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)

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.)

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

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

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

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)

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

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)

Alien calculus and a Schwinger-Dyson equation: two-point function with a nonperturbative mass scale

Science.gov (United States)

Bellon, Marc P.; Clavier, Pierre J.

2018-02-01

Starting from the Schwinger-Dyson equation and the renormalization group equation for the massless Wess-Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep euclidean domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive β -function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.

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

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.

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.

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

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

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

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 .

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}.}

Infrared asymptotics and Dyson-Schwinger equations for the gauge-invariant spinor Green function in quantum electrodynamics

International Nuclear Information System (INIS)

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

1985-01-01

The Dayson-Schwinger equations for the gauge-invariant (G.I.) spinor Green function are derived for an Abelian case. On the basis of these equations as well as the functional integration method the behaviour of the G.I. spinor propagator is studied in the infrared region. It is shown that the G.I. propagator has a singularity of a simple pole in this region

Renormalization of self-consistent Schwinger-Dyson equations at finite temperature

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2002-01-01

We show that Dyson resummation schemes based on Baym's Φ-derivable approximations can be renormalized with counter term structures solely defined on the vacuum level. First applications to the self-consistent solution of the sunset self-energy in φ 4 -theory are presented. (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.

Large N saddle formulation of quadratic building block theories

International Nuclear Information System (INIS)

Halpern, M.B.

1980-01-01

I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)

Rarita-Schwinger field and multicomponent wave equation

International Nuclear Information System (INIS)

Kaloshin, A.E.; Lomov, V.P.

2011-01-01

We suggest a simple method to solve a wave equation for Rarita-Schwinger field without additional constraints. This method based on the use of off-shell projection operators allows one to diagonalize spin-1/2 sector of the field

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

Gauge covariance of the fermion Schwinger–Dyson equation in QED

Energy Technology Data Exchange (ETDEWEB)

Jia, Shaoyang, E-mail: sjia@email.wm.edu [Physics Department, College of William & Mary, Williamsburg, VA 23187 (United States); Pennington, M.R., E-mail: michaelp@jlab.org [Physics Department, College of William & Mary, Williamsburg, VA 23187 (United States); Theory Center, Thomas Jefferson National Accelerator Facility, Newport News, VA 23606 (United States)

2017-06-10

Any practical application of the Schwinger–Dyson equations to the study of n-point Green's functions in a strong coupling field theory requires truncations. In the case of QED, the gauge covariance, governed by the Landau–Khalatnikov–Fradkin transformations (LKFT), provides a unique constraint on such truncation. By using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the LKFT are linear operations on the spectral densities. We formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gauge covariance of any viable truncation of the Schwinger–Dyson equation for the fermion 2-point function.

Strong coupling phase in QED

International Nuclear Information System (INIS)

Aoki, Ken-ichi

1988-01-01

Existence of a strong coupling phase in QED has been suggested in solutions of the Schwinger-Dyson equation and in Monte Carlo simulation of lattice QED. In this article we recapitulate the previous arguments, and formulate the problem in the modern framework of the renormalization theory, Wilsonian renormalization. This scheme of renormalization gives the best understanding of the basic structure of a field theory especially when it has a multi-phase structure. We resolve some misleading arguments in the previous literature. Then we set up a strategy to attack the strong phase, if any. We describe a trial; a coupled Schwinger-Dyson equation. Possible picture of the strong coupling phase QED is presented. (author)

Nonadiabatic quantum Vlasov equation for Schwinger pair production

International Nuclear Information System (INIS)

Kim, Sang Pyo; Schubert, Christian

2011-01-01

Using Lewis-Riesenfeld theory, we derive an exact nonadiabatic master equation describing the time evolution of the QED Schwinger pair-production rate for a general time-varying electric field. This equation can be written equivalently as a first-order matrix equation, as a Vlasov-type integral equation, or as a third-order differential equation. In the last version it relates to the Korteweg-de Vries equation, which allows us to construct an exact solution using the well-known one-soliton solution to that equation. The case of timelike delta function pulse fields is also briefly considered.

Phase diagram of two-color QCD in a Dyson-Schwinger approach

Energy Technology Data Exchange (ETDEWEB)

Buescher, Pascal Joachim

2014-04-28

We investigate two-color QCD with N{sub f}=2 at finite temperatures and chemical potentials using a Dyson-Schwinger approach. We employ two different truncations for the quark loop in the gluon DSE: one based on the Hard-Dense/Hard-Thermal Loop (HDTL) approximation of the quark loop and one based on the back-coupling of the full, self-consistent quark propagator (SCQL). We compare results for the different truncations with each other as well as with other approaches. As expected, we find a phase dominated by the condensation of quark-quark pairs. This diquark condensation phase overshadows the critical end point and first-order phase transition which one finds if diquark condensation is neglected. The phase transition from the phase without diquark condensation to the diquark-condensation phase is of second order. We observe that the dressing with massless quarks in the HDTL approximation leads to a significant violation of the Silver Blaze property and to a too small diquark condensate. The SCQL truncation, on the other hand, is found to reproduce all expected features of the μ-dependent quark condensates. Moreover, with parameters adapted to the situation in other approaches, we also find good to very good agreement with model and lattice calculations in all quark quantities. We find indictions that the physics in recent lattice calculations is likely to be driven solely by the explicit chiral symmetry breaking. Discrepancies w.r.t. the lattice are, however, observed in two quantities that are very sensitive to the screening of the gluon propagator, the dressed gluon propagator itself and the phase-transition line at high temperatures.

Integration of Schwinger equation for (φ* φ)d2 theory

International Nuclear Information System (INIS)

Rochev, V.E.

1993-01-01

A general solution for the Schwinger equation for the generating functional of the complex scalar field theory with (φ * φ) d 2 interaction has been constructed. The method is based on the reduction of the order of this equation using the particular solution

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

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

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)

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.

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.

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

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

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.

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

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...

Non-perturbative QCD and hadron physics

International Nuclear Information System (INIS)

Cobos-Martínez, J J

2016-01-01

A brief exposition of contemporary non-perturbative methods based on the Schwinger-Dyson (SDE) and Bethe-Salpeter equations (BSE) of Quantum Chromodynamics (QCD) and their application to hadron physics is given. These equations provide a non-perturbative continuum formulation of QCD and are a powerful and promising tool for the study of hadron physics. Results on some properties of hadrons based on this approach, with particular attention to the pion distribution amplitude, elastic, and transition electromagnetic form factors, and their comparison to experimental data are presented. (paper)

Low equation, pion-nucleon scattering, and Castillejo-Dalitz-Dyson pole

International Nuclear Information System (INIS)

Nakano, K.; Nogami, Y.

1986-01-01

We examine the p-wave πN scattering at medium energies by means of the Low equation with a view to determining the form factor of the πN interaction. Solutions of the equation with and without a Castillejo-Dalitz-Dyson (CDD) pole are used. The solution with no CDD pole corresponds to the old Chew-Low model, whereas the one with a CDD pole corresponds to the quark version of the Chew-Low model. The πN interaction form factor is determined so that the Δ resonance is well reproduced. We find that the solution with a CDD pole leads to a softer form factor but is not as soft as those expected from the nucleon size in the quark model. Using the solutions and form factors thus determined, we also examine the pionic contributions to the nucleon magnetic moment and the nucleon mass

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)

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.

Landau ghost pole problem in quantum field theory: From 50th of last century to the present day

Energy Technology Data Exchange (ETDEWEB)

Jafarov, Rauf G., E-mail: rauf-jafarov@hotmail.com [Institute for Physical Problems, Baku State University, Baku (Azerbaijan); Mutallimov, Mutallim M. [Institute of Applied Mathematics, Baku State University, Baku (Azerbaijan)

2016-03-25

In this paper we present our results of the investigation of asymptotical behavior of amplitude at short distances in four-dimensional scalar field theory with ϕ{sup 4} interaction. To formulate of our calculating model – two-particle approximation of the mean-field expansion we have used an Rochev’s iteration scheme of solution of the Schwinger-Dyson equations with the fermion bilocal source. We have considered the nonlinear integral equations in deep-inelastic region of momenta. As result we have a non-trivial behavior of amplitude at large momenta.

A New Comment on Dyson's Exposition of Feynman's Proof of Maxwell Equations

International Nuclear Information System (INIS)

Pombo, Claudia

2009-01-01

A paper by Dyson, published nearly two decades ago, describing Feynman's proof of Maxwell equations, has generated many comments, analysis, discussions and generalizations of the proof. Feynman's derivation is assumed to be based on two main sets of equations. One is supposed to be the second law of Newton and the other a set of basic commutation relations from quantum physics.Here we present a new comment on this paper, focusing mainly on the initial arguments and applying a new method of analysis and interpretation of physics, named observational realism. The present discussion does not alter the technical steps of Feynman, but do clarify their basis. We show that Newton's physics is not a starting point in Feynman's derivation, neither is quantum physics involved in it, but the foundations of relativity only.

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.)

Dyson shells: a retrospective

Science.gov (United States)

Bradbury, Robert J.

2001-08-01

More than 40 years have passed since Freeman Dyson suggested that advanced technological civilizations are likely to dismantle planets in their solar systems to harvest all of the energy their stars wastefully radiate into space. Clearly this was an idea that was ahead of its time. Since that time, dozens of SETI searches have been conducted and almost all of them have focused their attention on stars which by definition cannot be the advanced civilizations that Dyson envisioned. I will review the data that created the confusion between Dyson spheres and Dyson shells. The sources that disprove Dyson spheres while still allowing Dyson shells will be discussed. The use of outmoded ideas that have biased the few searches for Dyson Shells that have occurred will be pointed out. An update of the concept of Dyson shells to include our current knowledge of biotechnology, nanotechnology and computer science will be explored. Finally, an approach to setting limits on the abundance of Dyson shells in our galaxy using existing optical astronomical data and future optical satellites will be proposed.

Consistent method of truncating the electron self-energy in nonperturbative QED

International Nuclear Information System (INIS)

Rembiesa, P.

1986-01-01

A nonperturbative method of solving the Dyson-Schwinger equations for the fermion propagator is considered. The solution satisfies the Ward-Takahashi identity, allows multiplicative regularization, and exhibits a physical-mass pole

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.)

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.

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

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

Spectrum of Charmonia within a Contact Interaction

International Nuclear Information System (INIS)

Bedolla, Marco Antonio

2016-01-01

For the flavour-singlet heavy quark system of charmonia, we compute the masses of the ground state mesons in four different channels: pseudo-scalar (η c (1 S )), vector ( J /ψ(1 S )), scalar (χ s0 (1 P )) and axial vector (χ c1 (1 P )), as well as the weak decay constants of the η c (1S) and J/ψ(1 S ). The framework for this analysis is provided by a symmetry-preserving Schwinger- Dyson equation (SDEs) treatment of a vector x vector contact interaction (CI). The results found for the meson masses and the weak decay constants, for the spin-spin combinations studied, are in fairly good agreement with experimental data and earlier model calculations based upon Schwinger-Dyson and Bethe-Salpeter equations (BSEs) involving sophisticated interaction kernels. (paper)

Yang-Mills theory - a string theory in disguise

International Nuclear Information System (INIS)

Foerster, D.

1979-01-01

An examination of the Schwinger-Dyson equations of U(N) lattice Yang-Mills theory shows that this theory is exactly equivalent to a theory of strings that interact with one another only through their topology. (Auth.)

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

On the Coulomb gauge quark propagator

International Nuclear Information System (INIS)

Kloker, M.; Alkofer, R.; Krassnigg, A.; Krenn, R.

2006-01-01

Full text: A solution of the quark Dyson-Schwinger equation including transverse gluons is presented. The corresponding retardation effects in the quark propagator are discussed. Especially, their effects on confinement properties and dynamical mass generation are described. (author)

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.)

On the implications of confinement

International Nuclear Information System (INIS)

Roberts, C.D.

1992-01-01

In this paper, the authors consider some implications of confinement starting from the basic observation that cross-sections for the production of colored asymptotic states, such as free quarks and gluons, from color singlet initial states must be zero if QCD is to be confining. The authors discuss two pictures of confinement: the failure of the cluster decomposition property and the absence of a pole at timelike momenta in the propagator of a confined particle. The authors use QCD-based models as a framework to relate the failure of the cluster decomposition property to other ideas, such as the role of a nonzero gluon condensate. The authors' primary interest is to address the question of the absence of a mass pole through a study of model Schwinger-Dyson equations. These equations contain some of the dynamical information that is present in the study of the cluster decomposition property. The authors discuss the problems within this idea and its study using the Schwinger-Dyson equations

The quark Schwinger-Dyson equation in temporal Euclidean space

Czech Academy of Sciences Publication Activity Database

Šauli, Vladimír; Batiz, Z.

2009-01-01

Roč. 36, č. 3 (2009), 035002/1-035002/13 ISSN 0954-3899 Institutional research plan: CEZ:AV0Z10480505 Keywords : ANALYTIC PERTURBATION-THEORY * DYNAMICAL SYMMETRY-BREAKING * BACKGROUND FIELD METHOD Subject RIV: BE - Theoretical Physics Impact factor: 2.124, year: 2009

The Feynman-Dyson view

International Nuclear Information System (INIS)

Gill, Tepper L.

2017-01-01

This paper is a survey of our work on the mathematical foundations for the Feynman-Dyson program in quantum electrodynamics (QED). After a brief discussion of the history, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson’s second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman’s path integral, and to prove Dyson’s first conjecture that the divergences are in part due to a violation of Heisenberg’s uncertainly relations. As a by-product, we also prove Feynman’s conjecture about the relationship between the operator calculus and has path integral. Thus, providing the first rigorous justification for the Feynman formulation of quantum mechanics. (paper)

The Feynman-Dyson view

Science.gov (United States)

Gill, Tepper L.

2017-05-01

This paper is a survey of our work on the mathematical foundations for the Feynman-Dyson program in quantum electrodynamics (QED). After a brief discussion of the history, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson’s second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman’s path integral, and to prove Dyson’s first conjecture that the divergences are in part due to a violation of Heisenberg’s uncertainly relations. As a by-product, we also prove Feynman’s conjecture about the relationship between the operator calculus and has path integral. Thus, providing the first rigorous justification for the Feynman formulation of quantum mechanics.

Strong Coupling Continuum QCD

International Nuclear Information System (INIS)

Pennington, Michael

2011-01-01

The Schwinger-Dyson, Bethe-Salpeter system of equations are the link between coloured quarks and gluons, and colourless hadrons and their properties. This talk reviews some aspects of these studies from the infrared behavior of ghosts to the prediction of electromagnetic form-factors.

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.

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)

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

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

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

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.

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

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 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.

Chiral Schwinger model with the Faddeevian regularization in the light-front frame: construction of the gauge-invariant theory through the Stueckelberg term, Hamiltonian and BRST formulations

International Nuclear Information System (INIS)

Kulshreshtha, U.

1998-01-01

A chiral Schwinger model with the Faddeevian regularization a la Mitra is studied in the light-front frame. The front-form theory is found to be gauge-non-invariant. The Hamiltonian formulation of this gauge-non-invariant theory is first investigated and then the Stueckelberg term for this theory is constructed. Finally, the Hamiltonian and BRST formulations of the resulting gauge-invariant theory, obtained by the inclusion of the Stueckelberg term in the action of the above gauge-non-invariant theory, are investigated with some specific gauge choices. (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.

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

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)

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

Perspective on rainbow-ladder truncation

International Nuclear Information System (INIS)

Eichmann, G.; Alkofer, R.; Krassnigg, A.; Cloeet, I. C.; Roberts, C. D.

2008-01-01

Prima facie the systematic implementation of corrections to the rainbow-ladder truncation of QCD's Dyson-Schwinger equations will uniformly reduce in magnitude those calculated mass-dimensioned results for pseudoscalar and vector meson properties that are not tightly constrained by symmetries. The aim and interpretation of studies employing rainbow-ladder truncation are reconsidered in this light

Dynamical Symmetry Breaking in RN Quantum Gravity

Directory of Open Access Journals (Sweden)

A. T. Kotvytskiy

2011-01-01

Full Text Available We show that in the RN gravitation model, there is no dynamical symmetry breaking effect in the formalism of the Schwinger-Dyson equation (in flat background space-time. A general formula for the second variation of the gravitational action is obtained from the quantum corrections hμν (in arbitrary background metrics.

TOPICAL REVIEW: Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model

Science.gov (United States)

Meurice, Y.

2007-06-01

We review recent results concerning the renormalization group (RG) transformation of Dyson's hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice. We introduce the HM and show that its large group of symmetry simplifies drastically the blockspinning procedure. Several equivalent forms of the recursion formula are presented with unified notations. Rigourous and numerical results concerning the recursion formula are summarized. It is pointed out that the recursion formula of the HM is inequivalent to both Wilson's approximate recursion formula and Polchinski's equation in the local potential approximation (despite the very small difference with the exponents of the latter). We draw a comparison between the RG of the HM and functional RG equations in the local potential approximation. The construction of the linear and nonlinear scaling variables is discussed in an operational way. We describe the calculation of non-universal critical amplitudes in terms of the scaling variables of two fixed points. This question appears as a problem of interpolation between these fixed points. Universal amplitude ratios are calculated. We discuss the large-N limit and the complex singularities of the critical potential calculable in this limit. The interpolation between the HM and more conventional lattice models is presented as a symmetry breaking problem. We briefly introduce models with an approximate supersymmetry. One important goal of this review is to present a configuration space counterpart, suitable for lattice formulations, of functional RG equations formulated in momentum space (often called exact RG equations and abbreviated ERGE).

Systematic Equation Formulation

DEFF Research Database (Denmark)

Lindberg, Erik

2007-01-01

A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....

q-bar q condensate for light quarks beyond the chiral limit

International Nuclear Information System (INIS)

Williams, R.; Fischer, C.S.; Pennington, M.R.

2007-01-01

We determine the q-bar q condensate for quark masses from zero up to that of the strange quark within a phenomenologically successful modelling of continuum QCD by solving the quark Schwinger-Dyson equation. The existence of multiple solutions to this equation is the key to an accurate and reliable extraction of this condensate using the operator product expansion. We explain why alternative definitions fail to give the physical condensate

External gauge invariance and anomaly in BS vertices and boundstates

International Nuclear Information System (INIS)

Bando, Masako; Harada, Masayasu; Kugo, Taichiro

1994-01-01

A systematic method is given for obtaining consistent approximations to the Schwinger-Dyson (SD) and Bethe-Salpeter (BS) equations which maintain the external gauge invariance. We show that for any order of approximation to the SD equation there is a corresponding approximation to the BS equations such that the solutions to those equations satisfy the Ward-Takahashi identities of the external gauge symmetry. This formulation also clarifies the way how we can calculate the Green functions of current operators in a consistent manner with the gauge invariance and the axial anomaly. We show which type of diagrams for the π 0 → γγ amplitude using the pion BS amplitude give result consistent with the low-energy theorem. An interesting phenomenon is observed in the ladder approximation that the low-energy theorem is saturated by the zeroth order terms in the external momenta of the pseudoscalar BS amplitude and the vector vertex functions. (author)

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

Science.gov (United States)

Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So

2018-02-01

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

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

Chiral symmetry breaking in QED for weak coupling

Energy Technology Data Exchange (ETDEWEB)

Huang, J.C. (Missouri Univ., Columbia, MO (USA). Dept. of Physics and Astronomy); Shen, T.C. (Illinois Univ., Urbana, IL (USA). Beckman Inst.)

1991-05-01

We examine the procedure for studying chiral symmetry breaking for weak coupling in QED. We note that while the lowest non-trivial order calculations using numerical solutions to the Schwinger-Dyson equation indicate a breaking of chiral symmetry, the neglected higher-order contributions to the effective potential have imaginary values which can indicate possible instabilities in the theory. (author).

Chiral symmetry breaking in QED for weak coupling

International Nuclear Information System (INIS)

Huang, J.C.; Shen, T.C.

1991-01-01

We examine the procedure for studying chiral symmetry breaking for weak coupling in QED. We note that while the lowest non-trivial order calculations using numerical solutions to the Schwinger-Dyson equation indicate a breaking of chiral symmetry, the neglected higher-order contributions to the effective potential have imaginary values which can indicate possible instabilities in the theory. (author)

Dynamical breakdown of chiral symmetry in vectorial theories: QED and QCD

International Nuclear Information System (INIS)

Garcia, J.C.M.

1987-01-01

Using a variational approach for the Effective Potential for composite operators we dicuss the dynamical breakdown of chiral symmetry in two vectorial theories: Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD). We study the energetic aspects of the problem calculating the Effective Potential with the asymptotic nonperturbative solutions of the Schwinger-Dyson equation for the fermion selfenergy. (author) [pt

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.)

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

The Boltzmann equation in the difference formulation

Energy Technology Data Exchange (ETDEWEB)

Szoke, Abraham [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Brooks III, Eugene D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-05-06

First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

Nonperturbative infrared dynamics in three dimensional QED

International Nuclear Information System (INIS)

Gusynin, V.P.

2000-01-01

A non-linear Schwinger-Dyson (SD) equation for the gauge boson propagator of massless QED in 2 + 1 dimensions is studied. It is shown that the nonperturbative solution leads to a non-trivial renormalization-group infrared fixed point quantitatively close to the one found in the leading order of the 1/N expansion, with N the number of fermion flavors

Dynamical Mass Generation and Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics

International Nuclear Information System (INIS)

Sanchez Madrigal, S; Raya, A; Hofmann, C P

2011-01-01

We study the non-perturbative phenomena of Dynamical Mass Generation and Confinement by truncating at the non-perturbative level the Schwinger-Dyson equations in Maxwell-Chern-Simons planar quantum electrodynamics. We obtain numerical solutions for the fermion propagator in Landau gauge within the so-called rainbow approximation. A comparison with the ordinary theory without the Chern-Simons term is presented.

On the large-N dynamics of gauge symmetry breaking

International Nuclear Information System (INIS)

Karchev, N.I.

1983-07-01

We consider a Gsub(W)xUsub(TC)(N) gauge theory. A method of colour singlet bilocal collective coordinates is proposed to show, large-N colour dynamics is responsible for the Gsub(W) gauge symmetry breaking if the large-N Schwinger-Dyson equation admits anomalous solutions. The dynamically generated mass matrix is computed through these solutions. The technicolour model is discussed. (author)

Two-Quark Condensate Changes with Quark Current Mass

International Nuclear Information System (INIS)

Lu Changfang; Lue Xiaofu; Wu Xiaohua; Zhan Yongxin

2009-01-01

Using the Schwinger-Dyson equation and perturbation theory, we calculate the two-quark condensates for the light quarks u, d, strange quark s and a heavy quark c with their current masses respectively. The results show that the two-quark condensate will decrease when the quark mass increases, which hints the chiral symmetry may be restored for the heavy quarks.

Non-ladder extended renormalization group analysis of the dynamical chiral symmetry breaking

Energy Technology Data Exchange (ETDEWEB)

Aoki, Ken-Ichi; Takagi, Kaoru; Terao, Haruhiko; Tomoyose, Masashi [Kanazawa Univ., Inst. for Theoretical Physics, Kanazawa, Ishikawa (Japan)

2000-04-01

The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the non-perturbative renormalization group (NPRG) equations. We employ an approximation scheme beyond 'the ladder', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced in comparison with the ladder approximation, which is phenomenologically favorable. The gauge dependence of the order parameters is reduced significantly in this scheme. (author)

Non-ladder extended renormalization group analysis of the dynamical chiral symmetry breaking

International Nuclear Information System (INIS)

Aoki, Ken-Ichi; Takagi, Kaoru; Terao, Haruhiko; Tomoyose, Masashi

2000-01-01

The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the non-perturbative renormalization group (NPRG) equations. We employ an approximation scheme beyond 'the ladder', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced in comparison with the ladder approximation, which is phenomenologically favorable. The gauge dependence of the order parameters is reduced significantly in this scheme. (author)

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 Greenian approach to the solution of the Schroedinger equation for periodic lattice potentials

International Nuclear Information System (INIS)

Minelli, T.A.

1976-01-01

A modified structural Green's function (MSGF), exploiting all the information contained in the previously solved Schroedinger equation for the electron interacting with a single lattice site, has been introduced and used in order to obtain, from a Dyson-type equation, a kernel whose poles and residues give the E-vs.-k relation and, respectively, the Bloch functions. Such a formulation suggests an alternative technique for the approximate solution of the KKR equations. The MSGF formalism has been also used in order to determine the structure constants of a one-dimensional lattice in a general representation

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

Freezing of the QCD coupling constant and the pion form factor

International Nuclear Information System (INIS)

Aguilar, A.C.; Mihara, A.; Natale, A.A.

2003-01-01

The possibility that the QCD coupling constant (α s ) has an infrared finite behavior (freezing) has been extensively studied in recent years. We compare phenomenological values of the 'frozen' the QCD running coupling between different classes of solutions obtained through non-perturbative Schwinger-Dyson Equations. With these solutions were computed QCD predictions for the asymptotic pion form factor which, in turn, were compared with experiment. (author)

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.)

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

Two-photon processes of π0, η, η', ηc and ηb

International Nuclear Information System (INIS)

Klabucar, D.

1997-01-01

Two-photon processes of π 0 , η, η', η c and η b are studied in the consistently coupled Schwinger-Dyson (SD) and Bethe-Salpeter (BS) approach, where dynamical chiral symmetry breaking (DχSB) is obtained through the SD equation for the quark propagator which is then used in the BS equation. It is shown that the coupled SD-BS approach is similarly successful in the description of two-photon processes of pseudoscalar mesons over a wide range of masses. (K.A.)

Contribution from the interaction Hamiltonian to the expectation value of particle number with the non-equilibrium quantum field theory

International Nuclear Information System (INIS)

Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki

2012-01-01

We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.

Covariance dynamics and symmetries, and hadron form factors

International Nuclear Information System (INIS)

Bhagwat, M.S.; Cloet, I.C.; Roberts, C.D.

2007-01-01

We summarize applications of Dyson-Schwinger equations to the theory and phenomenology of hadrons. Some exact results for pseudoscalar mesons are highlighted with details relating to the U A (1) problem. We describe inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass. We recapitulate upon studies of nucleon electromagnetic form factors, providing a comparison of the ln-weighted ratios of Pauli and Dirac form factors for the neutron and proton.

Maverick genius the pioneering odyssey of Freeman Dyson

CERN Document Server

Schewe, Phillip F

2013-01-01

Scientist. Innovator. Rebel. For decades, Freeman Dyson has been regarded as one of the world’s most important thinkers. The Atlantic wrote, “In the range of his genius, Freeman Dyson is heir to Einstein – a visionary who has reshaped thinking in fields from math to astrophysics to medicine, and who has conceived nuclear-propelled spaceships designed to transport human colonists to distance planets.” Salon.com says that, “what sets Dyson apart among an elite group of scientists is the conscience and compassion he brings to his work.” Now, in this first complete biography of Dyson, author Phillip F. Schewe examines the life of a man whose accomplishments have shaped our world in many ways. From quantum physics to national defense, from space to biotechnology, Dyson’s work has cemented his position as a man whose influence goes far beyond the field of theoretical physics. It even won him the million dollar Templeton prize for his writing about science and religion. Recently, Dyson has made head...

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)

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)

Photon propagator and pair production in stationary electric field

International Nuclear Information System (INIS)

Makhlin, A.N.; Olejnik, V.P.

1978-01-01

Effects related to pair production by an external field are discussed. It is shown that vacuum instability against pair production leads to an essential difference between the propagator and Feynman Green's function. Analysis of Yang-Feldman equations and of boundary conditions imposed upon the Green's function shows that using Feynman Green's function as a propagator contradicts the causality principle. The physical causality principle is satisfied by Heisenberg Green's function for which usual Schwinger-Dyson equations cannot be formulated. Heisenberg and Feynman Green's functions coincide for the case of stable vacuum state. All calculations are carried out using the technique of the so-called generalized Green's functions in terms of which the propagators are written. The polarization operator in the electric field is calculated in the one-loop approximation. Its' general structure is found. The photon propagator is obtained. Self oscillations of the photon vacuum are determined. It is shown that new modes correspond to collective excitations of the type ''photon+electron-positron pairs''

A new formulation of equations of compressible fluids by analogy with Maxwell's equations

International Nuclear Information System (INIS)

Kambe, Tsutomu

2010-01-01

A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.

Research in theoretical particle physics

International Nuclear Information System (INIS)

McKay, D.W.; Munczek, H.; Ralston, J.

1992-05-01

This report discusses the following topics in high energy physics: dynamical symmetry breaking and Schwinger-Dyson equation; consistency bound on the minimal model Higgs mass; tests of physics beyond the standard model; particle astrophysics; the interface between perturbative and non-perturbative QCD; cosmology; anisotropy in quantum networks and integer quantum hall behavior; anomalous color transparency; quantum treatment of solitons; color transparency; quantum stabilization of skyrmions; and casimir effect

Crowdfunding isn’t just about money Mr Dyson

OpenAIRE

Cox, Joe

2014-01-01

Serial entrepreneur and inventor James Dyson has spoken out against crowdfunding, arguing that the emerging trend is no good for supporting meaningful inventions. However, Dyson may have overlooked some of the benefits to inventors besides simply raising cash.

Nonperturbative quantum electrodynamics in a photon-condensate background field

International Nuclear Information System (INIS)

Kikuchi, Y.; Ng, Y.J.

1988-01-01

Analyses of the Schwinger-Dyson (SD) equation for the fermion self-energy have revealed the existence of a QED ultraviolet nonperturbative fixed point which separates a strong-coupling regime from a weak-coupling regime. Here we study the SD equation in the presence of a weak constant photon-condensate background field. This background field does not seem to affect the fixed point. Better approximations or some more realistic background fields may change the result. The investigation is partly motivated by recent heavy-ion experiments

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)

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

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).

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

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)

Quantum fields and processes a combinatorial approach

CERN Document Server

Gough, John

2018-01-01

Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson-Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom-Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson-Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathematical physicists, quant...

{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

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.)

Properties of the vacuum in models for QCD. Holography vs. resummed field theory. A comparative study

Energy Technology Data Exchange (ETDEWEB)

Zayakin, Andrey V.

2011-01-17

This Thesis is dedicated to a comparison of the two means of studying the electromagnetic properties of the QCD vacuum - holography and resummed field theory. I compare two classes of distinct models for the dynamics of the condensates. The first class consists of the so-called holographic models of QCD. Based upon the Maldacena conjecture, it tries to establish the properties of QCD correlation functions from the behavior of classical solutions of field equations in a higher-dimensional theory. Yet in many aspects the holographic approach has been found to be in an excellent agreement with data. These successes are the prediction of the very small viscosity-to-entropy ratio and the predictions of meson spectra up to 5% accuracy in several models. On the other hand, the resummation methods in field theory have not been discarded so far. Both classes of methods have access to condensates. Thus a comprehensive study of condensates becomes possible, in which I compare my calculations in holography and resummed field theory with each other, as well as with lattice results, field theory and experiment. I prove that the low-energy theorems of QCD keep their validity in holographic models with a gluon condensate in a non-trivial way. I also show that the so-called decoupling relation holds in holography models with chiral and gluon condensates, whereas this relation fails in the Dyson-Schwinger approach. On the contrary, my results on the chiral magnetic effect in holography disagree with the weak-field prediction; the chiral magnetic effect (that is, the electric current generation in a magnetic field) is three times less than the current in the weakly-coupled QCD. The chiral condensate behavior is found to be quadratic in external field both in the Dyson-Schwinger approach and in holography, yet we know that in the exact limit the condensate must be linear, thus both classes of models are concluded to be deficient for establishing the correct condensate behaviour in the

Properties of the vacuum in models for QCD. Holography vs. resummed field theory. A comparative study

International Nuclear Information System (INIS)

Zayakin, Andrey V.

2011-01-01

This Thesis is dedicated to a comparison of the two means of studying the electromagnetic properties of the QCD vacuum - holography and resummed field theory. I compare two classes of distinct models for the dynamics of the condensates. The first class consists of the so-called holographic models of QCD. Based upon the Maldacena conjecture, it tries to establish the properties of QCD correlation functions from the behavior of classical solutions of field equations in a higher-dimensional theory. Yet in many aspects the holographic approach has been found to be in an excellent agreement with data. These successes are the prediction of the very small viscosity-to-entropy ratio and the predictions of meson spectra up to 5% accuracy in several models. On the other hand, the resummation methods in field theory have not been discarded so far. Both classes of methods have access to condensates. Thus a comprehensive study of condensates becomes possible, in which I compare my calculations in holography and resummed field theory with each other, as well as with lattice results, field theory and experiment. I prove that the low-energy theorems of QCD keep their validity in holographic models with a gluon condensate in a non-trivial way. I also show that the so-called decoupling relation holds in holography models with chiral and gluon condensates, whereas this relation fails in the Dyson-Schwinger approach. On the contrary, my results on the chiral magnetic effect in holography disagree with the weak-field prediction; the chiral magnetic effect (that is, the electric current generation in a magnetic field) is three times less than the current in the weakly-coupled QCD. The chiral condensate behavior is found to be quadratic in external field both in the Dyson-Schwinger approach and in holography, yet we know that in the exact limit the condensate must be linear, thus both classes of models are concluded to be deficient for establishing the correct condensate behaviour in the

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

Aspects of open-flavour mesons in a comprehensive DSBSE study

Energy Technology Data Exchange (ETDEWEB)

Hilger, T. [University of Graz, NAWI Graz, Institute of Physics, Graz (Austria); Austrian Academy of Sciences, Institute of High Energy Physics, Vienna (Austria); Gomez-Rocha, M. [ECT*, Villazzano (Trento) (Italy); Krassnigg, A. [University of Graz, NAWI Graz, Institute of Physics, Graz (Austria); Lucha, W. [Austrian Academy of Sciences, Institute of High Energy Physics, Vienna (Austria)

2017-10-15

Open-flavour meson studies are the necessary completion to any comprehensive investigation of quarkonia. We extend recent studies of quarkonia in the Dyson-Schwinger-Bethe-Salpeter equation approach to explore their results for all possible flavour combinations. Within the inherent limitations of the setup, we present the most comprehensive results for meson masses and leptonic decay constants currently available and put them in perspective with respect to experiment and other approaches. (orig.)

The infrared behaviour of the running coupling in Landau gauge QCD

International Nuclear Information System (INIS)

Alkofer, R.; Fischer, C.S.; Smekal, L. von.

2002-01-01

Approximate solutions for the gluon and ghost propagators as well as the running coupling in Landau gauge Yang-Mills theories are presented. These propagators obtained from the corresponding Dyson-Schwinger equations are in remarkable agreement with those of recent lattice calculations. The resulting running coupling possesses an infrared fixed point, α s (0) = 8.92/N for all gauge SU(N). Above one GeV the running coupling rapidly approaches its perturbative form (Authors)

Topics on field theories at finite temperature

International Nuclear Information System (INIS)

Eboli, O.J.P.

1985-01-01

The dynamics of a first order phase transition through the study of the decay rate of the false vacuum in the high temperature limit are analysed. An alternative approach to obtain the phase diagram of a field theory which is based on the study of the free energy of topological defects, is developed the behavior of coupling constants with the help of the Dyson-Schwinger equations at finite temperature, is evaluated. (author) [pt

Zero field Quantum Hall Effect in QED3

International Nuclear Information System (INIS)

Raya, K; Sánchez-Madrigal, S; Raya, A

2013-01-01

We study analytic structure of the fermion propagator in the Quantum Electrodynamics in 2+1 dimensions (QED3) in the Landau gauge, both in perturbation theory and nonperturbatively, by solving the corresponding Schwinger-Dyson equation in rainbow approximation. In the chiral limit, we found many nodal solutions, which could be interpreted as vacuum excitations. Armed with these solutions, we use the Kubo formula and calculate the filling factor for the zero field Quantum Hall Effect

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

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.

Elliptic Determinantal Processes and Elliptic Dyson Models

Science.gov (United States)

Katori, Makoto

2017-10-01

We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single function called the spatio-temporal correlation kernel. For the four families {A}_{N-1}, {B}_N, {C}_N and {D}_N, we identify the systems of stochastic differential equations solved by these determinantal processes, which will be regarded as the elliptic extensions of the Dyson model. Here we use the notion of martingales in probability theory and the elliptic determinant evaluations of the Macdonald denominators of irreducible reduced affine root systems given by Rosengren and Schlosser.

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

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

TECHNOS Interview: Esther Dyson.

Science.gov (United States)

Raney, Mardell

1997-01-01

This interview with Esther Dyson, who is president and owner of EDventure Holdings which focuses on emerging information technology worldwide, discusses personal responsibility for technology; government's role; content ownership and intellectual property; Internet development; education and computers; parents' role in education; teacher…

Matsubara-Fradkin thermodynamical quantization of Podolsky electrodynamics

International Nuclear Information System (INIS)

Bonin, C. A.; Pimentel, B. M.

2011-01-01

In this work, we apply the Matsubara-Fradkin formalism and the Nakanishi's auxiliary field method to the quantization of the Podolsky electrodynamics in thermodynamic equilibrium. This approach allows us to write consistently the path integral representation for the partition function of gauge theories in a simple manner. Furthermore, we find the Dyson-Schwinger-Fradkin equations and the Ward-Fradkin-Takahashi identities for the Podolsky theory. We also write the most general form for the polarization tensor in thermodynamic equilibrium.

The chiral Ward-Takahashi identity in the ladder approximation

International Nuclear Information System (INIS)

Kugo, Taichiro; Mitchard, M.G.

1992-01-01

We show that the ladder approximation to the Schwinger-Dyson and Bethe-Salpeter equations preserves the Ward-Takahashi identity for the axial vector vertex if and only if we use the gluon momentum as the argument of the running coupling constant. However, in the usual Landau gauge this is inconsistent with the vector Ward identity. We propose a new method for making the ladder approximation scheme consistent with both vector and axial vector Ward identities. (orig.)

Solutions of the Low equation in the no-crossing approximation

International Nuclear Information System (INIS)

Kumar, K.S.; Nogami, Y.

1979-01-01

In solving the Low equation for the Chew-Low model, if the crossing term is dropped a ghost state appears in the repulsive channels for a sufficiently large coupling constant. Ernst et al. suggested recently that this difficulty could be avoided by adopting a solution with a Castillejo-Dalitz-Dyson (CDD) pole in its denominator. Contrary to this suggestion, we show that the inclusion of the CDD pole, rather than avoiding the difficulty, only compounds it. We also reexamine Dyson's interpretation of the ''redundant'' CDD solutions, and point out that the Low equation we study possesses solutions to which Dyson's interpretation does not seem to apply

On the nonperturbative foundations of the dipole picture

Energy Technology Data Exchange (ETDEWEB)

Ewerz, C. [Milano Univ., INFN, Dipt. di Fisica (Italy); ECT, Villazzano (Trento) (Italy); Nachtmannc, B.O. [Heidelberg Univ., Institut fur Theoretische Physik (Germany)

2005-07-01

Starting from a completely non-perturbative formulation of photon-proton scattering we have identified the assumptions and approximations that are needed in order to obtain the dipole picture at high energies. At the same time we have found corrections to the dipole picture which can become large at small photon virtualities. We consider it as an important task for the future to investigate in detail the validity of the assumptions, the accuracy of the approximations, and the size of the corrections. In our opinion these issues should be addressed in order to put the results obtained in the framework of the dipole picture on solid ground. The framework developed here should be suitable for studying the effects caused by the non-existence of a mass-shell for quarks, and for using non-perturbative quark propagators, obtained for example from Dyson-Schwinger equations or from lattice simulations.

Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach

Energy Technology Data Exchange (ETDEWEB)

Hilger, T.; Krassnigg, A. [University of Graz, NAWI Graz, Institute of Physics, Graz (Austria); Gomez-Rocha, M. [ECT*, Villazzano, Trento (Italy)

2017-09-15

We investigate the light-quarkonium spectrum using a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach to QCD. We discuss splittings among as well as orbital angular momentum properties of various states in detail and analyze common features of mass splittings with regard to properties of the effective interaction. In particular, we predict the mass of anti ss exotic 1{sup -+} states, and identify orbital angular momentum content in the excitations of the ρ meson. Comparing our covariant model results, the ρ and its second excitation being predominantly S-wave, the first excitation being predominantly D-wave, to corresponding conflicting lattice-QCD studies, we investigate the pion-mass dependence of the orbital-angular-momentum assignment and find a crossing at a scale of m{sub π} ∝ 1.4 GeV. If this crossing turns out to be a feature of the spectrum generated by lattice-QCD studies as well, it may reconcile the different results, since they have been obtained at different values of m{sub π}. (orig.)

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

Dear Professor Dyson twenty years of correspondence between Freeman Dyson and undergraduate students on science, technology, society and life

CERN Document Server

Neuenschwander, Dwight E

2016-01-01

Freeman Dyson has designed nuclear reactors and bomb-powered spacecraft; he has studied the origins of life and the possibilities for the long-term future; he showed quantum mechanics to be consistent with electrodynamics and started cosmological eschatology; he has won international recognition for his work in science and for his work in reconciling science to religion; he has advised generals and congressional committees. An STS (Science, Technology, Society) curriculum or discussion group that engages topics such as nuclear policies, genetic technologies, environmental sustainability, the role of religion in a scientific society, and a hard look towards the future, would count itself privileged to include Professor Dyson as a class participant and mentor. In this book, STS topics are not discussed as objectified abstractions, but through personal stories. The reader is invited to observe Dyson's influence on a generation of young people as they wrestle with issues of science, technology, society, life in g...

Two- and three dimensional electrons and photons and their supersymmetric partners

International Nuclear Information System (INIS)

Steringa, J.J.

1989-01-01

This thesis contains a study of supersymmetric gauge theories in two and tree spacetime dimensions. Supersymmetric gauge theories in less than four spacetime dimensions are useful for trying out field theoretical methods which ultimately will be applied to realistic models. In ch. 1 all the aspects of field theory that are necessary for later chapters are treated. In ch. 2 sypersymmetry in two- and three-dimensional space time is treated, and superfields and superspace techniques are introduced. With these a simple Abelian supersymmetric gauge theory in two spacetime dimensions is constructed, the Schwinger model. Ch. 3 deals with general properties and a perturbative analysis of the model. Ch. 4 contains a non-perturbative analysis by means of Dyson-Schwinger equations. A supersummetric extension of theSalam-Delbourgo Gauge Technique is presented and is applied with some seccess to the supersymmetric Schwinger model. In ch. 5 prperties of three-dimensional supersymmetric gauge theories are investigated. (author). 55 refs.; 7 figs.; schemes

A supersymmetric SYK-like tensor model

Energy Technology Data Exchange (ETDEWEB)

Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence, RI, 02912 (United States)

2017-05-11

We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.

Scale solutions and coupling constant in electrodynamics of vector particles

International Nuclear Information System (INIS)

Arbuzov, B.A.; Boos, E.E.; Kurennoy, S.S.

1980-01-01

A new approach in nonrenormalizable gauge theories is studied, the electrodynamics of vector particles being taken as an example. One and two-loop approximations in Schwinger-Dyson set of equations are considered with account for conditions imposed by gauge invariance. It is shown, that solutions with scale asymptotics can occur in this case but only for a particular value of coupling constant. This value in solutions obtained is close to the value of the fine structure constant α=1/137

A supersymmetric SYK-like tensor model

International Nuclear Information System (INIS)

Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia

2017-01-01

We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.

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.

Unified formulation of radiation conditions for the wave equation

DEFF Research Database (Denmark)

Krenk, Steen

2002-01-01

A family of radiation conditions for the wave equation is derived by truncating a rational function approxiamtion of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second......-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choice of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms...

Dyson Orbitals, Quasi-Particle effects and Compton scattering

OpenAIRE

Barbiellini, B.; Bansil, A.

2004-01-01

Dyson orbitals play an important role in understanding quasi-particle effects in the correlated ground state of a many-particle system and are relevant for describing the Compton scattering cross section beyond the frameworks of the impulse approximation (IA) and the independent particle model (IPM). Here we discuss corrections to the Kohn-Sham energies due to quasi-particle effects in terms of Dyson orbitals and obtain a relatively simple local form of the exchange-correlation energy. Illust...

Towards a nonpotential scattering theory

International Nuclear Information System (INIS)

Mignani, R.

1985-01-01

We present a formal approach to nonpotential scattering theory (i.e. scattering under unrestricted nonlocal non-Hamiltonian forces), based on the generalization of the concept of scattering matrix (and related topics) to the Lie-isotopic and Lie-admissible case. In the time-dependent formalism, the main taks is the determination of the evolution operator, from which the S matrix is found as a double infinite limit. The study of time-development operators is carried out in detail in the isotopic case, and involves the isotopic generalizations of Moller wave operators, in- and out-states, and temporal (retarded and advanced) propagators. We give also expansion techniques for the S matrix, which extend to the Lie-isotopic formulation the Feynman-Dyson perturbation series, the Magnus expansion, and the Wei-Norman theorem. In the time-independent approach, we solve the isotopic Schroedinger eigenvalue equation by exploiting the properties of isotopic Green operators, Lippmann-Schwinger equations, and incoming and outgoing states, which turn out to be suitable generalizations of the conventional ones. The changes in cross sections due to nonpotential forces are explicitly worked out in some simple cases. A purely algebraic approach to nonpotential scattering, essentially based on the properties of the isowave operators, is presented. The Lie-admissible formulation of the main results is briefly outlined

Improved Dyson series expansion for steady-state quantum transport beyond the weak coupling limit: Divergences and resolution

International Nuclear Information System (INIS)

Thingna, Juzar; Zhou, Hangbo; Wang, Jian-Sheng

2014-01-01

We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process

On fictitious domain formulations for Maxwell's equations

DEFF Research Database (Denmark)

Dahmen, W.; Jensen, Torben Klint; Urban, K.

2003-01-01

We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Omega) derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic formu...

Gauge-invariant Yang-Mills fields and the role of Lorentz gauge condition

International Nuclear Information System (INIS)

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

1985-01-01

A new class of gauge-invariant (G.I.) fields is constructed. The inversion formulae that express these fields through the G.I. strength tensor are obtained. It is shown that for the G.I. fields the Lorentz gauge condition appears as the secondary constraint. These fields coincide with the usual ones in some definite gauges. The Dyson-Schwinger equations for the G.I. spinor propagator are derived. It is found that in QED this propagator has a simple pole singularity (p-m) -1 in the infrared limit

Confinement, diquarks and goldstone's theorem

International Nuclear Information System (INIS)

Roberts, C.D.

1996-01-01

Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavor-octet axial- vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone's theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD N c =2 , where the color singlet diquark is the ''baryon'' of the theory

Scalar-vector unitarity mixing in ξ gauge

International Nuclear Information System (INIS)

Kaloshin, A.E.; Radzhabov, A.E.

2003-01-01

The effect of unitary mixing of scalar and vector fields in general ξ gauge is studied. This effect takes place for nonconserved vector currents and ξ gauge generates some additional problems with unphysical scalar field. Solutions of Dyson-Schwinger equations and performed the renormalization of full propagators are obtained. The key feature of renormalization is the usage of Ward identity which relates some different Green functions. It is found that using of Ward identity leads to disappearing of ξ dependence in renormalization matrix element [ru

Fermion condensate and vacuum current density induced by homogeneous and inhomogeneous magnetic fields in (2+1) dimensions

International Nuclear Information System (INIS)

Raya, Alfredo; Reyes, Edward

2010-01-01

We calculate the condensate and the vacuum current density induced by external static magnetic fields in (2+1) dimensions. At the perturbative level, we consider an exponentially decaying magnetic field along one Cartesian coordinate. Nonperturbatively, we obtain the fermion propagator in the presence of a uniform magnetic field by solving the Schwinger-Dyson equation in the rainbow-ladder approximation. In the large flux limit, we observe that both these quantities, either perturbative (inhomogeneous) and nonperturbative (homogeneous), are proportional to the external field, in agreement with early expectations.

Confinement, Chiral Symmetry Breaking and it's Restoration using Dual QCD Formalism

Directory of Open Access Journals (Sweden)

Punetha Garima

2018-01-01

Full Text Available Utilizing the dual QCD model in term of magnetic symmetry structure of non- Abelian gauge theories, the dynamical chiral-symmetry breaking using Schwinger-Dyson equation has been investigated. A close relation among the color confinement and chiralsymmetry breaking has been observed and demonstrated by computing dynamical parameters. The recovery of the chiral symmetry has also been discussed at finite temperature through the variation of quark mass function and quark condensate which gradually decreases with temperature and vanishes suddenly near the critical temperature.

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 ...

A momentum-space formulation without partial wave decomposition for scattering of two spin-half particles

Energy Technology Data Exchange (ETDEWEB)

Fachruddin, Imam, E-mail: imam.fachruddin@sci.ui.ac.id; Salam, Agus [Departemen Fisika, Universitas Indonesia, Depok 16424 (Indonesia)

2016-03-11

A new momentum-space formulation for scattering of two spin-half particles, both either identical or unidentical, is formulated. As basis states the free linear-momentum states are not expanded into the angular-momentum states, the system’s spin states are described by the product of the spin states of the two particles, and the system’s isospin states by the total isospin states of the two particles. We evaluate the Lippmann-Schwinger equations for the T-matrix elements in these basis states. The azimuthal behavior of the potential and of the T-matrix elements leads to a set of coupled integral equations for the T-matrix elements in two variables only, which are the magnitude of the relative momentum and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved. A set of six spin operators to express any interaction of two spin-half particles is introduced. We show the spin-averaged differential cross section as being calculated in terms of the solution of the set of the integral equations.

The effective action approach applied to nuclear matter (1)

International Nuclear Information System (INIS)

Tran Huu Phat; Nguyen Tuan Anh.

1996-11-01

Within the framework of the Walecka model (QHD-I) the application of the Cornwall-Jackiw-Tomboulis (CJT) effective action to nuclear matter is presented. The main feature is the treating of the meson condensates for the system of finite nuclear density. The system of couple Schwinger-Dyson (SD) equations is derived. It is shown that SD equations for sigma-omega mixings are absent in this formalism. Instead, the energy density of the nuclear ground state does explicitly contain the contributions from the ring diagrams, amongst others. In the bare-vertex approximation, the expression for energy density is written down for numerical computation in the next paper. (author). 14 refs, 3 figs

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.

New formulation of Hardin-Pope equations for aeroacoustics

DEFF Research Database (Denmark)

Ekaterinaris, J.A.

1999-01-01

Dynamics, Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed information about the unsteady aerodynamic flowfield, which usually is obtained from a computational fluid dynamics solution. A new, conservative formulation of the equations governing acoustic disturbances is presented....... The conservative form of the governing equations is obtained after application of a transformation of variables that produces a set of inhomogeneous equations similar to the conservation-law form of the compressible Euler equations. The source term of these equations depends only on the derivatives...... of the hydrodynamic variables. Explicit time marching is performed. A high-order accurate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-biased formulas and flux-vector splitting. Solutions are obtained for the acoustic...

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

Rainbow tensor model with enhanced symmetry and extreme melonic dominance

Science.gov (United States)

Itoyama, H.; Mironov, A.; Morozov, A.

2017-08-01

We introduce and briefly analyze the rainbow tensor model where all planar diagrams are melonic. This leads to considerable simplification of the large N limit as compared to that of the matrix model: in particular, what are dressed in this limit are propagators only, which leads to an oversimplified closed set of Schwinger-Dyson equations for multi-point correlators. We briefly touch upon the Ward identities, the substitute of the spectral curve and the AMM/EO topological recursion and their possible connections to Connes-Kreimer theory and forest formulas.

Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory

International Nuclear Information System (INIS)

Watson, Peter; Alkofer, Reinhard

2001-01-01

Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mills theory

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.

Lagrangian vector field and Lagrangian formulation of partial differential equations

Directory of Open Access Journals (Sweden)

M.Chen

2005-01-01

Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.

The thermal coupling constant and the gap equation in the λ φ 4D model

International Nuclear Information System (INIS)

Ananos, G.N.J.; Malbouisson, A.P.C.; Svaiter, N.F.

1998-05-01

By the concurrent use of two different resummation methods, the composite operator formalism and the Dyson-Schwinger equation, we re-examine the behaviour at finite temperature of the O(N)-symmetric λψ 4 model in a generic D-dimensional Euclidean space. In the cases D = 3 and D = 4, an analysis of the thermal behaviour of the renormalized squared mass and coupling constant are done for all temperatures. It results that the thermal renormalized squared mass is positive and increases monotonically with the temperature. The behavior of the thermal coupling constant is quite different in odd or even dimensional space. In D = 3, the thermal coupling constant decreases up to a minimum value different from zero and ten grows up monotonically as the temperature increases. In the case D = 4, it is found that the thermal renormalized coupling constant tends in the high temperature limit to a constant asymptotic value. Also for general D-dimensional Euclidean space, we are able to obtain a formula for the critical temperature of the second order phase transition. This formula agrees with previous known values at D = 3 and D 4. (author)

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

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.)

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.

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.

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)

Variational formulation and projectional methods for the second order transport equation

International Nuclear Information System (INIS)

Borysiewicz, M.; Stankiewicz, R.

1979-01-01

Herein the variational problem for a second-order boundary value problem for the neutron transport equation is formulated. The projectional methods solving the problem are examined. The approach is compared with that based on the original untransformed form of the neutron transport equation

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

New Formulation of the Governing Equations for Analyzing Outrigger Structures

International Nuclear Information System (INIS)

Er, G.-K.

2010-01-01

In this paper, an easily comprehensible solution procedure is proposed for the analysis of outrigger-braced structures. The idea is based on the compatibility of the columns' axial deformation. The unknowns are selected to be the axial forces in the columns. The resulted governing equations and the equations for the optimum analysis of the outrigger locations are different from the conventional ones, but numerical analysis shows that the results obtained with the new equations are same as those obtained with conventional equations. The relations between the new equations and the conventional ones are also figured out. The new procedure of formulating the governing equations can be easily extended to more complicated cases of outrigger-braced structures.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

Science.gov (United States)

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

Mean-value identities as an opportunity for Monte Carlo error reduction.

Science.gov (United States)

Fernandez, L A; Martin-Mayor, V

2009-05-01

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the two-dimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

Quark virtuality and QCD vacuum condensates

International Nuclear Information System (INIS)

Zhou Lijuan; Ma Weixing

2004-01-01

Based on the Dyson-Schwinger equations (DSEs) in the 'rainbow' approximation, the authors investigate the quark virtuality in the vacuum state and quantum-chromodynamics (QCD) vacuum condensates. In particular, authors calculate the local quark vacuum condensate and quark-gluon mixed condensates, and then the virtuality of quark. The calculated quark virtualities are λ u,d 2 =0.7 GeV 2 for u, d quarks, and λ s 2 =1.6 GeV 2 for s quark. The theoretical predictions are consistent with empirical values used in QCD sum rules, and also fit to lattice QCD predictions

Symmetry Relations and the Nonperturbative Form of Interactions

Institute of Scientific and Technical Information of China (English)

2001-01-01

Applying QCD to study and understand hadronic physics and nuclear physics is one of basic goals of modern nuclear physics. Developing nonperturbative approach of QCD to understand the dynamical chiral-symmetry breaking and color confinement then becomes one of our most important challenges. Besides the lattice gauge theory, the Dyson-Schwinger equation (DSE) formalism is such an appropriate nonperturbative approach. In undertaking nonperturbative studies using DSEs, we immediately have to confront the issue of what is the nonperturbative form of interactions. In recent 20 years, there have been considerable efforts to solve this open problem, however, all such attempts

Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD

International Nuclear Information System (INIS)

von Smekal, L.; Hauck, A.; Alkofer, R.

1997-01-01

A truncation scheme for the Dyson-Schwinger equations of Euclidean QCD in Landau gauge is presented. It implements the Slavnov-Taylor identities for the three-gluon and ghost-gluon vertices, whereas irreducible four-gluon couplings as well as the gluon-ghost and ghost-ghost scattering kernels are neglected. The infrared behavior of gluon and ghost propagators is obtained analytically: The gluon propagator vanishes for small momenta, whereas the ghost propagator diverges strongly. The numerical solutions are compared with recent lattice results. The running coupling approaches a fixed point, α c ≅9.5 , in the infrared. copyright 1997 The American Physical Society

Infrared finite ghost propagator in the Feynman gauge

International Nuclear Information System (INIS)

Aguilar, A. C.; Papavassiliou, J.

2008-01-01

We demonstrate how to obtain from the Schwinger-Dyson equations of QCD an infrared finite ghost propagator in the Feynman gauge. The key ingredient in this construction is the longitudinal form factor of the nonperturbative gluon-ghost vertex, which, contrary to what happens in the Landau gauge, contributes nontrivially to the gap equation of the ghost. The detailed study of the corresponding vertex equation reveals that in the presence of a dynamical infrared cutoff this form factor remains finite in the limit of vanishing ghost momentum. This, in turn, allows the ghost self-energy to reach a finite value in the infrared, without having to assume any additional properties for the gluon-ghost vertex, such as the presence of massless poles. The implications of this result and possible future directions are briefly outlined

Analysis of chiral symmetry breaking mechanism

International Nuclear Information System (INIS)

Guo, X. H.; Academia Sinica, Beijing; Huang, T.; CCAST

1997-01-01

The renormalization group invariant quark condensate μ is determined both from the consistent equation for quark condensate in the chiral limit and from the Schwinger-Dyson (SD) equation improved by the intermediate range QCD force singular like δ (q) which is associated with the gluon condensate. The solutions of μ in these two equations are consistent. The authors also obtain the critical strong coupling constant α c above which chiral symmetry breaks in these two approaches. The nonperturbative kernel of the SD equation makes α c smaller and μ bigger. An intuitive picture of the condensation above α c is discussed. In addition, with the help of the Slavnov-Taylor-Ward (STW) identity they derive the equations for the nonperturbative quark propagator from the SD equation in the presence of the intermediate range force and find that the intermediate-range force is also responsible for dynamical chiral symmetry breaking

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.)

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)

Instabilities of the chiral-symmetry-breaking ground state in a truncation-free expansion

International Nuclear Information System (INIS)

Rembiesa, P.

1988-01-01

We use the composite-field effective-action method to examine the stability of the chiral-symmetry-breaking vacua in a QED-like model of interacting fermion fields. Unlike most of the existing approaches, ours does not rely on the truncated Baker-Johnson-Willey expansion. Instead, we break the hierarchy of the Dyson-Schwinger equations by the requirement that the vertex function is dominated by the contributions from the vicinity of the mass shell of the exchanged gluon and that it explicitly satisfies the Ward identity. The composite-field effective potential is then expanded in terms of the eigenfunctions of the Bethe-Salpeter equation. The signature of the second derivatives of the effective potential shows that the broken-symmetry vacua are unstable

Bootstrap calculation of the dynamical quark mass in QCD4 at finite temperature

International Nuclear Information System (INIS)

Cabo, A.; Kalashnikov, O.K.; Veliev, E.Kh.

1988-01-01

Nonperturbative calculations of the dynamical quark mass m(T) are given in QCD 4 , based on the bootstrap solution of the Schwinger-Dyson equation for the quark Green function at finite temperatures. A closed nonlinear equation is obtained for m(T) whose solution is found under some simplifying assumptions. We used a particular approximation for the effective charge and the nonperturbative expressions of the gluon magnetic and electric masses. The singular behavior of m(T) is established and its parameters are determined numerically. The singularity found is shown to correctly reproduce the chiral phase transition and the temperature limits obtained for m(T) are qualitatively correct. The complete phase diagram of QCD 4 in the (μ,T) plane is briefly discussed. (orig.)

Foundations for relativistic quantum theory. I. Feynman's operator calculus and the Dyson conjectures

International Nuclear Information System (INIS)

Gill, Tepper L.; Zachary, W.W.

2002-01-01

In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman's path integral, and to prove Dyson's first conjecture that the divergences are in part due to a violation of Heisenberg's uncertainly relations

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)

Hydrostatic pressure of the O(N) φ4 theory in the large N limit

International Nuclear Information System (INIS)

Jizba, Petr

2004-01-01

With nonequilibrium applications in mind we present in this paper (the first in a series of three) a self-contained calculation of the hydrostatic pressure of the O(N) λφ 4 theory at finite temperature. By combining the Keldysh-Schwinger closed-time path formalism with thermal Dyson-Schwinger equations we compute in the large N limit the hydrostatic pressure in a fully resumed form. We also calculate the high-temperature expansion for the pressure (in D=4) using the Mellin transform technique. The result obtained extends the results found by Drummond et al. [Nucl. Phys. B524, 579 (1998)] and Amelino-Camelia and Pi [Phys. Rev. D 47, 2356 (1993)]. The latter are reproduced in the limits m r (0)→0, T→∞, and T→∞, respectively. Important issues of renormalizibility of composite operators at finite temperature are addressed and the improved energy-momentum tensor is constructed. The utility of the hydrostatic pressure in the nonequilibrium quantum systems is discussed

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

NOAA Ship Oscar Dyson Underway Meteorological Data, Quality Controlled

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — NOAA Ship Oscar Dyson Underway Meteorological Data (delayed ~10 days for quality control) are from the Shipboard Automated Meteorological and Oceanographic System...

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

Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2004-01-01

We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least

Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations

International Nuclear Information System (INIS)

Tanimura, Shogo

1992-01-01

R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs

Are the Dyson rings around pulsars detectable?

Science.gov (United States)

Osmanov, Z.

2018-04-01

In the previous paper ring (Osmanov 2016) (henceforth Paper-I) we have extended the idea of Freeman Dyson and have shown that a supercivilization has to use ring-like megastructures around pulsars instead of a spherical shell. In this work we reexamine the same problem in the observational context and we show that facilities of modern infrared (IR) telescopes (Very Large Telescope Interferometer and Wide-field Infrared Survey Explorer (WISE)) might efficiently monitor the nearby zone of the solar system and search for the IR Dyson-rings up to distances of the order of 0.2 kpc, corresponding to the current highest achievable angular resolution, 0.001 mas. In this case the total number of pulsars in the observationally reachable area is about 64 +/- 21. We show that pulsars from the distance of the order of ~ 1 kpc are still visible for WISE as point-like sources but in order to confirm that the object is the neutron star, one has to use the ultraviolet telescopes, which at this moment cannot provide enough sensitivity.

RG analysis of magnetic catalysis in dynamical symmetry breaking

International Nuclear Information System (INIS)

Hong, Deog Ki; Kim, Youngman

1996-01-01

We perform the renormalization group analysis on the dynamical symmetry breaking under strong external magnetic field, studied recently by Gusynin, Miransky and Shovkovy. We find that any attractive four-Fermi interaction becomes strong in the low energy, thus leading to dynamical symmetry breaking. When the four-Fermi interaction is absent, the β-function for the electromagnetic coupling vanishes in the leading order in 1/N. By solving the Schwinger-Dyson equation for the fermion propagator, we show that in 1/N expansion, for any electromagnetic coupling, dynamical symmetry breaking occurs due to the presence of Landau energy gap by the external magnetic field. 5 refs

Chiral-symmetry restoration at finite densities in Coulomb-gauge QCD

International Nuclear Information System (INIS)

Kocic, A.

1986-01-01

Using the Schwinger-Dyson equation in the Hartree-Fock approximation, we show that, within a potential model motivated by the QCD Hamiltonian in the Coulomb gauge, chiral symmetry is restored at finite densities. Two cases are studied: a delta-function potential and a linear confining potential. For the former case the phase diagram is obtained analytically, whereas for the latter case numerical techniques are used. The values of physical quantities calculated for the linear confining model are consistently smaller than the experimental ones indicating that a potential with additional short-range attraction is needed to describe the quark interaction in the high-density regime

Behavior of the S parameter in the crossover region between walking and QCD-like regimes of an SU(N) gauge theory

International Nuclear Information System (INIS)

Kurachi, Masafumi; Shrock, Robert

2006-01-01

We consider a vectorial, confining SU(N) gauge theory with a variable number, N f , of massless fermions transforming according to the fundamental representation. Using the Schwinger-Dyson and Bethe-Salpeter equations, we calculate the S parameter in terms of the current-current correlation functions. We focus on values of N f such that the theory is in the crossover region between the regimes of walking behavior and QCD-like (nonwalking) behavior. Our calculations indicate that the contribution to S from a given fermion decreases as one moves from the QCD-like to the walking regimes. The implications of this result for technicolor theories are discussed

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

Dipole moments of the rho meson

International Nuclear Information System (INIS)

Hecht, M.B.; McKellar, B.H.P.

1997-04-01

The electric and magnetic dipole moments (EDM) of the rho meson are calculated using the propagators and vertices derived from the quantum chromodynamics Dyson-Schwinger equations. Results obtained from using the Bethe-Salpeter amplitude studied by Chappell, Mitchell et. al., and Pichowsky and Lee, are compared. The rho meson EDM is generated through the inclusion of a quark electric dipole moment, which is left as a free variable. These results are compared to the perturbative results to obtain a measure of the effects of quark interactions and confinement. The two dipole moments are also calculated using the phenomenological MIT bag model to provide a further basis for comparison

Are the dressed gluon and ghost propagators in the Landau gauge presently determined in the confinement regime of QCD?

International Nuclear Information System (INIS)

Pennington, M. R.; Wilson, D. J.

2011-01-01

The gluon and ghost propagators in Landau gauge QCD are investigated using the Schwinger-Dyson equation approach. Working in Euclidean spacetime, we solve for these propagators using a selection of vertex inputs, initially for the ghost equation alone and then for both propagators simultaneously. The results are shown to be highly sensitive to the choices of vertices. We favor the infrared finite ghost solution from studying the ghost equation alone where we argue for a specific unique solution. In order to solve this simultaneously with the gluon using a dressed-one-loop truncation, we find that a nontrivial full ghost-gluon vertex is required in the vanishing gluon momentum limit. The self-consistent solutions we obtain correspond to having a masslike term in the gluon propagator dressing, in agreement with similar studies supporting the long-held proposal of Cornwall.

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.

Equivalent formulations of “the equation of life”

International Nuclear Information System (INIS)

Ao Ping

2014-01-01

Motivated by progress in theoretical biology a recent proposal on a general and quantitative dynamical framework for nonequilibrium processes and dynamics of complex systems is briefly reviewed. It is nothing but the evolutionary process discovered by Charles Darwin and Alfred Wallace. Such general and structured dynamics may be tentatively named “the equation of life”. Three equivalent formulations are discussed, and it is also pointed out that such a quantitative dynamical framework leads naturally to the powerful Boltzmann-Gibbs distribution and the second law in physics. In this way, the equation of life provides a logically consistent foundation for thermodynamics. This view clarifies a particular outstanding problem and further suggests a unifying principle for physics and biology. (topical review - statistical physics and complex systems)

Determinantal method for complex angular momenta in potential scattering

Energy Technology Data Exchange (ETDEWEB)

Lee, B. W. [University of Pennsylvania, Philadelphia, PA (United States)

1963-01-15

In this paper I would like do describe a formulation of the complex angular momenta in potential scattering based on the Lippmann-Schwinger integral equation rather than on the Schrödinger differential equation. This is intended as a preliminary to the paper by SAWYER on the Regge poles and high energy limits in field theory (Bethe-Salpeter amplitudes), where the integral formulation is definitely more advantageous than the differential formulation.

Evolution of magnetic field and atmospheric response. I - Three-dimensional formulation by the method of projected characteristics. II - Formulation of proper boundary equations. [stellar magnetohydrodynamics

Science.gov (United States)

Nakagawa, Y.

1981-01-01

The method described as the method of nearcharacteristics by Nakagawa (1980) is renamed the method of projected characteristics. Making full use of properties of the projected characteristics, a new and simpler formulation is developed. As a result, the formulation for the examination of the general three-dimensional problems is presented. It is noted that since in practice numerical solutions must be obtained, the final formulation is given in the form of difference equations. The possibility of including effects of viscous and ohmic dissipations in the formulation is considered, and the physical interpretation is discussed. A systematic manner is then presented for deriving physically self-consistent, time-dependent boundary equations for MHD initial boundary problems. It is demonstrated that the full use of the compatibility equations (differential equations relating variations at two spatial locations and times) is required in determining the time-dependent boundary conditions. In order to provide a clear physical picture as an example, the evolution of axisymmetric global magnetic field by photospheric differential rotation is considered.

Phenomenological dynamics in QCD at large distances

International Nuclear Information System (INIS)

Gogohia, V.Sh.; Kluge, Gy.

1991-07-01

A gauge-invariant, nonperturbative approach to QCD at large distances in the context of the Schwinger-Dyson equations and corresponding Slavnov-Taylor identities in the quark sector is presented. Making only one widely accepted assumption that the full gluon propagator becomes an infrared singular like (q 2 ) -2 in the covariant gauge, we find three and only three confinement-type solutions for the quark propagator (quark confinement theorem.) The approach is free from ghost complications. Also show that multiplication by the quark infrared renormalization constant only, would make all the Green's functions infrared finite (multiplicative renormalizability). The bound-state problem in framework of Bethe-Salpeter equation is discussed as well. Some basic physical parameters of chiral QCD as pion decay constant and quark condensate, have been calculated within our approach. (author) 75 refs.; 14 figs

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.

NOAA Ship Oscar Dyson Underway Meteorological Data, Near Real Time

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — NOAA Ship Oscar Dyson Underway Meteorological Data (Near Real Time, updated daily) are from the Shipboard Automated Meteorological and Oceanographic System (SAMOS)...

A range of formulations to couple mass and momentum equations

International Nuclear Information System (INIS)

Darbandi, M.; Schneider, G.E.

2002-01-01

Since the innovation of control-volume-based methods, the issue of pressure-velocity decoupling has prompted the researcher to develop and employ staggered grid arrangement. The difficulties and disadvantages of staggered-grid-based schemes have encouraged the workers to investigate more in alternative scheme, i.e., the collocated-grid-based scheme. The primitive idea in collocated scheme is to couple the mass and momentum equations with the help of two types of velocity definitions instead of two types of grid arrangements. Following the work of preceding workers, we introduce a general strategy which enables the workers to develop a wide range of velocity definitions which can be properly used in collocated formulations. The developed formulations are then tested in a domain with source and sink. The results of the extended formulations are eventually discussed. (author)

Spectral/hp least-squares finite element formulation for the Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2003-01-01

We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation

KAUST Repository

Mélykúti, Bence

2010-01-01

The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1 + m2 Wiener processes, whereas the standard approach uses 2 m1 + m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch. © 2010 American Institute of Physics.

Path Integral Formulation of Anomalous Diffusion Processes

OpenAIRE

Friedrich, Rudolf; Eule, Stephan

2011-01-01

We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of processes under consideration. We show that Continuous Time Random Walks (CTRWs) are included in our framework. A closed expression for the path probability distribution of CTRWs is found in terms of their waiting time distribution as the solution of a Dyson ...

A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

Science.gov (United States)

Sohn, J. L.; Heinrich, J. C.

1990-01-01

The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

Boundary-integral equation formulation for time-dependent inelastic deformation in metals

Energy Technology Data Exchange (ETDEWEB)

Kumar, V; Mukherjee, S

1977-01-01

The mathematical structure of various constitutive relations proposed in recent years for representing time-dependent inelastic deformation behavior of metals at elevated temperatues has certain features which permit a simple formulation of the three-dimensional inelasticity problem in terms of real time rates. A direct formulation of the boundary-integral equation method in terms of rates is discussed for the analysis of time-dependent inelastic deformation of arbitrarily shaped three-dimensional metallic bodies subjected to arbitrary mechanical and thermal loading histories and obeying constitutive relations of the kind mentioned above. The formulation is based on the assumption of infinitesimal deformations. Several illustrative examples involving creep of thick-walled spheres, long thick-walled cylinders, and rotating discs are discussed. The implementation of the method appears to be far easier than analogous BIE formulations that have been suggested for elastoplastic problems.

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

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.

Gluon mass generation without seagull divergences

International Nuclear Information System (INIS)

Aguilar, Arlene C.; Papavassiliou, Joannis

2010-01-01

Dynamical gluon mass generation has been traditionally plagued with seagull divergences, and all regularization procedures proposed over the years yield finite but scheme-dependent gluon masses. In this work we show how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger the aforementioned identity hinges crucially on the particular Ansatz employed for the three-gluon vertex entering into the Schwinger-Dyson equation governing the gluon propagator. The use of the appropriate three-gluon vertex brings about an additional advantage: one obtains two separate (but coupled) integral equations, one for the effective charge and one for the gluon mass. This system of integral equations has a unique solution, which unambiguously determines these two quantities. Most notably, the effective charge freezes in the infrared, and the gluon mass displays power-law running in the ultraviolet, in agreement with earlier considerations.

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 ...

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

T-duality transformation and universal structure of noncritical string field theory

International Nuclear Information System (INIS)

Asatani, T.; Kuroki, T.; Okawa, Y.; Sugino, F.; Yoneya, T.

1997-01-01

We discuss a T-duality transformation for the c=1/2 matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling limit of the Schwinger-Dyson equations and the stochastic Hamiltonian in terms of the dual variables and then compare the results with those using the original spin variables. It is shown that the c=1/2 model in the scaling limit is T-duality symmetric in the sphere approximation. In the case of the standard two-matrix model, however, the duality symmetry is violated when the higher-genus effects are taken into account, due to the nonsymmetrical appearence of global Z 2 vector fields corresponding to nontrivial homology cycles. Some universal properties of the stochastic Hamiltonians which play an important role in discussing the scaling limit and have been discussed in a previous work by Sugino and Yoneya are refined in both the original and dual formulations. We also report a number of new explicit results for various amplitudes containing macroscopic loop operators. copyright 1997 The American Physical Society

Bethe-Salpeter dynamics and the constituent mass concept for heavy quark mesons

International Nuclear Information System (INIS)

Souchlas, N.; Stratakis, D.

2010-01-01

The definition of a quark as heavy requires a comparison of its mass with the nonperturbative chiral symmetry breaking scale which is about 1 GeV (Λ χ ∼1 GeV) or with the scale Λ QCD ∼0.2 GeV that characterizes the distinction between perturbative and nonperturbative QCD. For quark masses significantly larger than these scales, nonperturbative dressing effects, or equivalently nonperturbative self-energy contributions, and relativistic effects are believed to be less important for physical observables. We explore the concept of a constituent mass for heavy quarks in the Dyson-Schwinger equations formalism, for light-heavy and heavy-heavy quark mesons by studying their masses and electroweak decay constants.

Looking into the Matter of Light-Quark Hadrons

International Nuclear Information System (INIS)

Roberts, C.D.

2012-01-01

In tackling QCD, a constructive feedback between theory and extant and forthcoming experiments is necessary in order to place constraints on the infrared behaviour of QCD's β-function, a key nonperturbative quantity in hadron physics. The Dyson-Schwinger equations provide a tool with which to work toward this goal. They connect confinement with dynamical chiral symmetry breaking, both with the observable properties of hadrons, and hence can plausibly provide a means of elucidating the material content of real-world QCD. This contribution illustrates these points via comments on: in-hadron condensates; dressed-quark anomalous chromo- and electro-magnetic moments; the spectra of mesons and baryons, and the critical role played by hadron-hadron interactions in producing these spectra. (author)

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.

Derivation of a macroscale formulation for a class of nonlinear partial differential equations

International Nuclear Information System (INIS)

Pantelis, G.

1995-05-01

A macroscale formulation is constructed from a system of partial differential equations which govern the microscale dependent variables. The construction is based upon the requirement that the solutions of the macroscale partial differential equations satisfy, in some approximate sense, the system of partial differential equations associated with the microscale. These results are restricted to the class of nonlinear partial differential equations which can be expressed as polynomials of the dependent variables and their partial derivatives up to second order. A linear approximation of transformations of second order contact manifolds is employed. 6 refs

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.))

The Yang-Mills vacuum wave functional in Coulomb gauge

International Nuclear Information System (INIS)

Campagnari, Davide R.

2011-01-01

Yang-Mills theories are the building blocks of today's Standard Model of elementary particle physics. Besides methods based on a discretization of space-time (lattice gauge theory), also analytic methods are feasible, either in the Lagrangian or in the Hamiltonian formulation of the theory. This thesis focuses on the Hamiltonian approach to Yang-Mills theories in Coulomb gauge. The thesis is presented in cumulative form. After an introduction into the general formulation of Yang-Mills theories, the Hamilton operator in Coulomb gauge is derived. Chap. 1 deals with the heat-kernel expansion of the Faddeev-Popov determinant. In Chapters 2 and 3, the high-energy behaviour of the theory is investigated. To this purpose, perturbative methods are applied, and the results are compared with the ones stemming from functional methods in Coulomb and Landau gauge. Chap. 4 is devoted to the variational approach. Variational ansatzes going beyond the Gaussian form for the vacuum wave functional are considered and treated using Dyson-Schwinger techniques. Equations for the higher-order variational kernels are derived and their effects are estimated. Chap. 5 presents an application of the previously obtained propagators, namely the evaluation of the topological susceptibility, which is related to the mass of the η meson. Finally, a short overview of the perturbative treatment of dynamical fermion fields is presented.

Compressibility of binary powder formulations: investigation and evaluation with compaction equations.

Science.gov (United States)

Gentis, Nicolaos D; Betz, Gabriele

2012-02-01

The purpose of this work was to investigate and evaluate the powder compressibility of binary mixtures containing a well-compressible compound (microcrystalline cellulose) and a brittle active drug (paracetamol and mefenamic acid) and its progression after a drug load increase. Drug concentration range was 0%-100% (m/m) with 10% intervals. The powder formulations were compacted to several relative densities with the Zwick material tester. The compaction force and tensile strength were fitted to several mathematical models that give representative factors for the powder compressibility. The factors k and C (Heckel and modified Heckel equation) showed mostly a nonlinear correlation with increasing drug load. The biggest drop in both factors occurred at far regions and drug load ranges. This outcome is crucial because in binary mixtures the drug load regions with higher changeover of plotted factors could be a hint for an existing percolation threshold. The susceptibility value (Leuenberger equation) showed varying values for each formulation without the expected trend of decrease for higher drug loads. The outcomes of this study showed the main challenges for good formulation design. Thus, we conclude that such mathematical plots are mandatory for a scientific evaluation and prediction of the powder compaction process. Copyright © 2011 Wiley Periodicals, Inc.

The covariant formulation of Maxwell's equations expressed in a form independent of specific units

International Nuclear Information System (INIS)

Heras, Jose A; Baez, G

2009-01-01

The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants α, β and γ into these equations. Maxwell's equations involving these constants are then specialized to the most commonly used systems of units: Gaussian, SI and Heaviside-Lorentz by giving the constants α, β and γ the values appropriate to each system

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)

Excision technique in constrained formulations of Einstein equations: collapse scenario

International Nuclear Information System (INIS)

Cordero-Carrión, I; Vasset, N; Novak, J; Jaramillo, J L

2015-01-01

We present a new excision technique used in constrained formulations of Einstein equations to deal with black hole in numerical simulations. We show the applicability of this scheme in several scenarios. In particular, we present the dynamical evolution of the collapse of a neutron star to a black hole, using the CoCoNuT code and this excision technique. (paper)

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

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

Chern-Simons theory with vector fermion matter

International Nuclear Information System (INIS)

Giombi, Simone; Minwalla, Shiraz; Prakash, Shiroman; Trivedi, Sandip P.; Wadia, Spenta R.; Yin, Xi

2012-01-01

We study three-dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on R 2 as a function of the 't Hooft coupling λ=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at vertical stroke λvertical stroke =1; the conformal theory does not exist for vertical stroke λvertical stroke >1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three-point functions up to two loops. We also discuss a light-cone Hamiltonian formulation of this theory where a W ∞ algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory. (orig.)

Modified Hermitian treatment of Dyson boson expansion theory

International Nuclear Information System (INIS)

Kajiyama, Atsushi

2009-01-01

The Hermitian treatment of the Dyson-type boson expansion theory is reinvestigated with the aid of small-parameter expansion. A naive application of the Hermitization formula sometimes yields an unrealistic phase that spoils the conventional treatment. The complementary use of another formula having the form of the arithmetic mean can avoid that problem. This modification will improve the accuracy of the Hermitian treatment. (author)

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.

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

Infrared behavior of the effective coupling in quantum chromodynamics: A non-perturbative approach

International Nuclear Information System (INIS)

Bar-Gadda, U.

1980-01-01

In this paper we examine a different viewpoint, based on a self-consistent approach. This means that rather than attempting to identify any particular physical mechanism as dominating the QCD vacuum state we use the non-perturbative Schwinger-Dyson equations and Slavnov-Taylor identities of QCD as well as the renormalization group equation to obtain the self-consistent behavior of the effective coupling in the infrared region. We show that the infrared effective coupling behavior anti g(q 2 /μ 2 , gsub(R)(μ)) = (μ 2 /q 2 )sup(lambda/2)gsub(R)(μ) in the infrared limit q 2 /μ 2 → 0, where μ 2 is the euclidean subtraction point; lambda = 1/2(d - 2), where d is the space-time dimension, is the preferred solution if a sufficient self-consistency condition is satisfied. Finally we briefly discuss the nature of the dynamical mass Λ and the 1/N expansion as well as an effective bound state equation. (orig.)

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)

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)

Commemorating John Dyson

Science.gov (United States)

Pittard, Julian M.

2015-03-01

John Dyson was born on the 7th January 1941 in Meltham Mills, West Yorkshire, England, and later grew up in Harrogate and Leeds. The proudest moment of John's early life was meeting Freddie Trueman, who became one of the greatest fast bowlers of English cricket. John used a state scholarship to study at Kings College London, after hearing a radio lecture by D. M. McKay. He received a first class BSc Special Honours Degree in Physics in 1962, and began a Ph.D. at the University of Manchester Department of Astronomy after being attracted to astronomy by an article of Zdenek Kopal in the semi-popular journal New Scientist. John soon started work with Franz Kahn, and studied the possibility that the broad emission lines seen from the Orion Nebula were due to flows driven by the photoevaporation of neutral globules embedded in a HII region. John's thesis was entitled ``The Age and Dynamics of the Orion Nebula`` and he passed his oral examination on 28th February 1966.

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.

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

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.)

Field theory

CERN Multimedia

1999-11-08

In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.

The scalar-photon 3-point vertex in massless quenched scalar QED

International Nuclear Information System (INIS)

Concha-Sánchez, Y; Gutiérrez-Guerrero, L X; Fernández-Rangel, L A

2016-01-01

Non perturbative studies of Schwinger-Dyson equations (SDEs) require their infinite, coupled tower to be truncated in order to reduce them to a practically solvable set. In this connection, a physically acceptable ansatz for the three point vertex is the most favorite choice. Scalar quantum electrodynamics (sQED) provides a simple and neat platform to address this problem. The most general form of the scalar-photon three point vertex can be expressed in terms of only two independent form factors, longitudinal and transverse. Ball and Chiu have demonstrated that the longitudinal vertex is fixed by requiring the Ward-Fradkin-Green- Takahashi identity (WFGTI), while the transverse vertex remains undetermined. In massless quenched sQED, we propose the transverse part of the non perturbative scalar-photon vertex. (paper)

Chiral symmetry in the strong color-electric field in terms of Nambu-Jona-Lasinio model

International Nuclear Information System (INIS)

Suganuma, Hideo

1990-01-01

We examine the behavior of chiral symmetry in an external gluon field using Nambu-Jona-Lasinio model, which is an effective theory of QCD. The Dyson equation for the dynamical quark mass in the presence of the external color-electric field is obtained. By solving it in the color flux tube inside mesons, chiral symmetry would be restored in the flux tube of mesons and this result supports Chiral Bag picture for mesons. Next we consider the flux tubes formed in the central region for ultra-relativistic heavy-ion collisions, and find the chiral restoration occurs there, so that the current quark mass seems to be suitable in calculating the q-q-bar pair creation rate by the Schwinger formula in the flux-tube picture. (author)

Combined Helmholtz Integral Equation - Fourier series formulation of acoustical radiation and scattering problems

CSIR Research Space (South Africa)

Fedotov, I

2006-07-01

Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...

Temperature, chemical potential and the ρ meson

International Nuclear Information System (INIS)

Roberts, C. D.; Schmidt, S. M.

2000-01-01

Models of QCD must confront nonperturbative phenomena such as confinement, dynamical chiral symmetry breaking (DCSB) and the formation of bound states. In addition, a unified approach should describe the deconfinement and chiral symmetry restoring phase transition exhibited by strongly-interacting matter under extreme conditions of temperature and density. Nonperturbative Dyson-Schwinger equation (DSE) models provide insight into a wide range of zero temperature hadronic phenomena; e.g., non-hadronic electroweak interactions of light- and heavy-mesons, and diverse meson-meson and meson-nucleon form factors. This is the foundation for their application at nonzero-(T, μ). Herein the authors describe the calculation of the reconfinement and chiral symmetry restoring phase boundary, and the medium dependence of ρ-meson properties. They also introduce an extension to describe the time-evolution in the plasma of the quark's scalar and vector self energies based on a Vlasov equation

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

Microscopic structure of an interacting boson model in terms of the dyson boson mapping

International Nuclear Information System (INIS)

Geyer, H.B.; Lee, S.Y.

1982-01-01

In an application of the generalized Dyson boson mapping to a shell model Hamiltonian acting in a single j shell, a clear distinction emerges between pair bosons and kinematically determined seniority bosons. As in the Otsuka-Arima-Iachello method it is found that the latter type of boson determines the structure of an interactive boson-model-like Hamiltonian for the single j-shell model. It is furthermore shown that the Dyson boson mapping formalism is equally well suited for investigating possible interactive boson-model-like structures in a multishell case, where dynamical considerations are expected to play a much more important role in determining the structure of physical bosons

Electromagnetic wave propagation over an inhomogeneous flat earth (two-dimensional integral equation formulation)

International Nuclear Information System (INIS)

de Jong, G.

1975-01-01

With the aid of a two-dimensional integral equation formulation, the ground wave propagation of electromagnetic waves transmitted by a vertical electric dipole over an inhomogeneous flat earth is investigated. For the configuration in which a ground wave is propagating across an ''island'' on a flat earth, the modulus and argument of the attenuation function have been computed. The results for the two-dimensional treatment are significantly more accurate in detail than the calculations using a one-dimensional integral equation

Dynamical equations for time-ordered Green’s functions: from the Keldysh time-loop contour to equilibrium at finite and zero temperature

International Nuclear Information System (INIS)

Ness, H; Dash, L K

2012-01-01

We study the dynamical equation of the time-ordered Green’s function at finite temperature. We show that the time-ordered Green’s function obeys a conventional Dyson equation only at equilibrium and in the limit of zero temperature. In all other cases, i.e. finite temperature at equilibrium or non-equilibrium, the time-ordered Green’s function obeys instead a modified Dyson equation. The derivation of this result is obtained from the general formalism of the non-equilibrium Green’s functions on the Keldysh time-loop contour. At equilibrium, our result is fully consistent with the Matsubara temperature Green’s function formalism and also justifies rigorously the correction terms introduced in an ad hoc way with Hedin and Lundqvist. Our results show that one should use the appropriate dynamical equation for the time-ordered Green’s function when working beyond the equilibrium zero-temperature limit.

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

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.)

Structure of Nonlocal quark vacuum condensate in non-perturbative QCD vacuum

International Nuclear Information System (INIS)

Xiang Qianfei; Ma Weixing; Zhou Lijuan; Jiang Weizhou

2014-01-01

Based on the Dyson-Schwinger Equations (DSEs) with the rainbow truncation, and Operator Product Expansion, the structure of nonlocal quark vacuum condensate in QCD, described by quark self-energy functions A_f and B_f given usually by the solutions of the DSEs of quark propagator, is predicted numerically. We also calculate the local quark vacuum condensate, quark-gluon mixed local vacuum condensate, and quark virtuality. The self-energy functions A_f and B_f are given by the parameterized quark propagator functions σ_v"f (p"2) and σ_s"f (p"2) of Roberts and Williams, instead of the numerical solutions of the DSEs. Our calculated results are in reasonable agreement with those of QCD sum rules, Lattice QCD calculations, and instanton model predictions, although the resulting local quark vacuum condensate for light quarks, u, d, s, are a little bit larger than those of the above theoretical predictions. We think the differences are caused by model dependence. The larger of strange quark vacuum condensate than u, d quark is due to the s quark mass which is more larger than u, d quark masses. Of course, the Roberts-Williams parameterized quark propagator is an empirical formulism, which approximately describes quark propagation. (authors)

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.

Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

Energy Technology Data Exchange (ETDEWEB)

Seiler, Jennifer; Szilagyi, Bela; Pollney, Denis; Rezzolla, Luciano [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany)

2008-09-07

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions.

Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

International Nuclear Information System (INIS)

Seiler, Jennifer; Szilagyi, Bela; Pollney, Denis; Rezzolla, Luciano

2008-01-01

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions

On iteration-separable method on the multichannel scattering theory

International Nuclear Information System (INIS)

Zubarev, A.L.; Ivlieva, I.N.; Podkopaev, A.P.

1975-01-01

The iteration-separable method for solving the equations of the Lippman-Schwinger type is suggested. Exponential convergency of the method of proven. Numerical convergency is clarified on the e + H scattering. Application of the method to the theory of multichannel scattering is formulated

The covariant formulation of Maxwell's equations expressed in a form independent of specific units

Energy Technology Data Exchange (ETDEWEB)

Heras, Jose A; Baez, G [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200 Mexico DF (Mexico)], E-mail: herasgomez@gmail.com, E-mail: gbaez@correo.azc.uam.mx

2009-01-15

The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants {alpha}, {beta} and {gamma} into these equations. Maxwell's equations involving these constants are then specialized to the most commonly used systems of units: Gaussian, SI and Heaviside-Lorentz by giving the constants {alpha}, {beta} and {gamma} the values appropriate to each system.

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)

Spinning gas clouds with precession: a new formulation

International Nuclear Information System (INIS)

Gaffet, B

2010-01-01

We consider Dyson's model (Dyson F J 1968 J. Math. Mech. 18 91) of an ellipsoidally stratified ideal gas cloud expanding adiabatically into a vacuum, in the Liouville integrable case where the gas is monatomic (γ = 5/3) and there is no vorticity (Gaffet B 2001a J. Phys. A: Math. Gen. 34 2097; Paper I). In the cases of rotation about a fixed axis the separation of variables can be achieved, and the separable variables are linearly related to a set of three variables denoted by ρ, R, W (Gaffet B 2001b J. Phys. A: Math. Gen. 34 9195; Paper II). We show in the present work that these variables admit a natural generalization to cases of rotation about a movable axis (precessing motion). The present study is restricted to the consideration of the so-called degenerate cases (see Gaffet B 2006 J. Phys. A: Math. Gen. 39 99; Paper III), but we hope to generalize our results in the future to the non-degenerate ones as well. We also present a new, compact and generally valid formulation of one of the integrals of motion, of the sixth degree in the momenta, denoted by I 6 .

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

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.

Dynamical mass generation in QED with weak magnetic fields

International Nuclear Information System (INIS)

Ayala, A.; Rojas, E.; Bashir, A.; Raya, A.

2006-01-01

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics in the presence of magnetic fields using Schwinger-Dyson equations. We show that, contrary to the case where the magnetic field is strong, in the weak field limit eB << m(0)2, where m(0) is the value of the dynamically generated mass in the absence of the magnetic field, masses are generated above a critical value of the coupling and that this value is the same as in the case with no magnetic field. We carry out a numerical analysis to study the magnetic field dependence of the mass function above critical coupling and show that in this regime the dynamically generated mass and the chiral condensate for the lowest Landau level increase proportionally to (eB)2

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.

The Quark-Gluon Plasma Collective Dynamics and Hard Thermal Loops

CERN Document Server

Blaizot, J P; Blaizot, Jean-Paul; Iancu, Edmond

2002-01-01

We present a unified description of the high temperature phase of QCD, the so-called quark-gluon plasma, in a regime where the effective gauge coupling $g$ is sufficiently small to allow for weak coupling calculations. The main focuss is the construction of the effective theory for the collective excitations which develop at a typical scale $gT$, which is well separated from the typical energy of single particle excitations which is the temperature $T$. We show that the plasma particles provide a source for long wavelength oscillations of average fields which carry the quantum numbers of the plasma constituents, the quarks and the gluons. To leading order in $g$, the plasma particles obey simple gauge-covariant kinetic equations, whose derivation from the general Dyson-Schwinger equations is outlined. As a by-product, the ``hard thermal loops'' emerge naturally in a physically transparent framework. We show that the collective excitations can be described in terms of classical fields, and develop for these a ...

The ghost propagator in Coulomb gauge

International Nuclear Information System (INIS)

Watson, P.; Reinhardt, H.

2011-01-01

We present results for a numerical study of the ghost propagator in Coulomb gauge whereby lattice results for the spatial gluon propagator are used as input to solving the ghost Dyson-Schwinger equation. We show that in order to solve completely, the ghost equation must be supplemented by a boundary condition (the value of the inverse ghost propagator dressing function at zero momentum) which determines if the solution is critical (zero value for the boundary condition) or subcritical (finite value). The various solutions exhibit a characteristic behavior where all curves follow the same (critical) solution when going from high to low momenta until 'forced' to freeze out in the infrared to the value of the boundary condition. The boundary condition can be interpreted in terms of the Gribov gauge-fixing ambiguity; we also demonstrate that this is not connected to the renormalization. Further, the connection to the temporal gluon propagator and the infrared slavery picture of confinement is discussed.

Nonperturbative aspects of the quark-photon vertex

International Nuclear Information System (INIS)

Frank, M.R.

1994-01-01

The electromagnetic interaction with quarks is investigated through a relativistic, electromagnetic gauge-invariant treatment. Gluon dressing of the quark-photon vertex and the quark self-energy functions is described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger-Dyson equation in the rainbow approximation respectively. Results for the calculation of the quark-photon vertex are presented in both the time-like and space-like regions of photon momentum squared, however emphasis is placed on the space-like region relevant to electron scattering. The treatment presented here simultaneously addresses the role of dynamically generated q bar q vector bound states and the approach to asymptotic behavior. The resulting description is therefore applicable over the entire range of momentum transfers available in electron scattering experiments. Input parameters are limited to the model gluon two-point function which is chosen to reflect confinement and asymptotic freedom and are largely constrained by the obtained bound-state spectrum

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.

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

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

Conformal and covariant Z4 formulation of the Einstein equations: Strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes

Science.gov (United States)

Dumbser, Michael; Guercilena, Federico; Köppel, Sven; Rezzolla, Luciano; Zanotti, Olindo

2018-04-01

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of standard gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in nonconservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

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

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.)

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)

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…

An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part one: Single Rigid Bodies

Directory of Open Access Journals (Sweden)

Pål Johan From

2012-04-01

Full Text Available This paper presents the explicit dynamic equations of a mechanical system. The equations are presented so that they can easily be implemented in a simulation software or controller environment and are also well suited for system and controller analysis. The dynamics of a general mechanical system consisting of one or more rigid bodies can be derived from the Lagrangian. We can then use several well known properties of Lie groups to guarantee that these equations are well defined. This will, however, often lead to rather abstract formulation of the dynamic equations that cannot be implemented in a simulation software directly. In this paper we close this gap and show what the explicit dynamic equations look like. These equations can then be implemented directly in a simulation software and no background knowledge on Lie theory and differential geometry on the practitioner's side is required. This is the first of two papers on this topic. In this paper we derive the dynamics for single rigid bodies, while in the second part we study multibody systems. In addition to making the equations more accessible to practitioners, a motivation behind the papers is to correct a few errors commonly found in literature. For the first time, we show the detailed derivations and how to arrive at the correct set of equations. We also show through some simple examples that these correspond with the classical formulations found from Lagrange's equations. The dynamics is derived from the Boltzmann--Hamel equations of motion in terms of local position and velocity variables and the mapping to the corresponding quasi-velocities. Finally we present a new theorem which states that the Boltzmann--Hamel formulation of the dynamics is valid for all transformations with a Lie group topology. This has previously only been indicated through examples, but here we also present the formal proof. The main motivation of these papers is to allow practitioners not familiar with

The resonating group method in an harmonic oscillator basis

International Nuclear Information System (INIS)

Silvestre-Brac, B.; Gignoux, C.; Ayant, Y.

1987-05-01

The scattering states for a general many body system is formulated within the resonating group method. The resulting Lippman-Schwinger equation is solved in an harmonic oscillator basis for which a number of advantages are emphasized. The analytical formula giving the free propagator in that basis is fully derived

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

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

Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations

International Nuclear Information System (INIS)

Montgomery, R.

1984-01-01

Wong (1970) introduced equations of motion for a spin 0 particle in a Yang-Mills field which was widely accepted among physicists. It is shown that these are equivalent to the various mathematical formulations for the motion of such particles as given by the Kaluza-Klein formulation of Kerner, and those of Sternberg, and Weinstein. In doing this, we show that Sternberg's space is, in a natural way, a symplectic leaf of a reduced Poisson manifold and relations to a construction of Kummer's for dynamics on the cotangent bundle of a principle bundle are clarified. (orig.)

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...

Formulation of stiffness equation for a three-dimensional isoparametric element with elastic-plastic material and large deformation

International Nuclear Information System (INIS)

Chang, T.Y.; Prachuktam, S.; Reich, M.

1975-01-01

The formulation of the stiffness equation for an 8 to 21 node isoparametric element with elastic-plastic material and large deformation is presented. The formulation has been implemented in a nonlinear finite element program for the analysis of three-dimensional continuums. To demonstrate the utility of the formulation, a thick-walled cylinder was analyzed and the results are compared favorably with a known solution. The element type presented can be applied not only to 3-D continuums, but also to plate or shell structures, for which degenerated isoparametric elements may be used

Vector-Interaction-Enhanced Bag Model

Science.gov (United States)

Cierniak, Mateusz; Klähn, Thomas; Fischer, Tobias; Bastian, Niels-Uwe

2018-02-01

A commonly applied quark matter model in astrophysics is the thermodynamic bag model (tdBAG). The original MIT bag model approximates the effect of quark confinement, but does not explicitly account for the breaking of chiral symmetry, an important property of Quantum Chromodynamics (QCD). It further ignores vector repulsion. The vector-interaction-enhanced bag model (vBag) improves the tdBAG approach by accounting for both dynamical chiral symmetry breaking and repulsive vector interactions. The latter is of particular importance to studies of dense matter in beta-equilibriumto explain the two solar mass maximum mass constraint for neutron stars. The model is motivated by analyses of QCD based Dyson-Schwinger equations (DSE), assuming a simple quark-quark contact interaction. Here, we focus on the study of hybrid neutron star properties resulting from the application of vBag and will discuss possible extensions.

Confinement in Maxwell-Chern-Simons planar quantum electrodynamics and the 1/N approximation

International Nuclear Information System (INIS)

Hofmann, Christoph P.; Raya, Alfredo; Madrigal, Saul Sanchez

2010-01-01

We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first-order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient θ reaches a critical value which depends upon the number of fermion families considered. Parity-violating masses, however, are generated for arbitrarily large values of the said coefficient. On the confinement scenario, complete charge screening - characteristic of the 1/N approximation - is observed in the entire (N,θ)-plane through the local and global properties of the vector part of the fermion propagator.

Chiral symmetry breaking is permitted in supersymmetric QED

International Nuclear Information System (INIS)

Walker, M.

2000-01-01

Full text: A chirally symmetric theory will generally have a chirally symmetric and a chirally asymmetric solution for the dressed fermionic propagator. It has been claimed that no chirally asymmetric solution for the fermionic propagator exists in supersymmetric QED. This result in the superfield formalism uses a gauge dependent argument whose validity has since been questioned. We present an analogous analysis using the component formalism which demonstrates that chiral symmetry breaking is permitted in this theory. We open the presentation with a brief introduction to supersymmetry, supersymmetric QED, and the superfield formalism. We describe chiral symmetry breaking and the Dyson-Schwinger equation used to analyse it. The derivation of the erroneous theorem claiming the lack of an a chiral propagator is outlined and its flaws discussed. We finish with the equivalent derivation in component fields and our contradictory result

High temperature phase transitions without infrared divergences

International Nuclear Information System (INIS)

Tetradis, N.; Wetterich, C.

1993-09-01

The most commonly used method for the study of high temperature phase transitions is based on the perturbative evaluation of the temperature dependent effective potential. This method becomes unreliable in the case of a second order or weakly first order phase transition, due to the appearance of infrared divergences. These divergences can be controlled through the method of the effective average action which employs renormalization group ideas. We report on the study of the high temperature phase transition for the N-component φ 4 theory. A detailed quantitative picture of the second order phase transition is presented, including the critical exponents for the behaviour in the vicinity of the critical temperature. An independent check of the results is obtained in the large N limit, and contact with the perturbative approach is established through the study of the Schwinger-Dyson equations. (orig.)

Influence of broken flavor and C and P symmetry on the quark propagator

Energy Technology Data Exchange (ETDEWEB)

Maas, Axel; Mian, Walid Ahmed [University of Graz, Institute of Physics, NAWI Graz, Graz (Austria)

2017-02-15

Embedding QCD into the standard model breaks various symmetries of QCD explicitly, especially C and P. While these effects are usually perturbatively small, they can be amplified in extreme environments like merging neutron stars or by the interplay with new physics. To correctly treat these cases requires fully backcoupled calculations. To pave the way for later investigations of hadronic physics, we study the QCD quark propagator coupled to an explicit breaking. This substantially increases the tensor structure even for this simplest correlation function. To cope with the symmetry structure, and covering all possible quark masses, from the top quark mass to the chiral limit, we employ Dyson-Schwinger equations. While at weak breaking the qualitative effects have similar trends as in perturbation theory, even moderately strong breakings lead to qualitatively different effects, non-linearly amplified by the strong interactions. (orig.)

Variational and potential formulation for stochastic partial differential equations

International Nuclear Information System (INIS)

Munoz S, A G; Ojeda, J; Sierra D, P; Soldovieri, T

2006-01-01

Recently there has been interest in finding a potential formulation for stochastic partial differential equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single expression. In this letter we formally provide a general Lagrangian formalism for SPDEs using the Hojman et al method. We show that it is possible to write the corresponding effective potential starting from an s-equivalent Lagrangian, and that this potential is able to reproduce all the dynamics of the system once a special differential operator has been applied. This procedure can be used to study the complete time evolution and spatial inhomogeneities of the system under consideration, and is also suitable for the statistical mechanics description of the problem. (letter to the editor)

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

From quarks and gluons to baryon form factors.

Science.gov (United States)

Eichmann, Gernot

2012-04-01

I briefly summarize recent results for nucleon and [Formula: see text] electromagnetic, axial and transition form factors in the Dyson-Schwinger approach. The calculation of the current diagrams from the quark-gluon level enables a transparent discussion of common features such as: the implications of dynamical chiral symmetry breaking and quark orbital angular momentum, the timelike structure of the form factors, and their interpretation in terms of missing pion-cloud effects.

An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part Two: Multibody Systems

Directory of Open Access Journals (Sweden)

Pål Johan From

2012-04-01

Full Text Available This paper presents the explicit dynamic equations of multibody mechanical systems. This is the second paper on this topic. In the first paper the dynamics of a single rigid body from the Boltzmann--Hamel equations were derived. In this paper these results are extended to also include multibody systems. We show that when quasi-velocities are used, the part of the dynamic equations that appear from the partial derivatives of the system kinematics are identical to the single rigid body case, but in addition we get terms that come from the partial derivatives of the inertia matrix, which are not present in the single rigid body case. We present for the first time the complete and correct derivation of multibody systems based on the Boltzmann--Hamel formulation of the dynamics in Lagrangian form where local position and velocity variables are used in the derivation to obtain the singularity-free dynamic equations. The final equations are written in global variables for both position and velocity. The main motivation of these papers is to allow practitioners not familiar with differential geometry to implement the dynamic equations of rigid bodies without the presence of singularities. Presenting the explicit dynamic equations also allows for more insight into the dynamic structure of the system. Another motivation is to correct some errors commonly found in the literature. Unfortunately, the formulation of the Boltzmann-Hamel equations used here are presented incorrectly. This has been corrected by the authors, but we present here, for the first time, the detailed mathematical details on how to arrive at the correct equations. We also show through examples that using the equations presented here, the dynamics of a single rigid body is reduced to the standard equations on a Lagrangian form, for example Euler's equations for rotational motion and Euler--Lagrange equations for free motion.

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.

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)

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.

Gaussian-windowed frame based method of moments formulation of surface-integral-equation for extended apertures

Energy Technology Data Exchange (ETDEWEB)

Shlivinski, A., E-mail: amirshli@ee.bgu.ac.il [Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Lomakin, V., E-mail: vlomakin@eng.ucsd.edu [Department of Electrical and Computer Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0407 (United States)

2016-03-01

Scattering or coupling of electromagnetic beam-field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation, which are solved by the Method of Moments with the aid of the Gabor-based Gaussian window frame set of basis and testing functions. The application of the Gaussian window frame provides (i) a mathematically exact and robust tool for spatial-spectral phase-space formulation and analysis of the problem; (ii) a system of linear equations in a transmission-line like form relating mode-like wave objects of one medium with mode-like wave objects of the second medium; (iii) furthermore, an appropriate setting of the frame parameters yields mode-like wave objects that blend plane wave properties (as if solving in the spectral domain) with Green's function properties (as if solving in the spatial domain); and (iv) a representation of the scattered field with Gaussian-beam propagators that may be used in many large (in terms of wavelengths) systems.

Stochastic quantization of field theories on the lattice and supersymmetrical models

International Nuclear Information System (INIS)

Aldazabal, Gerardo.

1984-01-01

Several aspects of the stochastic quantization method are considered. Specifically, field theories on the lattice and supersymmetrical models are studied. A non-linear sigma model is studied firstly, and it is shown that it is possible to obtain evolution equations written directly for invariant quantities. These ideas are generalized to obtain Langevin equations for the Wilson loops of non-abelian lattice gauge theories U (N) and SU (N). In order to write these equations, some different ways of introducing the constraints which the fields must satisfy are discussed. It is natural to have a strong coupling expansion in these equations. The correspondence with quantum field theory is established, and it is noticed that at all orders in the perturbation theory, Langevin equations reduce to Schwinger-Dyson equations. From another point of view, stochastic quantization is applied to large N matrix models on the lattice. As a result, a simple and systematic way of building reduced models is found. Referring to stochastic quantization in supersymmetric theories, a simple supersymmetric model is studied. It is shown that it is possible to write an evolution equation for the superfield wich leads to quantum field theory results in equilibrium. As the Langevin equation preserves supersymmetry, the property of dimensional reduction known for the quantum model is shown to be valid at all times. (M.E.L.) [es

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.

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)

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.

HELAC-Onia: an automatic matrix element generator for heavy quarkonium physics

CERN Document Server

Shao, Hua-Sheng

2013-01-01

By the virtues of the Dyson-Schwinger equations, we upgrade the published code \\mtt{HELAC} to be capable to calculate the heavy quarkonium helicity amplitudes in the framework of NRQCD factorization, which we dub \\mtt{HELAC-Onia}. We rewrote the original \\mtt{HELAC} to make the new program be able to calculate helicity amplitudes of multi P-wave quarkonium states production at hadron colliders and electron-positron colliders by including new P-wave off-shell currents. Therefore, besides the high efficiencies in computation of multi-leg processes within the Standard Model, \\mtt{HELAC-Onia} is also sufficiently numerical stable in dealing with P-wave quarkonia (e.g. $h_{c,b},\\chi_{c,b}$) and P-wave color-octet intermediate states. To the best of our knowledge, it is a first general-purpose automatic quarkonium matrix elements generator based on recursion relations on the market.

Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization

Directory of Open Access Journals (Sweden)

Nedelko Sergei N.

2017-01-01

Full Text Available An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-self-dual gluon fields is reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral SUL(Nf × SUR(Nf and UA(1 symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal n-point interaction vertices given by the quark-gluon loops averaged over the background ensemble. Systematic results for the mass spectrum and decay constants of radially excited light, heavy-light mesons and heavy quarkonia are presented. Relationship of this approach to the results of functional renormalization group and Dyson-Schwinger equations, and the picture of harmonic confinement is briefly outlined.

Infrared behavior of gluons and ghosts in ghost-antighost symmetric gauges

International Nuclear Information System (INIS)

Alkofer, R.; Fischer, C.S.; Reinhardt, H.; Smekal, L. von

2003-01-01

To investigate the possibility of a ghost-antighost condensate, the coupled Dyson-Schwinger equations for the gluon and ghost propagators in Yang-Mills theories are derived in general covariant gauges, including ghost-antighost symmetric gauges. The infrared behavior of these two-point functions is studied in a bare-vertex truncation scheme which has proven to be successful in the Landau gauge. In all linear covariant gauges the same infrared behavior as in the Landau gauge is found: The gluon propagator is infrared-suppressed whereas the ghost propagator is infrared-enhanced. This infrared singular behavior provides an indication against a ghost-antighost condensate. In the ghost-antighost symmetric gauges we find that the infrared behavior of the gluon and ghost propagators cannot be determined when replacing all dressed vertices by bare ones. The question of a BRS invariant dimension-2 condensate remains to be further studied

Deconfinement and hadron properties at extremes of temperature and density

International Nuclear Information System (INIS)

Blaschke, D.; Roberts, C.D.

1998-01-01

After introducing essential, qualitative concepts and results, the authors discuss the application of Dyson-Schwinger equations to QCD at finite T and μ. They summarize the calculation of the critical exponents of two-light-flavor QCD using the chiral and thermal susceptibilities; and an algebraic model that elucidates the origin of an anticorrelation between the μ- and T-dependence of a range of meson properties. That model also provides an algebraic understanding of why the finite-T behavior of bulk thermodynamic properties is mirrored in their μ-dependence, and why meson masses decrease with μ even though f π and - increase. The possibility of diquark condensation is canvassed. Its realization is uncertain because it is contingent upon an assumption abut the quark-quark scattering kernel that is demonstrably false in some applications; e.g., it predicts the existence of colored diquarks in the strong interaction spectrum, which are not observed

Nonabelian Debye screening and the {open_quotes}tsunami{close_quotes} problem

Energy Technology Data Exchange (ETDEWEB)

Pisarski, R.D. [Brookhaven National Lab., Upton, NY (United States)

1997-09-22

The phenomenon of Debye screening is familiar from electrolytes and many other systems. Recently, it has been recognized that in nonabelian gauge theories at high temperature, even perturbatively Debye screening is much more complicated than in nonrelativistic systems. This was originally derived as {open_quotes}hard thermal loops{close_quotes}. Hard thermal loops have been derived perturbatively, by a semiclassical truncation of the Schwinger-Dyson equations, and by classical kinetic theory. In this talk I give a pedagogical derivation, following that of Kelly, Liu, Lucchesi, and Manuel. The derivation is valid not just for a thermal distribution, but (modulo certain obvious restrictions) for an arbitrary initial distribution of particles. Consider, for example, the {open_quotes}tsunami{close_quotes} problem: suppose that one starts, at time t = 0, with a spatially homogenous, infinite wall of particles, all moving with the same velocity at the speed of light.

Random functions via Dyson Brownian Motion: progress and problems

International Nuclear Information System (INIS)

Wang, Gaoyuan; Battefeld, Thorsten

2016-01-01

We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C"2 locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.

Random functions via Dyson Brownian Motion: progress and problems

Energy Technology Data Exchange (ETDEWEB)

Wang, Gaoyuan; Battefeld, Thorsten [Institute for Astrophysics, University of Goettingen,Friedrich Hund Platz 1, D-37077 Goettingen (Germany)

2016-09-05

We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C{sup 2} locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.

Tensor formulation of the model equations on strong conservation form for an incompressible flow in general coordinates

DEFF Research Database (Denmark)

Jørgensen, Bo Hoffmann

2003-01-01

This brief report expresses the basic equations of an incompressible flow model in a form which can be translated easily into the form used by a numerical solver. The application of tensor notation makes is possible to effectively address the issue ofnumerical robustness and stating the model...... equations on a general form which accommodate curvilinear coordinates. Strong conservation form is obtained by formulating the equations so that the flow variables, velocity and pressure, are expressed in thephysical coordinate system while the location of evaluation is expressed within the transformed...... form of the equations is included which allows for special solutions to be developed in the transformedcoordinate system. Examples of applications are atmospheric flows over complex terrain, aerodynamically flows, industrial flows and environmental flows....

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 .

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

Science.gov (United States)

Daniele, C. J.; Lorenzo, C. F.

1979-01-01

Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

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...

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.)

Kaon-nucleon scattering in three-dimensional technique

International Nuclear Information System (INIS)

Salam, Agus; Fachruddin, Imam

2016-01-01

Kaon-nucleon (KN) scattering is formulated in the three-dimensional (3D) momentum space, in which the basis state is not expanded into partial waves. Based on this basis the Lippmann-Schwinger equation for the T-matrix is evaluated. We obtain as final equation for the T-matrix elements a set of two coupled integral equations in two variables, which are the momentum’s magnitude and the scattering angle. Calculations for the differential cross section and some spin observables are shown, for which we employ a hadrons exchange model with the second order contributions only.

Kaon-nucleon scattering in three-dimensional technique

Energy Technology Data Exchange (ETDEWEB)

Salam, Agus, E-mail: agus.salam@sci.ui.ac.id; Fachruddin, Imam [Departemen Fisika, FMIPA, Universitas Indonesia, Depok 16424 (Indonesia)

2016-03-11

Kaon-nucleon (KN) scattering is formulated in the three-dimensional (3D) momentum space, in which the basis state is not expanded into partial waves. Based on this basis the Lippmann-Schwinger equation for the T-matrix is evaluated. We obtain as final equation for the T-matrix elements a set of two coupled integral equations in two variables, which are the momentum’s magnitude and the scattering angle. Calculations for the differential cross section and some spin observables are shown, for which we employ a hadrons exchange model with the second order contributions only.

Implications of a wavepacket formulation for the nonlinear parabolized stability equations to hypersonic boundary layers

Science.gov (United States)

Kuehl, Joseph

2016-11-01

The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.

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...

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

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

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.)

A tensor formulation of the equation of transfer for spherically symmetric flows. [radiative transfer in seven dimensional Riemannian space

Science.gov (United States)

Haisch, B. M.

1976-01-01

A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

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

An upscaled two-equation model of transport in porous media through unsteady-state closure of volume averaged formulations

Science.gov (United States)

Chaynikov, S.; Porta, G.; Riva, M.; Guadagnini, A.

2012-04-01

We focus on a theoretical analysis of nonreactive solute transport in porous media through the volume averaging technique. Darcy-scale transport models based on continuum formulations typically include large scale dispersive processes which are embedded in a pore-scale advection diffusion equation through a Fickian analogy. This formulation has been extensively questioned in the literature due to its inability to depict observed solute breakthrough curves in diverse settings, ranging from the laboratory to the field scales. The heterogeneity of the pore-scale velocity field is one of the key sources of uncertainties giving rise to anomalous (non-Fickian) dispersion in macro-scale porous systems. Some of the models which are employed to interpret observed non-Fickian solute behavior make use of a continuum formulation of the porous system which assumes a two-region description and includes a bimodal velocity distribution. A first class of these models comprises the so-called ''mobile-immobile'' conceptualization, where convective and dispersive transport mechanisms are considered to dominate within a high velocity region (mobile zone), while convective effects are neglected in a low velocity region (immobile zone). The mass exchange between these two regions is assumed to be controlled by a diffusive process and is macroscopically described by a first-order kinetic. An extension of these ideas is the two equation ''mobile-mobile'' model, where both transport mechanisms are taken into account in each region and a first-order mass exchange between regions is employed. Here, we provide an analytical derivation of two region "mobile-mobile" meso-scale models through a rigorous upscaling of the pore-scale advection diffusion equation. Among the available upscaling methodologies, we employ the Volume Averaging technique. In this approach, the heterogeneous porous medium is supposed to be pseudo-periodic, and can be represented through a (spatially) periodic unit cell

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

Group integration for lattice gauge theory at large and at small coupling

International Nuclear Information System (INIS)

Brower, R.C.; Nauenberg, M.

1981-01-01

We consider the fundamental SU(N) invariant integrals encountered in Wilson's lattice QCD with an eye to analytical results for N → infinite and approximations for small g 2 at fixed N. We develop a new semiclassical technique starting from the Schwinger-Dyson equations cast in differential form to give an exact solution to the single-link integral for N → infinite. The third-order phase transition discovered by Gross and Witten for two-dimensional QCD occurs here for any dimension. Alternatively we parametrize directly the integral over the Haar measure and obtain approximate results for SU(N) using stationary phase at small g 2 . Remarkably the single-loop correction gives the exact answer at N = infinite. We show that the naive lattice string of Weingarten is obtained from N → infinite QCD in the limit of dimensions d → infinite. We discuss applications of our techniques to the 1/N expansion. (orig.)

Deconfinement and hadron properties at extremes of temperature and density

International Nuclear Information System (INIS)

Blaschke, D.

1998-01-01

After introducing essential, qualitative concepts and results, we discuss the application of Dyson-Schwinger equations to QCD at finite T and μ. We summarise the calculation of the critical exponents of two-light-flavour QCD using the chiral and thermal susceptibilities; and an algebraic model that elucidates the origin of an anticorrelation between the μ- and T-dependence of a range of meson properties. That model also provides an algebraic understanding of why the finite-T behaviour of bulk thermodynamic properties is mirrored in their μ-dependence, and why meson masses decrease with μ even though f π and - left angle anti qq right angle increase. The possibility of diquark condensation is canvassed. Its realisation is uncertain because it is contingent upon an assumption about the quark-quark scattering kernel that is demonstrably false in some applications; e.g., it predicts the existence of coloured diquarks in the strong interaction spectrum, which are not observed. (orig.)

Leading CFT constraints on multi-critical models in d>2

Energy Technology Data Exchange (ETDEWEB)

Codello, Alessandro [CP-Origins, University of Southern Denmark,Campusvej 55, 5230 Odense M (Denmark); INFN - Sezione di Bologna,via Irnerio 46, 40126 Bologna (Italy); Safari, Mahmoud [INFN - Sezione di Bologna,via Irnerio 46, 40126 Bologna (Italy); Dipartimento di Fisica e Astronomia, Università di Bologna,via Irnerio 46, 40126 Bologna (Italy); Vacca, Gian Paolo [INFN - Sezione di Bologna,via Irnerio 46, 40126 Bologna (Italy); Zanusso, Omar [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena,Max-Wien-Platz 1, 07743 Jena (Germany); INFN - Sezione di Bologna,via Irnerio 46, 40126 Bologna (Italy)

2017-04-21

We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial ϕ{sup m} below their upper critical dimensions d{sub c}=((2m)/(m−2)), and study them using a combination of CFT constraints, Schwinger-Dyson equation and the free theory behavior at the upper critical dimension. For even integers m≥4 these theories coincide with the Landau-Ginzburg description of multi-critical phenomena and interpolate with the unitary minimal models in d=2, while for odd m the theories are non-unitary and start at m=3 with the Lee-Yang universality class. For all the even potentials and for the Lee-Yang universality class, we show how the assumption of conformal invariance is enough to compute the scaling dimensions of the local operators ϕ{sup k} and of some families of structure constants in either the coupling’s or the ϵ-expansion. For all other odd potentials we express some scaling dimensions and structure constants in the coupling’s expansion.

Leading CFT constraints on multi-critical models in d > 2

DEFF Research Database (Denmark)

Codello, Alessandro; Safari, Mahmoud; Vacca, Gian Paolo

2017-01-01

We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial ϕm below their upper critical dimensions dc=2mm−2, and study them using a combination of CFT constraints, Schwinger-Dyson equation and the free theory behavior at the upper critical dimension....... For even integers m ≥ 4 these theories coincide with the Landau-Ginzburg description of multi-critical phenomena and interpolate with the unitary minimal models in d = 2, while for odd m the theories are non-unitary and start at m = 3 with the Lee-Yang universality class. For all the even potentials...... and for the Lee-Yang universality class, we show how the assumption of conformal invariance is enough to compute the scaling dimensions of the local operators ϕk and of some families of structure constants in either the coupling’s or the ϵ-expansion. For all other odd potentials we express some scaling dimensions...

Baryon Spectroscopy at ELSA and at MAMI - selected results

Science.gov (United States)

Krusche, B.

2014-05-01

Spectroscopy of baryons and their excited states plays a key role for our understanding of the strong interaction in the non-perturbative regime. Both, in theory and in experiment, large progress has been made during the last few years. The rapid developments in lattice gauge calculations and the application of the Dyson-Schwinger equation to QCD have opened new perspectives for the interpretation of the excitation spectrum of the nucleon. In parallel, large efforts have been undertaken world-wide, and are still running, to investigate excited nucleon states experimentally, in particular with photon-induced production of mesons. In the present contribution we discuss such experimental programs conducted at the tagged photon beams of the electron accelerators ELSA in Bonn and MAMI in Mainz. These programs are diverse. They include the measurement of cross sections, single- and double polarization observables for single meson production and production of meson pairs off free protons as well as of quasi-free nucleons bound in the deuteron (and sometimes other light nuclei).

Ghost-gluon vertex in the presence of the Gribov horizon

Science.gov (United States)

Mintz, B. W.; Palhares, L. F.; Sorella, S. P.; Pereira, A. D.

2018-02-01

We consider Yang-Mills theories quantized in the Landau gauge in the presence of the Gribov horizon via the refined Gribov-Zwanziger (RGZ) framework. As the restriction of the gauge path integral to the Gribov region is taken into account, the resulting gauge field propagators display a nontrivial infrared behavior, being very close to the ones observed in lattice gauge field theory simulations. In this work, we explore a higher correlation function in the refined Gribov-Zwanziger theory: the ghost-gluon interaction vertex, at one-loop level. We show explicit compatibility with kinematical constraints, as required by the Ward identities of the theory, and obtain analytical expressions in the limit of vanishing gluon momentum. We find that the RGZ results are nontrivial in the infrared regime, being compatible with lattice Yang-Mills simulations in both SU(2) and SU(3), as well as with solutions from Schwinger-Dyson equations in different truncation schemes, Functional Renormalization Group analysis, and the renormalization group-improved Curci-Ferrari model.

Colored Tensor Models - a Review

Directory of Open Access Journals (Sweden)

Razvan Gurau

2012-04-01

Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.

Deconfinement and hadron properties at extremes of temperature and density

Energy Technology Data Exchange (ETDEWEB)

Blaschke, D. [Univ. Rostock (Germany). Fachbereich Physik; Roberts, C.D. [Argonne National Lab., IL (United States). Physics Div.

1998-08-01

After introducing essential, qualitative concepts and results, the authors discuss the application of Dyson-Schwinger equations to QCD at finite T and {mu}. They summarize the calculation of the critical exponents of two-light-flavor QCD using the chiral and thermal susceptibilities; and an algebraic model that elucidates the origin of an anticorrelation between the {mu}- and T-dependence of a range of meson properties. That model also provides an algebraic understanding of why the finite-T behavior of bulk thermodynamic properties is mirrored in their {mu}-dependence, and why meson masses decrease with {mu} even though f{sub {pi}} and {minus}<{anti q}q> increase. The possibility of diquark condensation is canvassed. Its realization is uncertain because it is contingent upon an assumption abut the quark-quark scattering kernel that is demonstrably false in some applications; e.g., it predicts the existence of colored diquarks in the strong interaction spectrum, which are not observed.

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...

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.

Shield Optimization and Formulation of Regression Equations for Split-Ring Resonator

Directory of Open Access Journals (Sweden)

Tahir Ejaz

2016-01-01

Full Text Available Microwave resonators are widely used for numerous applications including communication, biomedical and chemical applications, material testing, and food grading. Split-ring resonators in both planar and nonplanar forms are a simple structure which has been in use for several decades. This type of resonator is characterized with low cost, ease of fabrication, moderate quality factor, low external noise interference, high stability, and so forth. Due to these attractive features and ease in handling, nonplanar form of structure has been utilized for material characterization in 1–5 GHz range. Resonant frequency and quality factor are two important parameters for determination of material properties utilizing perturbation theory. Shield made of conducting material is utilized to enclose split-ring resonator which enhances quality factor. This work presents a novel technique to develop shield around a predesigned nonplanar split-ring resonator to yield optimized quality factor. Based on this technique and statistical analysis regression equations have also been formulated for resonant frequency and quality factor which is a major outcome of this work. These equations quantify dependence of output parameters on various factors of shield made of different materials. Such analysis is instrumental in development of devices/designs where improved/optimum result is required.

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

International Nuclear Information System (INIS)

Nakawaki, Yuji; McCartor, Gary

2004-01-01

Canonical methods are not sufficient to properly quantize space-like axial gauges. In this paper, we obtain guiding principles that allow for the construction of an extended Hamiltonian formalism for pure space-like axial gauge fields. To do so, we clarify the general role that residual gauge fields play in the space-like axial gauge Schwinger model. In all the calculations, we fix the gauge using the rule n·A=0, where n is a space-like constant vector, and we refer to its direction as x - . Then, to begin with, we construct a formulation in which the quantization surface is space-like but not parallel to the direction of n. The quantization surface has a parameter that allows us to rotate it, but when we do so, we keep the gauge fixing direction fixed. In that formulation, we can use canonical methods. We bosonize the model to simplify the investigation. We find that the inverse differentiation, (∂ - ) -1 , is ill-defined whatever quantization coordinates we use, as long as the direction of n is space-like. We find that the physical part of the dipole ghost field includes infrared divergences. However, we also find that if we introduce residual gauge fields in such as way that the dipole ghost field satisfies the canonical commutation relations, then the residual gauge fields are determined so as to regularize the infrared divergences contained in the physical part. The propagators then take the form prescribed by Mandelstam and Leibbrandt. We make use of these properties to develop guiding principles that allow us to construct consistent operator solutions in the pure space-like case, in which the quantization surface is parallel to the direction of n, and canonical methods do not suffice. (author)

Ward-Takahashi identities in quantum electrodynamics

Energy Technology Data Exchange (ETDEWEB)

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

1975-03-01

The Ward-Takahashi identities are derived for connected Green's functions in quantum electrodynamics without recourse to equal-time commutation relations, field equations and the Feynman-Dyson perturbation expansions. The argument is based on the dispersion formulation of field theories and only finite expressions are used throughout this derivation. These identities are shown to be consequences of the subtraction conditions imposed upon the 2-, 3- and 4-point Green's functions.

Derivation of finite element formulation for electrochemical governing equations of ionic polymer actuators

International Nuclear Information System (INIS)

Kang, Sung Soo

2013-01-01

Ionic polymer actuators have recently attracted a great deal of interest as electroactive materials with potentials as soft actuators, sensors, artificial muscles, robotics, and microelectromechanical systems because of their numerous advantages, including low voltage requirement, high compliance, lightness, and flexibility. The platinum-plated Nafion, a perfluorosulfonic acid membrane made by Dupont, is commonly used as a polyelectrolyte in actuator applications. The bending of the ionic polymer actuators in an electric field is dominated by the electro-osmosis of hydrated ions and slow diffusion of free water molecules. The changes in hydration cause a local volumetric strain resulting in bending deformation, such as expansion and contraction. In this study, a two-dimensional finite element (FE) formulation based on the Galerkin method is derived for the governing equations describing these electrochemical responses. In addition, a three-dimensional FE deformation analysis is conducted on the bending behaviors of the platinum-plated ionic polymer actuators. Several numerical studies for ionic polymer actuators, such as plates with various electrode arrangements and disk models in electric field, are performed to confirm the validity of the proposed formulation.

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

A renormalizable extension of the NJL-model

International Nuclear Information System (INIS)

Langfeld, K.; Kettner, C.; Reinhardt, H.

1996-01-01

The Nambu-Jona-Lasinio model is supplemented by the quark interaction generated by the one-gluon exchange. The employed gluon propagator exhibits the correct large-momentum behavior of QCD, whereas the Landau pole at low energies is screened. The emerging constituent quark model is one-loop renormalizable and interpolates between the phenomenologically successful Nambu-Jona-Lasinio model (modified by a transversal projector) at low energies and perturbative QCD at high momenta. Consequently, the momentum dependence of the quark self-energy at high energy coincides with the prediction from perturbative QCD. The chiral phase transition is studied in dependence on the low-energy four-quark interaction strength in the Dyson-Schwinger equation approach. The critical exponents of the quark self-energy and the quark condensate are obtained. The latter exponent deviates from the NJL-result. Pion properties are addressed by means of the Bethe-Salpeter equation. The validity of the Gell-Mann-Oakes-Renner relation is verified. Finally, we study the conditions under which the Nambu-Jona-Lasinio model is a decent approximation to our renormalizable theory as well as the shortcoming of the NJL-model due to its inherent non-renormalizability. (orig.)

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.

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.)

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)

Exploring the Quark-Gluon Content of Hadrons: From Mesons to Nuclear Matter

International Nuclear Information System (INIS)

Hrayr Matevosyan

2007-01-01

Even though Quantum Chromodynamics (QCD) was formulated over three decades ago, it poses enormous challenges for describing the properties of hadrons from the underlying quark-gluon degrees of freedom. Moreover, the problem of describing the nuclear force from its quark-gluon origin is still open. While a direct solution of QCD to describe the hadrons and nuclear force is not possible at this time, we explore a variety of developed approaches ranging from phenomenology to first principle calculations at one or other level of approximation in linking the nuclear force to QCD. The Dyson Schwinger formulation (DSE) of coupled integral equations for the QCD Green's functions allows a non-perturbative approach to describe hadronic properties, starting from the level of QCD n-point functions. A significant approximation in this method is the employment of a finite truncation of the system of DSEs, that might distort the physical picture. In this work we explore the effects of including a more complete truncation of the quark-gluon vertex function on the resulting solutions for the quark 2-point functions as well as the pseudoscalar and vector meson masses. The exploration showed strong indications of possibly large contributions from the explicit inclusion of the gluon 3- and 4-point functions that are omitted in this and previous analyses. We then explore the possibility of extrapolating state of the art lattice QCD calculations of nucleon form factors to the physical regime using phenomenological models of nucleon structure. Finally, we further developed the Quark Meson Coupling model for describing atomic nuclei and nuclear matter, where the quark-gluon structure of nucleons is modeled by the MIT bag model and the nucleon many body interaction is mediated by the exchange of scalar and vector mesons. This approach allows us to formulate a fully relativistic theory, which can be expanded in the nonrelativistic limit to reproduce the well known phenomenological Skyrme

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.

Generalized variational formulations for extended exponentially fractional integral

Directory of Open Access Journals (Sweden)

Zuo-Jun Wang

2016-01-01

Full Text Available Recently, the fractional variational principles as well as their applications yield a special attention. For a fractional variational problem based on different types of fractional integral and derivatives operators, corresponding fractional Lagrangian and Hamiltonian formulation and relevant Euler–Lagrange type equations are already presented by scholars. The formulations of fractional variational principles still can be developed more. We make an attempt to generalize the formulations for fractional variational principles. As a result we obtain generalized and complementary fractional variational formulations for extended exponentially fractional integral for example and corresponding Euler–Lagrange equations. Two illustrative examples are presented. It is observed that the formulations are in exact agreement with the Euler–Lagrange equations.

Thermodynamic Green functions in theory of superconductivity

Directory of Open Access Journals (Sweden)

N.M.Plakida

2006-01-01

Full Text Available A general theory of superconductivity is formulated within the thermodynamic Green function method for various types of pairing mediated by phonons, spin fluctuations, and strong Coulomb correlations in the Hubbard and t-J models. A rigorous Dyson equation for matrix Green functions is derived in terms of a self-energy as a many-particle Green function. By applying the noncrossing approximation for the self-energy, a closed self-consistent system of equations is obtained, similar to the conventional Eliashberg equations. A brief discussion of superconductivity mediated by kinematic interaction with an estimation of a superconducting transition temperature in the Hubbard model is given.

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.

Nonequilibrium phenomena in QCD and BEC. Boltzmann and beyond

Energy Technology Data Exchange (ETDEWEB)

Stockamp, T.

2006-12-22

In chapter 2 we chose the real time formalism to discuss some basic principles in quantum field theory at finite temperature. This enables us to derive the quantum Boltzmann equation from the Schwinger-Dyson series. We then shortly introduce the basic concepts of QCD which are needed to understand the physics of QGP formation. After a detailed account on the bottom-up scenario we show the consistency of this approach by a diagramatical analysis of the relevant Boltzmann collision integrals. Chapter 3 deals with BEC dynamics out of equilibrium. After an introduction to the fundamental theoretical tool - namely the Gross-Pitaevskii equation - we focus on a generalization to finite temperature developed by Zaremba, Nikuni and Griffin (ZNG). These authors use a Boltzmann equation to describe the interactions between condensed and excited atoms and manage in this way to describe condensate growth. We then turn to a discussion on the 2PI effective action and derive equations of motion for a relativistic scalar field theory. In the nonrelativistic limit these equations are shown to coincide with the ZNG theory when a quasiparticle approximation is applied. Finally, we perform a numerical analysis of the full 2PI equations. These remain valid even at strong coupling and far from equilibrium, and thus go far beyond Boltzmann's approach. For simplicity, we limit ourselves to a homogeneous system and present the first 3+1 dimensional study of condensate melting. (orig.)

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.

Collecting, Preserving, and Interpreting the History of Electronic Games: An Interview with Jon-Paul C. Dyson

Science.gov (United States)

American Journal of Play, 2017

2017-01-01

Jon-Paul C. Dyson is vice president for exhibits and director of the International Center for the History of Electronic Games (ICHEG) at The Strong. Trained as a cultural and intellectual historian, he joined The Strong in 1998 and has worked on and supervised the development of dozens of exhibits on play and video games. He initiated the museum's…

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

Least-Squares PN Formulation of the Transport Equation Using Self-Adjoint-Angular-Flux Consistent Boundary Conditions

Energy Technology Data Exchange (ETDEWEB)

Laboure, Vincent M.; Wang, Yaqi; DeHart, Mark D.

2016-05-01

In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids [1] in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment [2], in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework [3] using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutions (MMS) and find the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.

Least-Squares PN Formulation of the Transport Equation Using Self-Adjoint-Angular-Flux Consistent Boundary Conditions.

Energy Technology Data Exchange (ETDEWEB)

Vincent M. Laboure; Yaqi Wang; Mark D. DeHart

2016-05-01

In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment, in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutions (MMS) and find the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.

Continuum-regularized quantum gravity

International Nuclear Information System (INIS)

Chan Huesum; Halpern, M.B.

1987-01-01

The recent continuum regularization of d-dimensional Euclidean gravity is generalized to arbitrary power-law measure and studied in some detail as a representative example of coordinate-invariant regularization. The weak-coupling expansion of the theory illustrates a generic geometrization of regularized Schwinger-Dyson rules, generalizing previous rules in flat space and flat superspace. The rules are applied in a non-trivial explicit check of Einstein invariance at one loop: the cosmological counterterm is computed and its contribution is included in a verification that the graviton mass is zero. (orig.)

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.

The exact Laplacian spectrum for the Dyson hierarchical network.

Science.gov (United States)

Agliari, Elena; Tavani, Flavia

2017-01-09

We consider the Dyson hierarchical graph , that is a weighted fully-connected graph, where the pattern of weights is ruled by the parameter σ ∈ (1/2, 1]. Exploiting the deterministic recursivity through which is built, we are able to derive explicitly the whole set of the eigenvalues and the eigenvectors for its Laplacian matrix. Given that the Laplacian operator is intrinsically implied in the analysis of dynamic processes (e.g., random walks) occurring on the graph, as well as in the investigation of the dynamical properties of connected structures themselves (e.g., vibrational structures and relaxation modes), this result allows addressing analytically a large class of problems. In particular, as examples of applications, we study the random walk and the continuous-time quantum walk embedded in , the relaxation times of a polymer whose structure is described by , and the community structure of in terms of modularity measures.

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

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 %.

A stabilized finite element formulation for the solution of the Navier-Stokes equations in axisymmetric geometry

International Nuclear Information System (INIS)

Souza, Altivo Monteiro de

2008-12-01

The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS S OLVER M PI 2 D A program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)

A Lagrange-Eulerian formulation of an axially moving beam based on the absolute nodal coordinate formulation

Energy Technology Data Exchange (ETDEWEB)

Pechstein, Astrid, E-mail: astrid.pechstein@jku.at [Johannes Kepler University Linz, Institute of Technical Mechanics (Austria); Gerstmayr, Johannes, E-mail: johannes.gerstmayr@accm.co.at [Austrian Center of Competence in Mechatronics (Austria)

2013-10-15

In the scope of this paper, a finite-element formulation for an axially moving beam is presented. The beam element is based on the absolute nodal coordinate formulation, where position and slope vectors are used as degrees of freedom instead of rotational parameters. The equations of motion for an axially moving beam are derived from generalized Lagrange equations in a Lagrange-Eulerian sense. This procedure yields equations which can be implemented as a straightforward augmentation to the standard equations of motion for a Bernoulli-Euler beam. Moreover, a contact model for frictional contact between an axially moving strip and rotating rolls is presented. To show the efficiency of the method, simulations of a belt drive are presented.

Estudi i modificació d’un difusor de ventilador tipus Dyson Air Multiplier

OpenAIRE

Soler Calderé, Roger

2014-01-01

[CATALÀ] El Dyson Air Multiplier és un tipus de ventilador de sobre taula sense aspes, que produeix un corrent d’aire continu. Per crear aquest corrent, l’aire és accelerat a través d’una obertura anular creant un cabal d’aire a alta velocitat. Aquest flux d’aire passa per una superfície aerodinàmica que canalitza la seva direcció i genera zones de baixa pressió. Aquest canvi de pressió aspira l’aire de l’entorn cap al corrent d’aire, augmentant el cabal mobilitzat. Per a realitzar el seu est...

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} %.

Stability of non-linear constitutive formulations for viscoelastic fluids

CERN Document Server

Siginer, Dennis A

2014-01-01

Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities.

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.)

Mass generation and the problem of seagull divergences

International Nuclear Information System (INIS)

Figueiredo, C. T.; Aguilar, A. C.

2016-01-01

The gluon mass generation is a purely non-perturbative effect, and the natural framework to study it in the continuum are the Schwinger-Dyson equations (SDEs) of the theory. At the level of the SDEs the generation of such a mass is associated with the existence of infrared finite solutions for the gluon propagator. From the theoretical point of view, the dynamical gluon mass generation has been traditionally plagued with seagull divergences. In this work, we will review how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. As a pedagogical example, we will first discuss in the context of scalar QED how it is possible to eliminate all seagull divergences, by triggering the aforementioned special identity, which enforces the masslessness of the photon. Then, we will discuss what happens in QCD and present an Ansatz for the three gluon vertex, which completely eliminates all seagull divergences and at same time allows for the possibility of a dynamical gluon mass generation. (paper)

Nucleon Resonance Physics

Energy Technology Data Exchange (ETDEWEB)

Burkert, Volker D.

2016-07-25

Recent results of meson photo-production at the existing electron machines with polarized real photon beams and the measurement of polarization observables of the final state baryons have provided high precision data that led to the discovery of new excited nucleon and $\\Delta$ states using multi-channel partial wave analyses procedures. The internal structure of several prominent excited states has been revealed employing meson electroproduction processes. On the theoretical front, lattice QCD is now predicting the baryon spectrum with very similar characteristics as the constituent quark model, and continuum QCD, such as is represented in the Dyson-Schwinger Equations approach and in light front relativistic quark models, describes the non-perturbative behavior of resonance excitations at photon virtuality of $Q^2 > 1.5GeV^2$. In this talk I discuss the need to continue a vigorous program of nucleon spectroscopy and the study of the internal structure of excited states as a way to reveal the effective degrees of freedom underlying the excited states and their dependence on the distance scale probed.

Superconductivity in 2+1 dimensions without parity or time-reversal violation

International Nuclear Information System (INIS)

Dorey, N.; Mavromatos, N.E.

1990-01-01

A model of dynamical holes in a planar quantum antiferromagnet is analysed in the limit of large spin and small doping concentration. The long-wavelength limit of this system is found to be a relativistic QFT of multiflavour Dirac fermions with both four-fermion and statistical chiral gauge interactions. The Schwinger-Dyson equation for the fermion self-energy is solved in the limit of many flavours and the theory is found to possess a phase in which the global vector symmetry of the effective action is realised in the Kosterlitz-Thouless mode. The theory exhibits superconductivity without parity or time-reversal violation in this phase and the charge quantum assumes the phenomenologically relevant value of 2e. The mechanism is conjectured to be 'holepair' condensation due primarily to the statistical gauge interaction. Although there is a formal similarity with BCS theory the physical origin of the attraction between holes is quite different. The model may provide a prototype for further studies in realistic microscopic systems that attempt to simulate planar high temperature superconducting oxides. (orig.)

Electromagnetic properties of the pion as a composite Nambu-Goldstone boson

International Nuclear Information System (INIS)

Ito, H.; Buck, W.W.; Gross, F.

1992-01-01

Motivated by the Nambu--Jona-Lasinio model of light mesons, we introduce a covariant separable interaction to model the structure of relativistic quark-antiquark systems. The Schwinger-Dyson equation for the quark self-energy is solved analytically, generating a dynamical quark mass through spontaneous breaking of chiral symmetry, and yielding a pion which has zero mass in the chiral limit. The Bethe-Salpeter vertex function for this q bar q pion, which has a momentum distribution and composite structure associated with the interaction, is obtained analytically. Using this vertex function, and a similar one for the ρ meson, we calculate the electromagnetic observables of this composite Nambu-Goldstone boson, including effects from ρ-meson dominance processes. Our calculation takes the composite structure of the mesons into account. The ρ-meson effects are found to be very small in the pion charge form factor, but substantial in the charge radius. Using the model, predictions are made for γ * π 0 →γ and ρπγ transition form factors

Thermalization dynamics of two correlated bosonic quantum wires after a split

Science.gov (United States)

Huber, Sebastian; Buchhold, Michael; Schmiedmayer, Jörg; Diehl, Sebastian

2018-04-01

Cherently splitting a one-dimensional Bose gas provides an attractive, experimentally established platform to investigate many-body quantum dynamics. At short enough times, the dynamics is dominated by the dephasing of single quasiparticles, and well described by the relaxation towards a generalized Gibbs ensemble corresponding to the free Luttinger theory. At later times on the other hand, the approach to a thermal Gibbs ensemble is expected for a generic, interacting quantum system. Here, we go one step beyond the quadratic Luttinger theory and include the leading phonon-phonon interactions. By applying kinetic theory and nonequilibrium Dyson-Schwinger equations, we analyze the full relaxation dynamics beyond dephasing and determine the asymptotic thermalization process in the two-wire system for a symmetric splitting protocol. The major observables are the different phonon occupation functions and the experimentally accessible coherence factor, as well as the phase correlations between the two wires. We demonstrate that, depending on the splitting protocol, the presence of phonon collisions can have significant influence on the asymptotic evolution of these observables, which makes the corresponding thermalization dynamics experimentally accessible.

Continuum regularized Yang-Mills theory

International Nuclear Information System (INIS)

Sadun, L.A.

1987-01-01

Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions

Lorentz-covariant reduced-density-operator theory for relativistic-quantum-information processing

International Nuclear Information System (INIS)

Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo

2003-01-01

In this paper, we derived a Lorentz-covariant quantum Liouville equation for the density operator which describes the relativistic-quantum-information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced density operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of the nonrelativistic case, which is valid only in some specified reference frame. To show that our formulation can be applied to practical problems, we derived the polarization of the vacuum in quantum electrodynamics up to the second order. The formulation presented in this work is general and could be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics

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

Mixed hyperbolic-second-order-parabolic formulations of general relativity

International Nuclear Information System (INIS)

Paschalidis, Vasileios

2008-01-01

Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt-Deser-Misner formulation and is derived by the addition of combinations of the constraints and their derivatives to the right-hand side of the Arnowitt-Deser-Misner evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic--second-order parabolic. The second formulation is a parabolization of the Kidder-Scheel-Teukolsky formulation and is a manifestly mixed strongly hyperbolic--second-order-parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint-violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.

Formulations to overcome the divergence of iterative method of fixed-point in nonlinear equations solution

Directory of Open Access Journals (Sweden)

Wilson Rodríguez Calderón

2015-04-01

Full Text Available When we need to determine the solution of a nonlinear equation there are two options: closed-methods which use intervals that contain the root and during the iterative process reduce the size of natural way, and, open-methods that represent an attractive option as they do not require an initial interval enclosure. In general, we know open-methods are more efficient computationally though they do not always converge. In this paper we are presenting a divergence case analysis when we use the method of fixed point iteration to find the normal height in a rectangular channel using the Manning equation. To solve this problem, we propose applying two strategies (developed by authors that allow to modifying the iteration function making additional formulations of the traditional method and its convergence theorem. Although Manning equation is solved with other methods like Newton when we use the iteration method of fixed-point an interesting divergence situation is presented which can be solved with a convergence higher than quadratic over the initial iterations. The proposed strategies have been tested in two cases; a study of divergence of square root of real numbers was made previously by authors for testing. Results in both cases have been successful. We present comparisons because are important for seeing the advantage of proposed strategies versus the most representative open-methods.

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.

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.

Formulation matricielle des equations du mouvement d'un solide ...

African Journals Online (AJOL)

Plusieurs formulations des équations du mouvement d'un rigide ont été développées. Le bien connu d'entre elles est celle de Newton-Euler; elle est généralement appelée «équations d'Euler classiques". Cette formulation donne six équations scalaires pour un corps rigide. Dans cet article, nous avons décrit les équations ...

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

International Nuclear Information System (INIS)

Geiger, K.

1996-01-01

A quantum-kinetic formalism is developed to study the dynamical interplay of quantum and statistical-kinetic properties of nonequilibrium multiparton 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 open-quote open-quote closed-time-path close-quote close-quote 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 two-point functions of the gluon and quark fields. By exploiting the open-quote open-quote two-scale nature close-quote close-quote 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 interactions, the quantum field equations of motion are converted into a corresponding set of open-quote open-quote renormalization equations close-quote close-quote and open-quote open-quote transport equations.close-quote close-quote The former describe renormalization and dissipation effects through the evolution of the spectral density of individual, dressed partons, whereas the latter determine the statistical occurrence of scattering processes among these dressed partons. The renormalization equations and the transport equations are coupled, and, hence, must be solved self-consistently. This amounts to evolving the multiparton system, from a specified initial configuration, in time and full seven-dimensional phase space, constrained by the Heisenberg uncertainty principle. (Abstract Truncated)

Path probabilities of continuous time random walks

International Nuclear Information System (INIS)

Eule, Stephan; Friedrich, Rudolf

2014-01-01

Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)

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

Petrov-Galerkin mixed formulations for bidimensional elasticity

International Nuclear Information System (INIS)

Toledo, E.M.; Loula, A.F.D.; Guerreiro, J.N.C.

1989-10-01

A new formulation for two-dimensional elasticity in stress and displacements is presented. Consistently adding to the Galerkin classical formulation residuals forms of constitutive and equilibrium equations, the original saddle point is transformed into a minimization problem without any restrictions. We also propose a stress post processing technique using both equilibrium and constitutive equations. Numerical analysis error estimates and numerical results are presented confirming the predicted rates of convergence. (A.C.A.S.) [pt

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.

Preliminary Formulation of Finite Element Solution for the 1-D, 1-G Time Dependent Neutron Diffusion Equation without Consideration about Delay Neutron

Energy Technology Data Exchange (ETDEWEB)

Ryu, Eun Hyun; Song, Yong Mann; Park, Joo Hwan [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2013-05-15

If time-dependent equation is solved with the FEM, the limitation of the input geometry will disappear. It has often been pointed out that the numerical methods implemented in the RFSP code are not state-of-the-art. Although an acceleration method such as the Coarse Mesh Finite Difference (CMFD) for Finite Difference Method (FDM) does not exist for the FEM, one should keep in mind that the number of time steps for the transient simulation is not large. The rigorous formulation in this study will richen the theoretical basis of the FEM and lead to an extension of the dynamics code to deal with a more complicated problem. In this study, the formulation for the 1-D, 1-G Time Dependent Neutron Diffusion Equation (TDNDE) without consideration of the delay neutron will first be done. A problem including one multiplying medium will be solved. Also several conclusions from a comparison between the numerical and analytic solutions, a comparison between solutions with various element orders, and a comparison between solutions with different time differencing will be made to be certain about the formulation and FEM solution. By investigating various cases with different values of albedo, theta, and the order of elements, it can be concluded that the finite element solution is agree well with the analytic solution. The higher the element order used, the higher the accuracy improvements are obtained.

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.

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∼

Lagrangian formulation of classical BMT-theory

International Nuclear Information System (INIS)

Pupasov-Maksimov, Andrey; Deriglazov, Alexei; Guzman, Walberto

2013-01-01

Full text: The most popular classical theory of electron has been formulated by Bargmann, Michel and Telegdi (BMT) in 1959. The BMT equations give classical relativistic description of a charged particle with spin and anomalous magnetic momentum moving in homogeneous electro-magnetic field. This allows to study spin dynamics of polarized beams in uniform fields. In particular, first experimental measurements of muon anomalous magnetic momentum were done using changing of helicity predicted by BMT equations. Surprisingly enough, a systematic formulation and the analysis of the BMT theory are absent in literature. In the present work we particularly fill this gap by deducing Lagrangian formulation (variational problem) for BMT equations. Various equivalent forms of Lagrangian will be discussed in details. An advantage of the obtained classical model is that the Lagrangian action describes a relativistic spinning particle without Grassmann variables, for both free and interacting cases. This implies also the possibility of canonical quantization. In the interacting case, an arbitrary electromagnetic background may be considered, which generalizes the BMT theory formulated to the case of homogeneous fields. The classical model has two local symmetries, which gives an interesting example of constrained classical dynamics. It is surprising, that the case of vanishing anomalous part of the magnetic momentum is naturally highlighted in our construction. (author)

Invalidity of the spectral Fokker-Planck equation forCauchy noise driven Langevin equation

DEFF Research Database (Denmark)

Ditlevsen, Ove Dalager

2004-01-01

-called alpha-stable noise (or Levy noise) the Fokker-Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. In stead it has been attempted to formulate an equation for the characteristic function (the Fourier transform...

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.

On integrability of the Killing equation

Science.gov (United States)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

Mathematical modeling of the dynamic stability of fluid conveying pipe based on integral equation formulations

International Nuclear Information System (INIS)

Elfelsoufi, Z.; Azrar, L.

2016-01-01

In this paper, a mathematical modeling of flutter and divergence analyses of fluid conveying pipes based on integral equation formulations is presented. Dynamic stability problems related to fluid pressure, velocity, tension, topography slope and viscoelastic supports and foundations are formulated. A methodological approach is presented and the required matrices, associated to the influencing fluid and pipe parameters, are explicitly given. Internal discretizations are used allowing to investigate the deformation, the bending moment, slope and shear force at internal points. Velocity–frequency, pressure-frequency and tension-frequency curves are analyzed for various fluid parameters and internal elastic supports. Critical values of divergence and flutter behaviors with respect to various fluid parameters are investigated. This model is general and allows the study of dynamic stability of tubes crossed by stationary and instationary fluid on various types of supports. Accurate predictions can be obtained and are of particular interest for a better performance and for an optimal safety of piping system installations. - Highlights: • Modeling the flutter and divergence of fluid conveying pipes based on RBF. • Dynamic analysis of a fluid conveying pipe with generalized boundary conditions. • Considered parameters fluid are the pressure, tension, slopes topography, velocity. • Internal support increase the critical velocity value. • This methodologies determine the fluid parameters effects.

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.

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

Science.gov (United States)

Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

2018-01-01

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

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.

Relations between nonlinear Riccati equations and other equations in fundamental physics

International Nuclear Information System (INIS)

Schuch, Dieter

2014-01-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown

Spectroscopy of pseudoscalar and vector mesons and their electroweak decays

International Nuclear Information System (INIS)

Ablakulov, Kh.

1997-01-01

Proceeding from the effective action of QCD for bilocal meson fields the formula for the action describing the spectroscopy of mesons and their electroweak decays is obtained. The numerical solutions of the Salpeter equation (SE) for the qq-bound state and the Schwinger-Dyson equation (SDE) for the quark phase function are obtained with potential as sum of the oscillator and Coulomb terms. It is shown that for the oscillator potential and current quark mass m 0 0 → γγ) are 3-4 times smaller than their experimentations. This discrepancy was not removed even choosing other shapes of the potential. In order to resolve this problem the modification of the SDE, which consists in introducing the additional terms that do not change asymptotical properties of solutions of this equation is proposed. Using such modification both constant fπ and Γ(π 0 → γγ) are reproduced on a good quantitative level. The new SE for vector mesons is proposed and its solution with potential mentioned above gives the mass spectra of these mesons. Considering the τ → ρν decay the representation for leptonic decay constant of ρ meson f π , which expresses via solutions of the SDE and the proposed SE with a given potential is obtained. It is shown that the proposed SE allows to describe both the spectroscopy of vector mesons and their leptonic decay constants on a satisfactory level in comparison with the experimental values. (author)

Equations of radiation hydrodynamics

International Nuclear Information System (INIS)

Mihalas, D.

1982-01-01

The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented

Spurious solutions in few-body equations

International Nuclear Information System (INIS)

Adhikari, S.K.; Gloeckle, W.

1979-01-01

After Faddeev and Yakubovskii showed how to write connected few-body equations which are free from discrete spurious solutions various authors have proposed different connected few-body scattering equations. Federbush first pointed out that Weinberg's formulation admits the existence of discrete spurious solutions. In this paper we investigate the possibility and consequence of the existence of spurious solutions in some of the few-body formulations. Contrary to a proof by Hahn, Kouri, and Levin and by Bencze and Tandy the channel coupling array scheme of Kouri, Levin, and Tobocman which is also the starting point of a formulation by Hahn is shown to admit spurious solutions. We can show that the set of six coupled four-body equations proposed independently by Mitra, Gillespie, Sugar, and Panchapakesan, by Rosenberg, by Alessandrini, and by Takahashi and Mishima and the seven coupled four-body equations proposed by Sloan and related by matrix multipliers to basic sets which correspond uniquely to the Schroedinger equation. These multipliers are likely to give spurious solutions to these equations. In all these cases spuriosities are shown to have no hazardous consequence if one is interested in studying the scattering problem

Boussinesq evolution equations

DEFF Research Database (Denmark)

Bredmose, Henrik; Schaffer, H.; Madsen, Per A.

2004-01-01

This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...

A well-conditioned integral-equation formulation for efficient transient analysis of electrically small microelectronic devices

KAUST Repository

Bagci, Hakan

2010-05-01

A hierarchically regularized coupled set of time-domain surface and volume electric field integral-equations (TD-S-EFIE and TD-V-EFIE) for analyzing electromagnetic wave interactions with electrically small and geometrically intricate composite structures comprising perfect electrically conducting surfaces and finite dielectric volumes is presented. A classically formulated coupled set of TD-S- and V-EFIEs is shown to be ill-conditioned at low frequencies owing to the hypersingular nature of the TD-S-EFIE. To eliminate low-frequency breakdown in marching-on-in-time solvers for these coupled equations, a hierarchical regularizer leveraging generalized RaoWiltonGlisson functions is applied to the TD-S-EFIE; no regularization is applied to the TD-V-EFIE as it is protected from low-frequency breakdown by an identity term. The resulting hierarchically regularized hybrid TD-S- and V-EFIE solver is applicable to the analysis of wave interactions with electrically small and densely meshed structures of arbitrary topology. The accuracy, efficiency, and applicability of the proposed solver are demonstrated by analyzing crosstalk in a six-port transmission line, radiation from a miniature radio-frequency identification antenna, and, plane-wave coupling onto a partially-shielded and fully loaded two-layer computer board. © 2006 IEEE.

Characterization of echoes: A Dyson-series representation of individual pulses

Science.gov (United States)

Correia, Miguel R.; Cardoso, Vitor

2018-04-01

The ability to detect and scrutinize gravitational waves from the merger and coalescence of compact binaries opens up the possibility to perform tests of fundamental physics. One such test concerns the dark nature of compact objects: are they really black holes? It was recently pointed out that the absence of horizons—while keeping the external geometry very close to that of General Relativity—would manifest itself in a series of echoes in gravitational wave signals. The observation of echoes by LIGO/Virgo or upcoming facilities would likely inform us on quantum gravity effects or unseen types of matter. Detection of such signals is in principle feasible with relatively simple tools but would benefit enormously from accurate templates. Here we analytically individualize each echo waveform and show that it can be written as a Dyson series, for arbitrary effective potential and boundary conditions. We further apply the formalism to explicitly determine the echoes of a simple toy model: the Dirac delta potential. Our results allow to read off a few known features of echoes and may find application in the modeling for data analysis.

Phasor Alternatives to Friis’ Transmission Equation

DEFF Research Database (Denmark)

Franek, Ondrej

2018-01-01

Two alternatives to Friis’ transmission equation in terms of phasor voltage waves are presented. In one formulation antennas are characterized by the complex effective length vectors. An additional form introducing field gain, that serves effectively as a phasor counterpart to the power gain......, is proposed. Both forms show the same degree of symmetry and modularity as the original Friis’ equation, but thanks to using phasors instead of power quantities they allow for superposition of fields or voltages. Although the new transmission equations are formulated in frequency domain, they also constitute...

Introduction to differential equations

CERN Document Server

Taylor, Michael E

2011-01-01

The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

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

Super-Group Field Cosmology in Batalin-Vilkovisky Formulation

Science.gov (United States)

Upadhyay, Sudhaker

2016-09-01

In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation.

Stationary scattering theory

International Nuclear Information System (INIS)

Combes, J.M.

1980-10-01

A complementary approach to the time dependent scattering theory for one-body Schroedinger operators is presented. The stationary theory is concerned with objects of quantum theory like scattering waves and amplitudes. In the more recent abstract stationary theory some generalized form of the Lippman-Schwinger equation plays the basic role. Solving this equation leads to a linear map between generalized eigenfunctions of the perturbed and unperturbed operators. This map is the section at fixed energy of the wave-operator from the time dependent theory. Although the radiation condition does not appears explicitely in this formulation it can be shown to hold a posteriori in a variety of situations thus restoring the link with physical theories

Anatomy of the magnetic catalysis by renormalization-group method

Science.gov (United States)

Hattori, Koichi; Itakura, Kazunori; Ozaki, Sho

2017-12-01

We first examine the scaling argument for a renormalization-group (RG) analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger-Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu-Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

Nonlinear quantum electrodynamic and electroweak processes in strong laser fields

Energy Technology Data Exchange (ETDEWEB)

Meuren, Sebastian

2015-06-24

Various nonlinear electrodynamic and electroweak processes in strong plane-wave laser fields are considered with an emphasis on short-pulse effects. In particular, the momentum distribution of photoproduced electron-positron pairs is calculated numerically and a semiclassical interpretation of its characteristic features is established. By proving the optical theorem, compact double-integral expressions for the total pair-creation probability are obtained and numerically evaluated. The exponential decay of the photon wave function in a plane wave is included by solving the Schwinger-Dyson equations to leading-order in the quasistatic approximation. In this respect, the polarization operator in a plane wave is investigated and its Ward-Takahashi identity verified. A classical analysis indicates that a photoproduced electron-positron pair recollides for certain initial conditions. The contributions of such recollision processes to the polarization operator are identified and calculated both analytically and numerically. Furthermore, the existence of nontrivial electron-spin dynamics induced by quantum fluctuations is verified for ultra-short laser pulses. Finally, the exchange of weak gauge bosons is considered, which is essential for neutrino-photon interactions. In particular, the axial-vector-vector coupling tensor is calculated and the so-called Adler-Bell-Jackiw (ABJ) anomaly investigated.

Fem Formulation for Heat and Mass Transfer in Porous Medium

Science.gov (United States)

Azeem; Soudagar, Manzoor Elahi M.; Salman Ahmed, N. J.; Anjum Badruddin, Irfan

2017-08-01

Heat and mass transfer in porous medium can be modelled using three partial differential equations namely, momentum equation, energy equation and mass diffusion. These three equations are coupled to each other by some common terms that turn the whole phenomenon into a complex problem with inter-dependable variables. The current article describes the finite element formulation of heat and mass transfer in porous medium with respect to Cartesian coordinates. The problem under study is formulated into algebraic form of equations by using Galerkin's method with the help of two-node linear triangular element having three nodes. The domain is meshed with smaller sized elements near the wall region and bigger size away from walls.

Multi-symplectic Preissmann methods for generalized Zakharov-Kuznetsov equation

International Nuclear Information System (INIS)

Wang Junjie; Yang Kuande; Wang Liantang

2012-01-01

Generalized Zakharov-Kuznetsov equation, a typical nonlinear wave equation, was studied based on the multi-symplectic theory in Hamilton space. The multi-symplectic formulations of generalized Zakharov-Kuznetsov equation with several conservation laws are presented. The multi-symplectic Preissmann method is used to discretize the formulations. The numerical experiment is given, and the results verify the efficiency of the multi-symplectic scheme. (authors)

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Multiple excitation of supports - Part 1. Formulation

International Nuclear Information System (INIS)

Galeao, A.C.N.R.; Barbosa, H.J.C.

1980-12-01

The formulation and the solution of a simple specific problem of support movement are presented. The formulation is extended to the general case of infinitesimal elasticity where the approximated solutions are obtained by the variational formulation with spatial discretization by Finite Element Method. Finally, the present usual numerical techniques for the treatment of the resulting ordinary differential equations system are discused: Direct integration, Modal overlap, Spectral response. (E.G.) [pt

Superspace formulation for the master equation

International Nuclear Information System (INIS)

Abreu, E.M.; Braga, N.R.

1996-01-01

It is shown that the quantum master equation of the field-antifield quantization method at one-loop order can be translated into the requirement of a superfield structure for the action. The Pauli-Villars regularization is implemented in this BRST superspace and the case of anomalous gauge theories is investigated. The quantum action, including Wess-Zumino terms, shows up as one of the components of a superfield that includes the BRST anomalies in the other component. The example of W2 quantum gravity is also discussed. copyright 1996 The American Physical Society

Multivector field formulation of Hamiltonian field theories: equations and symmetries

Energy Technology Data Exchange (ETDEWEB)

Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)

1999-12-03

We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)

Nystro¨m method applied to integral formulation of the neutron transport equation in X-Y geometry

Energy Technology Data Exchange (ETDEWEB)

Azevedo, Fabio S.; Sauter, Esequia; Konzen, Pedro H.A.; Barichello, Liliane B., E-mail: fabio.azevedo@ufrgs.br, E-mail: esequia.sauter@ufrgs.br, E-mail: pedro.konzen@ufrgs.br, E-mail: lbaric@mat.ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Matem´atica Pura e Aplicada

2017-07-01

Neutron transport problems in X-Y geometry have been solved with several techniques in last decades but it is still a challenge to produce a good balance between computational efficiency and accuracy. In this work, we address this problem by efficiently applying the Nystr¨om method to the integral formulation of the transport equation. Analytical techniques, modern numerical packages and optimized implementation were applied to reduce the computational time. This method presented results free of ray effects leading to high accurate numerical results for two-dimensional scalar flux. Our implementation simulates homogeneous problems with vacuum and reflective boundary conditions. Results were validated with up to seven significant digits and compared with those available in the literature. (author)

Ionization equilibrium and equation of state in the solar interior

International Nuclear Information System (INIS)

Rogers, F.J.

1984-01-01

Many-body formulations of the equations of state are restated as a set of Saha-like equations. It is shown that the resulting equations are unique and convergent. These equations are similar to the usual Saha equations to the order of the Debye-Huckel theory. Higher order corrections, however, require a more general formulation. It is demonstrated that the positive free energy resulting from the interaction of unscreened particles in high orbits depletes the occupation of these states, without the introduction of shifted energy levels

Alternative formulation of the monokinetic transport equation

International Nuclear Information System (INIS)

Coppa, G.; Ravetto, P.; Sumini, M.

1985-01-01

After recalling a technique already exploited in stationary neutron transport, the dynamic linear monokinetic equation for general geometry is cast into an integro-differential form where a second order space Laplace operator and both a second and first time derivatives appear. The introduced unknowns are given a physical interpretation for plane geometry and their relations with the total flux and current are derived

Physical interpretation and evaluation of the Kohn-Sham and Dyson components of the epsilon-I relations between the Kohn-Sham orbital energies and the ionization potentials

NARCIS (Netherlands)

Gritsenko, O.V.; Braida, B.; Baerends, E.J.

2003-01-01

Theoretical and numerical insight was gained into the relations between the Kohn-Sham orbital energies and relaxed vertical ionization potentials. A connection was made between the Kohn-Sham and Dyson one-electron theories. It was established that the energies of the occupied KS orbitals are

Canonical form of Euler-Lagrange equations and gauge symmetries

Energy Technology Data Exchange (ETDEWEB)

Geyer, B [Naturwissenschaftlich-Theoretisches Zentrum und Institut fuer Theoretische Physik, Universitaet Leipzig, Leipzig (Germany); Gitman, D M [Institute of Physics, University of Sao Paulo, Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)

2003-06-13

The structure of the Euler-Lagrange equations for a general Lagrangian theory (e.g. singular, with higher derivatives) is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to highest-order derivatives of nongauge coordinates, whereas gauge coordinates and their derivatives enter the right-hand sides of the equations as arbitrary functions of time. The reduction procedure reveals constraints in the Lagrangian formulation of singular systems and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the Euler-Lagrange equations. Thus, a constructive way of finding all the gauge generators within the Lagrangian formulation is presented. At the same time, it is proved that for local theories all the gauge generators are local in time operators.

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

Velocity statistics for interacting edge dislocations in one dimension from Dyson's Coulomb gas model.

Science.gov (United States)

Jafarpour, Farshid; Angheluta, Luiza; Goldenfeld, Nigel

2013-10-01

The dynamics of edge dislocations with parallel Burgers vectors, moving in the same slip plane, is mapped onto Dyson's model of a two-dimensional Coulomb gas confined in one dimension. We show that the tail distribution of the velocity of dislocations is power law in form, as a consequence of the pair interaction of nearest neighbors in one dimension. In two dimensions, we show the presence of a pairing phase transition in a system of interacting dislocations with parallel Burgers vectors. The scaling exponent of the velocity distribution at effective temperatures well below this pairing transition temperature can be derived from the nearest-neighbor interaction, while near the transition temperature, the distribution deviates from the form predicted by the nearest-neighbor interaction, suggesting the presence of collective effects.

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

A microscopic derivation of stochastic differential equations

International Nuclear Information System (INIS)

Arimitsu, Toshihico

1996-01-01

With the help of the formulation of Non-Equilibrium Thermo Field Dynamics, a unified canonical operator formalism is constructed for the quantum stochastic differential equations. In the course of its construction, it is found that there are at least two formulations, i.e. one is non-hermitian and the other is hermitian. Having settled which framework should be satisfied by the quantum stochastic differential equations, a microscopic derivation is performed for these stochastic differential equations by extending the projector methods. This investigation may open a new field for quantum systems in order to understand the deeper meaning of dissipation

Generalized Lorentz-Force equations

International Nuclear Information System (INIS)

Yamaleev, R.M.

2001-01-01

Guided by Nambu (n+1)-dimensional phase space formalism we build a new system of dynamic equations. These equations describe a dynamic state of the corporeal system composed of n subsystems. The dynamic equations are formulated in terms of dynamic variables of the subsystems as well as in terms of dynamic variables of the corporeal system. These two sets of variables are related respectively as roots and coefficients of the n-degree polynomial equation. In the special n=2 case, this formalism reproduces relativistic dynamics for the charged spinning particles

On the fairlie's Moyal formulation of M(atrix)-theory

International Nuclear Information System (INIS)

Hssaini, M.; Sedra, M.B.; Bennai, M.; Maroufi, B.

2000-07-01

Starting from the Moyal formulation of M-theory in the large N-limit, we propose to reexamine the associated membrane equations of motion in 10 dimensions formulated in terms of Poisson bracket. Among the results obtained, we rewrite the coupled first order Nahm's equations into a simple form leading in turn to their systematic relation with SU(∞) Yang Mills equations of motion. The former are interpreted as the vanishing condition of some conserved currents which we propose. We also develop an algebraic analysis in which an ansatz is considered and find an explicit form for the membrane solution of our problem. Typical solutions known in literature can also emerge as special cases of the proposed solution. (author)

Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

International Nuclear Information System (INIS)

Rhebergen, S.; Bokhove, O.; Vegt, J.J.W. van der

2008-01-01

We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form, then the formulation must reduce to that for conservative systems. Standard DGFEM formulations cannot be applied to nonconservative systems of partial differential equations. We therefore introduce the theory of weak solutions for nonconservative products into the DGFEM formulation leading to the new question how to define the path connecting left and right states across a discontinuity. The effect of different paths on the numerical solution is investigated and found to be small. We also introduce a new numerical flux that is able to deal with nonconservative products. Our scheme is applied to two different systems of partial differential equations. First, we consider the shallow water equations, where topography leads to nonconservative products, in which the known, possibly discontinuous, topography is formally taken as an unknown in the system. Second, we consider a simplification of a depth-averaged two-phase flow model which contains more intrinsic nonconservative products

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)

Partial differential equations in action complements and exercises

CERN Document Server

Salsa, Sandro

2015-01-01

This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Basic Functional Analysis and Distribution Theory; Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation. Thanks to the broad variety of exercises with complete solutions, it can be used in all basic and advanced PDE courses.

Formulation of 11-dimensional supergravity in superspace

International Nuclear Information System (INIS)

Cremmer, E.; Ferrara, S.

1980-01-01

We formulate on-shell 11-dimensional supergravity in superspace and express its equations of motion in terms of purely geometrical quantities. All torsion and curvature components are solved in terms of a single superfield Wsub(rstu), totally antisymmetric in its (flat vector) indices. The dimensional reduction of this formulation is expected to be related to the superspace formulation of N = 8 extended supergravity and might explain the origin of the hidden (local) SU(8) and (global) E 7 symmetries present in this theory. (orig.)

Differential equations for dummies

CERN Document Server

Holzner, Steven

2008-01-01

The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

Covariant Formulation of Hooke's Law.

Science.gov (United States)

Gron, O.

1981-01-01

Introducing a four-vector strain and a four-force stress, Hooke's law is written as a four-vector equation. This formulation is shown to clarify seemingly paradoxical results in connection with uniformly accelerated motion, and rotational motion with angular acceleration. (Author/JN)

Langevin formulation of quantum dynamics

International Nuclear Information System (INIS)

Roncadelli, M.

1989-03-01

We first show that nonrelativistic quantum mechanics formulated at imaginary-(h/2 π) can formally be viewed as the Fokker-Planck description of a frictionless brownian motion, which occurs (in general) in an absorbing medium. We next offer a new formulation of quantum mechanics, which is basically the Langevin treatment of this brownian motion. Explicitly, we derive a noise-average representation for the transition probability W(X'',t''|X',t'), in terms of the solutions to a Langevin equation with a Gaussian white-noise. Upon analytic continuation back to real-(h/2 π),W(X'',t''|X',t') becomes the propagator of the original Schroedinger equation. Our approach allows for a straightforward application to quantum dynamical problems of the mathematical techniques of classical stochastic processes. Moreover, computer simulations of quantum mechanical systems can be carried out by using numerical programs based on the Langevin dynamics. (author). 19 refs, 1 tab

Solving equations by topological methods

Directory of Open Access Journals (Sweden)

Lech Górniewicz

2005-01-01

Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.

An efficient algorithm for the generalized Foldy-Lax formulation

Science.gov (United States)

Huang, Kai; Li, Peijun; Zhao, Hongkai

2013-02-01

Consider the scattering of a time-harmonic plane wave incident on a two-scale heterogeneous medium, which consists of scatterers that are much smaller than the wavelength and extended scatterers that are comparable to the wavelength. In this work we treat those small scatterers as isotropic point scatterers and use a generalized Foldy-Lax formulation to model wave propagation and capture multiple scattering among point scatterers and extended scatterers. Our formulation is given as a coupled system, which combines the original Foldy-Lax formulation for the point scatterers and the regular boundary integral equation for the extended obstacle scatterers. The existence and uniqueness of the solution for the formulation is established in terms of physical parameters such as the scattering coefficient and the separation distances. Computationally, an efficient physically motivated Gauss-Seidel iterative method is proposed to solve the coupled system, where only a linear system of algebraic equations for point scatterers or a boundary integral equation for a single extended obstacle scatterer is required to solve at each step of iteration. The convergence of the iterative method is also characterized in terms of physical parameters. Numerical tests for the far-field patterns of scattered fields arising from uniformly or randomly distributed point scatterers and single or multiple extended obstacle scatterers are presented.

Initial value formulation of higher derivative gravity

International Nuclear Information System (INIS)

Noakes, D.R.

1983-01-01

The initial value problem is considered for the conformally coupled scalar field and higher derivative gravity, by expressing the equations of each theory in harmonic coordinates. For each theory it is shown that the (vacuum) equations can take the form of a diagonal hyperbolic system with constraints on the initial data. Consequently these theories possess well-posed initial value formulations

Numerical integration of some new unified plasticity-creep formulations

International Nuclear Information System (INIS)

Krieg, R.D.

1977-01-01

The usual constitutive description of metals at high temperature treats creep as a phenomenon which must be added to time independent phenomena. A new approach is now being advocated by some people, principally metallurgists. They all treat the inelastic strain as a unified quantity, incapable of being separated into time dependent and time independent parts. This paper examines the behavior of the differential formulations reported in the literature together with one proposed by the author. These formulations are capable of representing primary and secondary creep, cyclic hardening to a stable cyclic stress-strain loop, a conventional plasticity behavior, and a Bauchinger effect which may be creep induced and discernable either at fast or slow loading rates. The new unified formulations seem to lead to very non-linear systems of equations which are very well behaved in some regions and very stiff in other regions where the word 'stiff' is used in the mathematical sense. Simple conventional methods of integrating incremental constitutive equations are observed to be totally inadequate. A method of numerically integrating the equations is presented. (Auth.)

Gluon and ghost propagator studies in lattice QCD at finite temperature

International Nuclear Information System (INIS)

Aouane, Rafik

2013-01-01

Gluon and ghost propagators in quantum chromodynamics (QCD) computed in the infrared momentum region play an important role to understand quark and gluon confinement. They are the subject of intensive research thanks to non-perturbative methods based on Dyson-Schwinger (DS) and functional renormalization group (FRG) equations. Moreover, their temperature behavior might also help to explore the chiral and deconfinement phase transition or crossover within QCD at non-zero temperature. Our prime tool is the lattice discretized QCD (LQCD) providing a unique ab-initio non-perturbative approach to deal with the computation of various observables of the hadronic world. We investigate the temperature dependence of Landau gauge gluon and ghost propagators in pure gluodynamics and in full QCD. Regarding the gluon propagator, we compute its longitudinal D L as well its transversal D T components. The aim is to provide a data set in terms of fitting formulae which can be used as input for DS (or FRG) equations. We deal with full (N f =2) LQCD with the twisted mass fermion discretization. We employ gauge field configurations provided by the tmfT collaboration for temperatures in the crossover region and for three fixed pion mass values in the range [300,500] MeV. Finally, within SU(3) pure gauge theory (at T=0) we compute the Landau gauge gluon propagator according to different gauge fixing criteria. Our goal is to understand the influence of gauge copies with minimal (non-trivial) eigenvalues of the Faddeev-Popov operator.

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.

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

Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation

DEFF Research Database (Denmark)

Yoon, Gil Ho; Jensen, Jens Stissing; Sigmund, Ole

2007-01-01

given during the optimization process. In this paper we circumvent the explicit boundary representation by using a mixed finite element formulation with displacements and pressure as primary variables (a u/p-formulation). The Helmholtz equation is obtained as a special case of the mixed formulation...... for the elastic shear modulus equating to zero. Hence, by spatial variation of the mass density, shear and bulk moduli we are able to solve the coupled problem by the mixed formulation. Using this modelling approach, the topology optimization procedure is simply implemented as a standard density approach. Several...... two-dimensional acoustic-structure problems are optimized in order to verify the proposed method....

Photonic density of states in the vicinity of a single-wall finite-length carbon nanotube

International Nuclear Information System (INIS)

Nemilentsau, A; Ya Slepyan, G; Maksimenko, S A

2009-01-01

Photonic density of states in the vicinity of a single-wall finite-length carbon nanotube (CNT) is investigated theoretically in this paper. The analysis is based on the fluctuation-dissipative theorem in the Callen-Welton form. The Dyson equation for the Green dyadic of the electromagnetic field in the presence of CNT is formulated and a method for its numerical solution is elaborated. We show that the photonic density of states spectrum has a nontrivial resonant structure in the terahertz range in the vicinity of the metallic single-wall CNT. The origin of these resonances is the surface plasmon resonances on the CNT's edges.

Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3

Science.gov (United States)

Sitchin, A.

1972-01-01

Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.

Anatomy of the magnetic catalysis by renormalization-group method

Directory of Open Access Journals (Sweden)

Koichi Hattori

2017-12-01

Full Text Available We first examine the scaling argument for a renormalization-group (RG analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger–Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu–Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

Partial differential equations for scientists and engineers

CERN Document Server

Farlow, Stanley J

1993-01-01

Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th

A mixed finite element method for nonlinear diffusion equations

KAUST Repository

Burger, Martin; Carrillo, José ; Wolfram, Marie-Therese

2010-01-01

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.

Three-dimensional formulation of rigid-flexible multibody systems with flexible beam elements

International Nuclear Information System (INIS)

Garcia-Vallejo, D.; Mayo, J.; Escalona, J. L.; Dominguez, J.

2008-01-01

Multibody systems generally contain solids with appreciable deformations and which decisively influence the dynamics of the system. These solids have to be modeled by means of special formulations for flexible solids. At the same time, other solids are of such a high stiffness that they may be considered rigid, which simplifies their modeling. For these reasons, for a rigid-flexible multibody system, two types of formulations coexist in the equations of the system. Among the different possibilities provided in the literature on the material, the formulation in natural coordinates and the formulation in absolute nodal coordinates are utilized in this paper to model the rigid and flexible solids, respectively. This paper contains a mixed formulation based on the possibility of sharing coordinates between a rigid solid and a flexible solid. The global mass matrix of the system is shown to be constant and, in addition, many of the constraint equations obtained upon utilizing these formulations are linear and can be eliminated

Strong diffusion formulation of Markov chain ensembles and its optimal weaker reductions

Science.gov (United States)

Güler, Marifi

2017-10-01

Two self-contained diffusion formulations, in the form of coupled stochastic differential equations, are developed for the temporal evolution of state densities over an ensemble of Markov chains evolving independently under a common transition rate matrix. Our first formulation derives from Kurtz's strong approximation theorem of density-dependent Markov jump processes [Stoch. Process. Their Appl. 6, 223 (1978), 10.1016/0304-4149(78)90020-0] and, therefore, strongly converges with an error bound of the order of lnN /N for ensemble size N . The second formulation eliminates some fluctuation variables, and correspondingly some noise terms, within the governing equations of the strong formulation, with the objective of achieving a simpler analytic formulation and a faster computation algorithm when the transition rates are constant or slowly varying. There, the reduction of the structural complexity is optimal in the sense that the elimination of any given set of variables takes place with the lowest attainable increase in the error bound. The resultant formulations are supported by numerical simulations.

Differential equation analysis in biomedical science and engineering ordinary differential equation applications with R

CERN Document Server

Schiesser, William E

2014-01-01

Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-worldODE problems that are found in a variety of fields, including chemistry, physics, biology,and physiology. The book provides readers with the necessary knowledge to reproduce andextend the comp

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.

Fractional vector calculus and fractional Maxwell's equations

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2008-01-01

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered

The electromagnetic field equations for moving media

International Nuclear Information System (INIS)

Ivezić, T

2017-01-01

In this paper a formulation of the field equation for moving media is developed by the generalization of an axiomatic geometric formulation of the electromagnetism in vacuum (Ivezić T 2005 Found. Phys. Lett. 18 401). First, the field equations with bivectors F ( x ) and ℳ ( x ) are presented and then these equations are written with the 4D vectors E ( x ), B ( x ), P ( x ) and M ( x ). The latter contain both the 4D velocity vector u of a moving medium and the 4D velocity vector v of the observers who measure E and B fields. They do not appear in previous literature. All these equations are also written in the standard basis and compared with Maxwell’s equations with 3D vectors. In this approach the Ampère-Maxwell law and Gauss’s law are inseparably connected in one law and the same happens with Faraday’s law and the law that expresses the absence of magnetic charge. It is shown that Maxwell’s equations with 3D vectors and the field equations with 4D geometric quantities are not equivalent in 4D spacetime (paper)

Methods of mathematical modelling continuous systems and differential equations

CERN Document Server

Witelski, Thomas

2015-01-01

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

Collisional plasma transport: two-dimensional scalar formulation of the initial boundary value problem and quasi one-dimensional models

International Nuclear Information System (INIS)

Mugge, J.W.

1979-10-01

The collisional plasma transport problem is formulated as an initial boundary value problem for general characteristic boundary conditions. Starting from the full set of hydrodynamic and electrodynamic equations an expansion in the electron-ion mass ratio together with a multiple timescale method yields simplified equations on each timescale. On timescales where many collisions have taken place for the simplified equations the initial boundary value problem is formulated. Through the introduction of potentials a two-dimensional scalar formulation in terms of quasi-linear integro-differential equations of second order for a domain consisting of plasma and vacuum sub-domains is obtained. (Auth.)

Is Yang-Mills equation a totally integrable system. Lecture III

International Nuclear Information System (INIS)

Chau Wang, L.L.

1981-01-01

Topics covered include: loop-space formulation of gauge theory - loop-space chiral equation; two dimensional chiral equation - conservation laws, linear system and integrability; and parallel development for the loop-space chiral equation - subtlety

Variable thickness transient ground-water flow model. Volume 1. Formulation

International Nuclear Information System (INIS)

Reisenauer, A.E.

1979-12-01

Mathematical formulation for the variable thickness transient (VTT) model of an aquifer system is presented. The basic assumptions are described. Specific data requirements for the physical parameters are discussed. The boundary definitions and solution techniques of the numerical formulation of the system of equations are presented

General Eulerian formulation of the comoving-frame equation of radiative transfer

International Nuclear Information System (INIS)

Riffert, H.

1986-01-01

For a wide range of problems in radiation hydrodynamics the motion of the matter is best described in an Eulerian coordinate system, and here a comoving-frame equation of radiation transfer in such fixed coordinates is derived, using the radiation quantities measured in the comoving frame. The choice of coordinates is arbitrary, and the equation is given explicitly for an arbitrary diagonal metric, correct to all orders in v/c. All comoving frame equations derived earlier are included as special cases. An example is given for the case of a spherically symmetric flow in a Schwarzschild metric. 9 references