Showing papers on "Vertex function published in 1983"
TL;DR: In this paper, the SO(2,1)-invariant quantization of Liouville theory is elaborated, and a renormalized perturbation expansion is developed which preserves this symmetry to all orders, but spontaneously breaks Poincare invariance.
Abstract: The recently proposed SO(2,1)-invariant quantization of the Liouville theory is elaborated. We develop a renormalized perturbation expansion which preserves this symmetry to all orders, but spontaneously breaks Poincare invariance. Some Green's functions and scattering amplitudes are calculated in low perturbative order, and it is established that the S matrix is trivial in the tree approximation. Whether this is also true of the complete S matrix remains an open question.
84 citations
TL;DR: In this paper, a vertex function [y:',~(k)l~ is defined and shown to be proportional to a gauge independent quantity, and symmetry properties of the vertex function are derived in the case where the spin corresponds to the parallel component of the magnetic moment operator.
Abstract: Dirac's equation in the presence of a static magnetic field is solved in terms of both cartesian and cylindrical coordinates, and solutions are found for three different spin operators. Choosing the spin to correspond to the parallel component Ilz of the magnetic moment operator leads to wavefunctions (a) which are symmetric between electron and positron states and (b) which are eigenfunctions of the Hamiltonian including radiative corrections. A vertex function [y:',~(k)l~ is defined and shown to be proportional to a gauge independent quantity [T::~(k)l". Symmetry properties of [T~:~(k)l~ are derived in the case where the spin corresponds to Ilz. The use of the vertex function is illustrated by deriving the electron propagator in coordinate space from the vacuum expectation value. Properties of functions J~, _n(x) which appear extensively and are related to generalized Laguerre polynomials are derived and summarized in the Appendix.
69 citations
TL;DR: In this article, the general transition q i → q j + γ for arbitrary quark flavors in a non-linear R ξ gauge was calculated and the reduced number of Feynman diagrams as well as simplified Ward identities greatly facilitates this calculation.
63 citations
TL;DR: In this article, the vertex function of two vector and one axial vector currents was used to calculate the coupling constant g ωϱπ, which is in good agreement with experimental data.
42 citations
CERN1
TL;DR: The axial form factor of the nucleon in the Cloudy Bag Model is harder than the NNπ vertex function, and consistent with data for a bag radius about 1 fm.
39 citations
TL;DR: In this paper, a transverse vertex is constructed and added to the longitudinal vertex, which yields an equation for the electron propagator $S(p)$ which remains linear and exact in the infrared, but which is multiplicatively renormalizable and gauge covariant.
Abstract: It is known that the Schwinger-Dyson equation for the electron propagator $S(p)$ in quantum electrodynamics is linear if the full vertex in this equation is approximated by a special form (the longitudinal vertex) which satisfies the Ward identity and which yields exact results in the infrared regime. However, the approximate equation cannot be multiplicatively renormalized (nor is it properly gauge covariant) using only the longitudinal vertex. In the present work, we construct a transverse (i.e., identically conserved) vertex which, when added to the longitudinal vertex, yields an equation for $S(p)$ which remains linear and exact in the infrared, but which is multiplicatively renormalizable and gauge covariant. In the ultraviolet regime, the equation gives the known results of renormalization-group-improved perturbation theory. The essential difficulty which is overcome by the present analysis is that of overlapping divergences, which are mishandled if only the longitudinal vertex is kept.
34 citations
TL;DR: In this article, a physically motivated renormalization scheme for Coulomb-gauge QED is presented. But this scheme is useful in calculations involving QED bound states.
Abstract: In this article I present a physically motivated renormalization scheme for Coulomb-gauge QED. This scheme is useful in calculations involving QED bound states. I implement this scheme to one loop by calculating the electron self-energy, the electron self-mass, and the renormalization constants Z/sub 1/ and Z/sub 2/. Formulas for the dimensional regularization of some noncovariant integrals useful in one-loop Coulomb-gauge calculations are given.
27 citations
TL;DR: In this paper, it was shown that at long-range quantum Yang-Mills theory is equivalent to a classical Yang-mills theory in an anisotropic and inhomogeneous medium, the QCD vacuum.
22 citations
TL;DR: In this paper, a conformal-invariant quantum electrodynamics is proposed, in which new representations of the conformal group are used to obtain unusual laws for the electromagnetic potential and the transverse part of the current.
Abstract: A formulation of conformal-invariant quantum electrodynamics is suggested, in which new representations of the conformal group are used. This results in unusual laws for the electromagnetic potential and the transverse part of the current, and modified expressions are obtained for the vertex and three-point Green function. The program of the asymptotic charge calculation within the frames of conformal-invariant skeleton theory is formulated.
20 citations
TL;DR: In this paper, the vertex function of two vector and one axial vector currents is calculated using QCD sum rules for the vertex functions of two vectors and axial vectors, and the results obtained are consistent within 25% accuracy with vector meson dominance model predictions and can be regarded as its theoretical justification.
Abstract: Electromagnetic ρπ formfactor at intermediate momentum transfer, 0.7 GeV2≦Q2≦3 GeV2, is calculated using QCD sum rules for the vertex function of two vector and one axial vector currents. In this region the results obtained are consistent within 25% accuracy with the vector meson dominance model predictions and can be regarded as its theoretical justification.
9 citations
TL;DR: In this paper, the charge form factor of a scalar deuteron at high momentum transfer is examined in a model employing scalar nucleons and mesons, with an eye towards establishing consistency criteria for more realistic calculations, several aspects of the model are examined in detail: the role of nucleon and meson singularities in the one-loop impulse diagram, role of positive and negative energy nucleons, and the relationship to time-ordered perturbation theory.
Abstract: The charge form factor of a scalar deuteron at high momentum transfer is examined in a model employing scalar nucleons and mesons. With an eye towards establishing consistency criteria for more realistic calculations, several aspects of the model are examined in detail: the role of nucleon and meson singularities in the one-loop impulse diagram, the role of positive- and negative-energy nucleons, and the relationship to time-ordered perturbation theory. It is found that at large Q/sup 2/ (1) the form factor is dominated by a term in which the spectator nucleon is on the mass shell, and (2) the meson singularity structure of the d-n-p vertex function is unimportant in determining the overall high-Q/sup 2/ behavior of the form factor.
TL;DR: In this article, the authors studied the impact of scale breaking on the scale distribution of heavy ion collisions and proposed a dynamical derivation of the inclusive distribution for pion production.
Abstract: Relativistic heavy ion collisions are studied here taking into account the hard scattering model of Schmidt and Blankenbecler along with a dynamical derivation of the inclusive distribution for pp..--> pi..x, pp..-->..Kx, and pp..-->..p-barx and pp..-->..px proposed in an earlier paper. This scheme takes into account scale breaking and it is found that both A and B dependence occur in such processes as AB..--> pi../sup -/x, AB..-->..K-barx, AB..-->..p-barx, and AB..-->..px in the forward region. In the backward region the independent N-N collision model is also found satisfactory when the structural rearrangement factor is incorporated in the vertex function. It is found that although in the forward region scale breaking is not appreciable, it becomes quite significant in the backward region. The x distributions in the forward region as well as in the backward region have been computed on the basis of this independent N-N collision model. The results are found to be in very good agreement for inclusive pion production.
TL;DR: In this paper, the authors considered a finite massless QED with the electron mass totally dynamical of origin and the fine-structure constant as the (infinite order) zero of the Callan-Symanzik function.
Abstract: We consider finite massless QED with the electron mass totally dynamical of origin and the fine-structure constant as the (infinite order) zero of the Callan-Symanzik function. In spacelike regions, the electron propagator (in the generalized Landau gauge) and the photon propagator are then proportional to their free counterparts, and the integral equation for the vertex function GAMMA/sub sigma/ may be written solely as a function of GAMMA/sub sigma/ itself. Landau's approximation is used to obtain the asymptotics for GAMMA/sub sigma/(p,p-k;k) for p/sup 2/,k/sup 2/..-->..infinity, p/sup 2//k/sup 2/..-->..0 in spacelike regions.
TL;DR: For nuclear processes involving pions, such as pion production/absorption or exchange currents, it is shown in this paper that a natural organization involves adoption of the π-NN vertex function g/sub π..NN/(q/sup 2/)..gamma../sub 5/tau/sub..cap alpha, where q is the pion four-momentum and π ≈ 13.4 is the renormalized pion-nucleon coupling constant.
Abstract: For nuclear processes involving pions, such as pion production/absorption or exchange currents, it is shown that a natural organization involves adoption of the ..pi..NN vertex function g/sub ..pi../(q/sup 2/)..gamma../sub 5/tau/sub ..cap alpha../, where q is the pion four-momentum and g/sub ..pi../(m/sub ..pi../ /sup 2/)approx. =13.4 is the renormalized pion-nucleon coupling constant. The result is independent of the form and details of any fundamental interaction Lagrangian. The difference between g/sub ..pi../(q/sup 2/)..gamma../sub 5/tau/sub ..cap alpha../ and the fully-dressed ..pi..NN vertex function contributes to amplitudes involving more bosons, e.g., scattering amplitudes (..pi..N..--> pi..N), production amplitudes (..pi..N..--> pi pi..N), etc. Such contributions are mediated through either seagull-like terms or P11 intermediate states. It is pointed out that it is neither necessary nor practical to calculate these partial contributions to scattering and production amplitudes. One can always exploit other approaches, theoretical and phenomenological, to make reasonably good models for the full amplitudes. The usual procedure of including the effects of negative energy parts of the nucleon propagator in interaction potentials, exchange currents, etc., is easily included in the present organization. The result is that from scattering amplitudes, etc; the positive energy nucleon poles are deleted but Z graphs are included.
TL;DR: In this paper, it was shown that the Slavnov-Taylor identity does not put enough constraint on the longitudinal vertex function to allow unambiguous construction of an approximate Schwinger-Dyson equation for the gluon propagator.
Abstract: It is shown that the Slavnov-Taylor identity does not put enough constraint on the longitudinal vertex function to allow the unambiguous construction of an approximate Schwinger-Dyson equation for the gluon propagator.
TL;DR: In this article, it was shown that there is an ambiguity in the form of the off-shell vertex function in elastic scattering, and the degree of the ambiguity was reduced by the requirement that the vertex be free of kinematic singularities and the offshell isoscalar nucleon form factors be analytic.
Abstract: It is shown that there is an ambiguity in the form of the off-shell $\ensuremath{\gamma}\mathrm{NN}$ vertex function in $\mathrm{ed}$ elastic scattering. The degree of the ambiguity problem might be reduced by the requirement that the vertex be free of kinematic singularities and the off-shell isoscalar nucleon form factors be analytic.
TL;DR: In this paper, a logarithmic approximation for the infrared asymptotic behavior of a vertex function in a model of a massive isospinor field interacting with a massless isovector one was obtained.
Abstract: Equations have been obtained, in a logarithmic approximation, for the infrared asymptotic behavior of a vertex function in a model of a massive isospinor field interacting with a massless isovector one. The particular solution obtained indicates the essential absence of infrared asymptotics of the vertex function in quantum electrodynamics.
TL;DR: In this article, the leading and non-leading logarithm in electron-electron scattering at high energy and fixed angle was calculated by Pauli statistics, where the e-e scattering amplitude is equal to the difference of two terms related to each other by interchanging the two incoming particles.
Abstract: In this paper, we sum all (leading and nonleading) logarithms in electron-electron scattering at high energy and fixed angle. By Pauli statistics, the e-e scattering amplitude is equal to the difference of two terms related to each other by interchanging the two incoming particles. Each of these terms is in the form of a product of an exponential function, the wave-function renormalization constants, and a scaling function. While the exponent of this exponential function is complicated, it is related to that of the vertex function. Thus, each of these terms is in the form of a product of the two-electron vertex functions, a scaling function, and an exponential function which is explicitly given. The method we use is obtained by modifying slightly the one of Yennie and collaborators, which proves to be a powerful tool to deal with scattering problems of large momentum transfers.
TL;DR: In this paper, it was shown that solutions with this property do not exist, if the interacting gluon propagator has the same spin structure of the free one, and an integral equation for the discontinuity of the propagator, with its complete kinematical structure, was proposed.
Abstract: The possibility that solutions of the Schwinger-Dyson equation for the gluon propagator increase at large distances is investigated in the «gauge technique». Without any assumption on the four-gluon vertex function, we find that solutions with this property do not exist, if the interacting gluon propagator has the same spin structure of the free one. We set up an integral equation for the discontinuity of the propagator, with its complete kinematical structure, and show that a stronger infrared singularity is possible in this case.
TL;DR: In this article, the Ward identities between the three-point vertex functions and the single-particle Green functions were derived analytically for the Tomonaga-Luttinger model by using explicitly the boson algebra of the particle-hole operators.
Abstract: The Ward identities relating the three-point vertex functions to the single-particle Green functions as well as the generalised Ward identities between the four- and three-point vertex functions are derived analytically for the Tomonaga-Luttinger model by using explicitly the boson algebra of the particle-hole operators.
01 Jan 1983
TL;DR: In this article, a series of calculations based on a general nonperturbative continuum approach to the problem of the IR behavior of QCO was described, and it was shown that a 1/q4 singularity in the gluon propagator produces a consistant solution to the integral equation.
Abstract: In this talk I will describe a series of calculations based on a general non-perturbative continuum approach to the problem of the IR behavior of QCO. This investigation, done in collaboration with F. Zachariasen and M. Baker, Is based on using the Schwinger-Dyson eqs. (hereafter S.D. eq.) for the quark and gluon propagators and using the appropriate Ward identities to obtain closed integral equations for the quantities of interest [1]. In particular, we have been able to show that a 1/q4 singularity in the gluon propagator produces a consistant solution to the integral equation. When this propagator is used in the integral equation for the quark propagator the pole singularity of a free massless quark is weakened to a simple square root branch point; furthermore we find that a mass-like tern (breaking chiral symmetry) which is an entire function, is consistent with the equations, though not required [2]. Finally, we construct an effective classical Lagrangian which is consistent with our form for the gluon propagator and automatically Includes the long range quantum fluctuations of QCD [3].