Properties Of Vertices Research Articles

Transformation properties of proper vertices in gauge theories

The Ward-Takahashi identities for (single-particle irreducible) proper vertices are derived for non-Abelian gauge theories; the renormalization of such theories, previously discussed in terms of the Ward-Takahashi identities for Green functions, can now be considerably simplified.

The gauge properties of the dual model pomeron-reggeon vertex: Their derivation and their consequences

Study of the non-planar orientable single dual loop diagrams in 26 space-time dimensions has revealed an infinite positive-definite spectrum of “pomeron” intermediate states which couple to reggeons via a bilinear pomeron-reggeon vertex operator. General algebraic techniques are developed to derive the behaviour of this vertex with respect to the Virasoro gauge operators. A reflection and transmission behaviour is found, reminiscent of the behaviour of a wave incident at the interface between two different media (in this case reggeonic and pomeronic). These gauge properties are such as to guarantee the desired “good properties”, namely completeness of the transverse reggeon states when coupled between physical reggeon states on one side, and on the other side, either physical pomeron states or else physical reggeon states created via an intermediate pomeron. This is yet another example of the amazing and gratifying self-consistency of the dual model with respect to duality, transversality and unitarity.

General Vertex with Physical Excited Particles in the Dual Resonance Model of the Virasoro Case

We investigate the transformation properties of the asymmetrical general vertex of the dual resonance model under the projective group. We show that, in the Virasoro case, the vertex with the physical state is covariant under the group and is equivalent to the vertex introduced by Compagna et al. Using this equality, we can directly show that an amplitude for N external excited particles constructed by using the vertex is equal to the amplitude obtained from repeated factorization of tree dual graph.

The meson exchange current effect in radiative np capture

The pion exchange current contribution to the thermal neutron proton radiative capture cross section is calculated on the basis of potential theory by extracting a local “absorptive exchange potential” from the corresponding fourth order Feynman diagram with the deuteron nucleon vertex on the mass shell. Taking into account that the repulsive core of nucleon interaction leads to modifications not only of the wave functions (which include off-mass shell properties of the deuteron nucleon vertex) but also of this absorptive OPE potential a result is obtained which explains the main part (⋍ 2 3 ) of the well-known 10%-discrepancy between experiment and impulse approximation.

Contradiction Equations in a B Matrix of Vertex Weight Method and Their Correspondence with the k-Summability Property of Vertices

This note attempts to show that, in a vertex weight method [1], every contradiction equation bears a one-to-one correspondence with the summability pair C 1S , C 2S , where C 1S = {X 11 , X 12 , ..., X 1k }? C 1 C 2S = {X 21 , X 22 ,..., X 2k } ? C 2 and vector sums of the vertices plz check [Eqa] The vertices, X ki 's, K = 1, or 2, are not necessarily distinct, and C 1 , C 2 are two disjoint sets of vertices in En space. As a consequence, the contradiction equation is a necessary and sufficient condition that the homogeneous system, solved for a threshold function of order r, has no solution. This tells that the threshold function is of order greater than r.

Factorization of the pomeron sector and currents in the dual resonance model

The pomeron sector of the dual resonance model is exhibited by an explicit factorization of the non-planar orientable one-loop graph. A pomeron propagator and a pomeron-reggeon vertex are obtained. The pomeron propagator is shown to be essentially the same as in the Shapiro-Virasoro model. Gauge properties of the pomeron-reggeon vertex allow us to construct conserved or partially conserved vector and tensor currents of arbitrary rank and to exhibit a ghost-killing mechanism.

Dilute mixtures of 3He in superfluid 4He

Abstract This paper discusses the properties of a single 3He impurity in liquid 4He at zero temperature. An exact perturbation expansion is developed. All properties of the boson system are assumed known and the single particle fermion propagator is expressed in terms of these. An approximation is introduced which makes the diagrammatic expansion correspond to the fermion interacting with the elementary excitations of the Bose system. The analytical properties of the boson-fermion vertices are investigated. Various expressions for the effective mass of the fermion are discussed and temperature corrections are shown to be negligible. The main contribution to the change in mass is found to come from the interaction with virtual rotons. Experiments are used to estimate some of the parameters of the theory. It is found that the weight of the quasiparticle pole is only about 1 3 . Finally a comparison with other recent theoretical work is made.

Exchange current and deuteron photodisintegration at threshold

The contribution from the meson exchange current to the deuteron photodisintegration amplitude at threshold is calculated by taking into account the next nearby singularities beyond the nucleon exchange poles in the crossed channels. The procedure is based on potential theory. Starting with the corresponding fourth order Feynman amplitude with the deuteron-nucleon vertex on the mass shell a local “exchange potential” is derived. Its contribution to the amplitude is calculated by using the Hulthén function for the initial deuteron state (thus including the off-mass shell properties of the deuteron-nucleon vertex) and the effective range approximation for the final scattering state. The result is combined with the direct γ-nucleon contribution calculated by Austern and Rost 1) and agrees with experiment within the limits of error.

A Vertex Property for Banach Algebras with Identity.

A Vertex Property for Banach Algebras with Identity.

Dispersion Relations and Vertex Properties in Perturbation Theory

a) In the formula following (10) the last term should read 7μ2/64 instead of Fμ2/64. b) The statement in footnote *11) that the general method gives Δ2≤2M2+4Mε+O(ε2) is due to a calculational error. the correct value is Δ2≤2M2+O(ε2) and, therefore, the conclusion of the footnote is invalid. Cp. Y. Nambu, “Limitations on Momentum Transfer in Dispersion Relations of Scattering Amplitudes”, to appear in Nuovo Cimento

Dispersion Relations and Vertex Properties in Perturbation Theory

Dispersion relations for nucleon-nucleon scattering with momentum transfer 2|Δ| ≪ µ, for meson-nucleon scattering, and related properties of the meson-nucleon vertex, are shown to hold in every order perturbation theory. This is done by extending a method used by Nambu to discuss the perturbation-theoretical parametric representations of Green's function. In effect arbitrarily complicated Feynman diagrams are reduced to a few simple types.