating the quantum toys came from a renowned endeavor aimed, inter alia, at reforming high-school physics training in the United States: Harvard Project Physics. The pedagogical study of these quantum toys, finally, compels us to revisit the central role playful discovery performs in pedagogy, at all levels of training and in all fields of knowledge.

Exact solutions of a Schrodinger equation based on the Lambert function

International Nuclear Information System (INIS)

Williams, Brian Wesley

2005-01-01

An exactly solvable Schrodinger equation of the confluent Natanzon class is derived using the differential properties of the Lambert W function. This potential involves two constant parameters and is defined along the entire real line. Specific spatial forms demonstrating wells and deformed positive barriers are presented

A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions

Directory of Open Access Journals (Sweden)

Shou-qiang Du

2008-01-01

Full Text Available For solving nonsmooth systems of equations, the Levenberg-Marquardt method and its variants are of particular importance because of their locally fast convergent rates. Finitely many maximum functions systems are very useful in the study of nonlinear complementarity problems, variational inequality problems, Karush-Kuhn-Tucker systems of nonlinear programming problems, and many problems in mechanics and engineering. In this paper, we present a modified Levenberg-Marquardt method for nonsmooth equations with finitely many maximum functions. Under mild assumptions, the present method is shown to be convergent Q-linearly. Some numerical results comparing the proposed method with classical reformulations indicate that the modified Levenberg-Marquardt algorithm works quite well in practice.

Linear hyperbolic functional-differential equations with essentially bounded right-hand side

Czech Academy of Sciences Publication Activity Database

Domoshnitsky, A.; Lomtatidze, Alexander; Maghakyan, A.; Šremr, Jiří

2011-01-01

Roč. 2011, - (2011), s. 242965 ISSN 1085-3375 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear functional-differential equation of hyperbolic type * Darboux problem * unique solvability Subject RIV: BA - General Mathematics Impact factor: 1.318, year: 2011 http://www.hindawi.com/journals/ aaa /2011/242965/

Quantum field kinetics of QCD quark-gluon transport theory for light-cone dominated processes

CERN Document Server

Kinder-Geiger, Klaus

1996-01-01

A quantum kinetic formalism is developed to study the dynamical interplay of quantum and statistical-kinetic properties of non-equilibrium multi-parton systems produced in high-energy QCD processes. The approach provides the means to follow the quantum dynamics in both space-time and energy-momentum, starting from an arbitrary initial configuration of high-momentum quarks and gluons. Using a generalized functional integral representation and adopting the `closed-time-path' Green function techniques, a self-consistent set of equations of motions is obtained: a Ginzburg-Landau equation for a possible color background field, and Dyson-Schwinger equations for the 2-point functions of the gluon and quark fields. By exploiting the `two-scale nature' of light-cone dominated QCD processes, i.e. the separation between the quantum scale that specifies the range of short-distance quantum fluctuations, and the kinetic scale that characterizes the range of statistical binary inter- actions, the quantum-field equations of ...

Supersymmetric quasipotential equations

International Nuclear Information System (INIS)

Zaikov, R.P.

1981-01-01

A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru

The Schroeder functional equation and its relation to the invariant measures of chaotic maps

International Nuclear Information System (INIS)

Luevano, Jose-Ruben; Pina, Eduardo

2008-01-01

The aim of this paper is to show that the invariant measure for a class of one-dimensional chaotic maps, T(x), is an extended solution of the Schroeder functional equation, q(T(x)) = λq(x), induced by them. Hence, we give a unified treatment of a collection of exactly solved examples worked out in the current literature. In particular, we show that these examples belong to a class of functions introduced by Mira (see the text). Moreover, as a new example, we compute the invariant densities for a class of rational maps having the Weierstrass p function as an invariant one. Also, we study the relation between that equation and the well-known Frobenius-Perron and Koopman's operators

Schwinger variational principle in charged particle scattering by mesic atoms and atoms

International Nuclear Information System (INIS)

Zubarev, A.L.; Podkopaev, A.P.

1981-01-01

The way for solving the strong channel coupling method equation with the use of the Shcwinger variational method is proposed. The equation obtained is valid for atomic and mesoatomic physics when the account of the large number of closed channels is necessary and virtual transitions in continuum. In this variational method the trial functions are chosen in the form of expansion into eigenfunctions. The region of the equation validity is found. The problems of the e + H and p-dμ scattering are studied. The e + H scattering length turns out to be 1.8 a. u. which is in accordance with other results. The scattering cross section for p-dμ scattering is equal to 5.7x10 -21 cm -2 which also qualitatively is in agreement with results obtained elsewhere. The bound state which is stable relative to the decay into a positron and hydrogen atom is found for the e + H system [ru

Computation of Green function of the Schroedinger-like partial differential equations by the numerical functional integration

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.; Shahbagian, R.R.; Zhidkov, E.P.

1991-01-01

A new method for numerical solution of the boundary problem for Schroedinger-like partial differential equations in R n is elaborated. The method is based on representation of multidimensional Green function in the form of multiple functional integral and on the use of approximation formulas which are constructed for such integrals. The convergence of approximations to the exact value is proved, the remainder of the formulas is estimated. Method reduces the initial differential problem to quadratures. 16 refs.; 7 tabs

Efficient Estimating Functions for Stochastic Differential Equations

DEFF Research Database (Denmark)

Jakobsen, Nina Munkholt

The overall topic of this thesis is approximate martingale estimating function-based estimationfor solutions of stochastic differential equations, sampled at high frequency. Focuslies on the asymptotic properties of the estimators. The first part of the thesis deals with diffusions observed over...... a fixed time interval. Rate optimal and effcient estimators areobtained for a one-dimensional diffusion parameter. Stable convergence in distribution isused to achieve a practically applicable Gaussian limit distribution for suitably normalisedestimators. In a simulation example, the limit distributions...... multidimensional parameter. Conditions for rate optimality and effciency of estimatorsof drift-jump and diffusion parameters are given in some special cases. Theseconditions are found to extend the pre-existing conditions applicable to continuous diffusions,and impose much stronger requirements on the estimating...

Stability of Pexiderized Quadratic Functional Equation in Random 2-Normed Spaces

Directory of Open Access Journals (Sweden)

Mohammed A. Alghamdi

2015-01-01

Full Text Available The aim of this paper is to investigate the stability of Hyers-Ulam-Rassias type theorems by considering the pexiderized quadratic functional equation in the setting of random 2-normed spaces (RTNS, while the concept of random 2-normed space has been recently studied by Goleţ (2005.

Global existence for Volterra-Fredholm type neutral impulsive functional integrodifferential equations