Meson Field Theory Research Articles

Current definition and mass renormalization in a model field theory

It is demonstrated that a field theory of vector mesons interacting with massless fermions in a world of one spatial dimension has an infinite number of solutions in direct analogy to the case of the Thirring model. Each of these solutions corresponds to a different value of a certain parameter ξ which enters into the definition of the current operator of the theory. The physical mass of the vector meson is shown to depend linearly upon this parameter, attaining its bare value μ0 for the exceptional case in which the pseudovector current is exactly conserved. The limits μ02→∞ and μ02→0 are examined; the former yields results previously obtained for the Thirring model while the latter implies a unique value for ξ and defines the radiation gauge formulation of Schwinger’s two-dimensional model of electrodynamics.

Departures from Ũ12 in a relativistic quark model

Adopting a Ũ12 four-quark interaction as the potential input to the Bethe-Salpeter equation for the quark-antiquark system we can obtain nonets of bound 0− and 1− meson states. Owing to the presence of a spin-splitting term in the kernel, the masses and coupling constants of the composites deviate from the common values one uses in a phenomenological Ũ12 field theory of quarks and mesons; the magnitudes of these changes are calculated in detail.

A Field Theory of Weak Interactions. I

Higher order weak-interaction effects are studied in the framework of vector meson field theory. We find that such effects may be observable even at low energy. The cause of this can be traced precisely to the unrenormalizability of the theory in the sense of conventional perturbation expansions. These expansions are circumvented by new techniques for summing the most singular parts of perturbation graphs. In this first paper we study in detail the infinite subset of uncrossed ladder graphs. Purely leptonic processes are considered to begin with. The corresponding Bethe-Salpeter equation is soluble by a new iteration scheme. In leading order we reproduce the conventional zero-energy results provided ${g}^{2}$ is replaced by $\frac{3{g}^{2}}{4}$. ($g=\mathrm{bare}\mathrm{meson}\mathrm{lepton}\mathrm{coupling}\mathrm{constant}$). An argument is presented which leads to the conjecture that this result is valid for larger classes of graphs. However, there exist energy-dependent deviations from the conventional second-order results. These are in principle observable in $\ensuremath{\mu}$ decay. The applicability of the theory to semileptonic and nonleptonic phenomena depends on properties of the baryon and meson currents and on the effects of the strong interactions. Preliminary considerations along these lines are given.

A unified field theory of mesons and baryons

Some aspects of a field theory, similar to but more realistic than, that examined in the preceding paper are discussed. The way in which a non-linear meson field theory of this type may contain its own sources, and how these may be idealised to point singularities, as in the conventional field theories of interacting linear systems, is formulated. The structure of the particle source in the classical theory is calculated, and some qualitative features of the interactions between these particles and mesons are described.

Relativistic Lee Model

A relativistic version of the well-known exactly soluble Lee model of quantum field theory is constructed, which\char22{}unlike the original nonrelativistic Lee model\char22{}fulfills also the condition of microcausality (field operators commuting or anticommuting for space-like distances). Microcausality is, however, found compatible with solubility only if an indefinite metric is introduced on a much larger scale than was necessary in the nonrelativistic case. Notwithstanding the fact that a formalism of this type would seem to bear still less resemblance to physical reality than does the original Lee model, we arrive at a theory almost identical with the usual version of relativistic charged scalar (or pseudoscalar) meson field theory. From a certain point of view these two formalisms can even be considered identical. In fact, the difference between the realistic theory and the present Lee model hinges merely on whether one uses, for the representation of the Dirac standard ket $|0〉$ a physical vacuum or a suitably defined completely empty space. The form of the presentation follows closely that of the well-known Pauli-K\all\'en description of the nonrelativistic Lee model, up to the point where it is shown that some of the main results can also be obtained with help of a corresponding Chew-Low equation.

Die darstellungen der starken kopplung und das resonanzproblem der meson-nucleon-streuung

This paper deals with the completion of the strong-coupling method in meson field theory. By means of a canonical and non-linear transformation of variables the original meson field is split into a free meson part and a self field part of the nucleon. The transformation is defined so that the interaction between the compound nucleon system thus arising and the free mesons vanishes in the case of infinitely strong coupling. It is shown that there exists a family of transformations satisfying the conditions. A system of equations for certain transformation functions is stated as the consequence of the conditions. The solutions of the field-splitting problem are investigated. The general scheme for a strong-coupling approximation method based on this field splitting is derived, and the problem of calculating the pion-nucleon resonance scattering from the strong coupling theory is treated on this basis. A special approximation is made for calculations near the resonance. Numerical results obtained from such a calculation are discussed. For the sake of simplicity the symmetric scalar fixed-source meson theory is used. But the principle of the method will be the same in the more essential but more complicated symmetric pseudoscalar case. Thus the present considerations will serve to guide an analogous investigation using the symmetric pseudoscalar theory.

Particle states of a quantized meson field

A simple non-linear field theory is considered as the model for a recently proposed classical field theory of mesons and their particle sources. Quantization may be made according to canonical procedures; the problem is to show the existence of quantum states corresponding with the particle-like solutions of the classical field equations. A plausible way to do this is suggested.

A non-linear field theory

A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy,characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hyper-charge. The postulates include one constant of the dimensions of length, and another that is conjectured necessarily to have the value ђc , or perhaps ½ ђc , in the quantized theory.

Pion Production fromπ−−pCollisions in the Long-Range Interaction Model

Long-range interactions of negative pions with protons resulting in single and double pion production are examined in terms of a meson field theory model in which it is assumed that there is a pion-pion interaction and that the single virtual pion exchange graphs are dominant in large-impact-parameter collisions. This pion exchange leads, in single pion production, to an "excited state," ${\ensuremath{\pi}}^{*}$, which "decays" into two pions, and, in double pion production, also to an "excited state," ${N}^{*}$, which "decays" into a pion and a nucleon. For sufficiently high relative energy of the incident ${\ensuremath{\pi}}^{\ensuremath{-}}$ and proton, each of these processes can occur for small values of the invariant square of the virtual pion four-momentum, ${\ensuremath{\Delta}}^{2}$, in which case the virtual pion carries very little transverse three-momentum. For small ${\ensuremath{\Delta}}^{2}$ it is shown that it is reasonable to neglect final state interactions between the "decay products" of the ${\ensuremath{\pi}}^{*}$ and those of the ${N}^{*}$. It is found that in the limit ${\ensuremath{\Delta}}^{2}\ensuremath{\rightarrow}\ensuremath{-}{\ensuremath{\mu}}^{2}$, where $\ensuremath{\mu}$ is the pion rest mass, the virtual pion behaves kinematically, in the ${\ensuremath{\pi}}^{*}$ barycentric system, as an incoming pion which scatters elastically with the incident ${\ensuremath{\pi}}^{\ensuremath{-}}$, and also behaves, in the ${N}^{*}$ barycentric system, as an incoming pion which scatters elastically with the incident proton. Thus, for small ${\ensuremath{\Delta}}^{2}$ in the physical region the ${\ensuremath{\pi}}^{*}$ and ${N}^{*}$ vertices are defined as the corresponding off-the-mass-shell scattering amplitudes. A ratio of appropriately defined double-to-single pion production cross sections is obtained which is independent of the details of the assumed pion-pion interaction, and depends only on the relative strengths of ${N}^{*}$ and $N$ formation. This ratio is estimated by means of the $p$-wave static nucleon model, applied in appropriate coordinate systems. For incident 5-Bev/c pions this model leads to double pion production which is important compared to single pion production, both because of the $\frac{3}{2}\ensuremath{-}\frac{3}{2}$ pion-nucleon resonance and because of important phase-space factors. Kinematical considerations similar to those described above suggest that this model may also be the theoretical genesis of the "two fireballs" model proposed for ultrarelativistic nucleon-nucleon collisions.

A unified model of K - and π -mesons

On the foundation of an antecedent non-linear meson field theory it is suggested that the π -meson fields may be described in terms of collective motions of the K -meson fields. A particular model of the K -nucleon interaction is considered whose collective π -modes have symmetrical PV coupling with the nucleon system; parity is conserved to a great extent for the π -nucleon system in the absence of strange particles. The direct K -nucleon interactions do not conserve parity; their sign and symmetry are qualitatively acceptable. The masses and coupling constants of the meson fields are determinate in terms of one universal coupling constant and a cut-off. The structure of this model suggests a natural way for the introduction of the ‘spurion’, describing weak interactions that violate strangeness.

On nuclear magnetic moment in meson field theory

The nuclear magnetic moment is studied in pseudovectorpseudoscalar charged meson theory with a space-time extended source model and the equivalent energy-momentum cut-off.

Phenomenological Theory of Pion-Nucleon Reactions

A considerable part in the interpretation of pi -N reactions can be made independently of the details of meson field theory. Such part is discussed, separating the dynamical effects of pi -N interactions. A historical survey on this approach is given for the purpose of elucidating a trend of activities in Japan. Both the angular distributions of pions and the polarizations of recoil nucleons are calculated for pi -N scattering and photopion production. The relations between the two reactions were investigated by using the unitarity of the S-matrix. The possible violation of charge independence expected at low energies is discussed. Although the effects of charge dependent interactions are small, ex cept for Coulomb interference, estimates may facilitate the analysis of more accurate experiments. (auth)

Mesons and the structure of nucleons

An atomic model of the physical nucleons is considered in which the structure is represented as a nucleon core surrounded by a pion cloud in a p 1 2 state, the system being in a state of isotopic spin 1 2 . From the pion wave function, constructed on this basis, the static properties of the physical nucleons—magnetic moments, charge distributions, mass difference—are derived and compared with observation. Modifications are considered which could bring the predictions of this model into better accord with the experiments. It is shown that the core must be given properties, both of size and of structure, which deviate considerably from those of the Dirac nucleons. Some discussion is given of the relationships of the atomic model to meson field theories.

Collective motion in quantum mechanics

A general method of discussing quantum-mechanical problems involving collective motion is proposed, in which the emphasis is placed on consideration of sets of states rather than single states, and in which the additional collective co-ordinates are not redundant but used to describe the sets. The method is applied to a number of relatively simple examples: plasma oscillations of an electron gas; some problems of nuclear structure including the α-particle model and the collective model; and to two problems in meson field theory, concerning nucleon isobars in strong-coupling theory and concerning nucleon recoil. One of the main aims is to determine as well as possible the parameters of the collective motion; in particular, a formula is given for the moment of inertia of a rotating system.

Integral equations for meson field theory

A covariant method of approximating the nucleon Green’s functionS′F is described, in terms of the solution of a connected sequence of linear integral equations. Explicit expressions for the matrix elements for processes involving only one real nucleon are derived by formal functional differentiation ofS′F with respect to external boson fields. The solution is renormalized, in the sense that its power series expansion in the coupling constantg is the same that obtained by enumerating Feynman diagrams and renormalizing term by term. Closed loops are neglected, though virtual nucleon pairs not corresponding to closed loops are included.

Interpretation of Proton-Proton Interactions at Cosmotron Energies

In the absence of numerical predictions based on meson field theory, elastic $p\ensuremath{-}p$ interactions have been compared with a simple optical model and inelastic ones with statistical theories and considerations based on charge independence. Elastic scattering data are fitted satisfactorily by a spherical interaction region with uniform density, radius 0.93\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm and absorption coefficient from 4.3 to 2.7\ifmmode\times\else\texttimes\fi{}${10}^{13}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. Inelastic interactions provide a confirmatory test of charge independence at 0.81 Bev. Pion multiplicities at 1.5 and 2.75 Bev are higher than predicted by the Fermi statistical theory, but the difference is less than that observed for $n\ensuremath{-}p$ interactions. The multiplicities observed for $p\ensuremath{-}p$ interactions are lower than those calculated by Kovacs. Distributions of angle and momentum of particles, and correlation angle and $Q$ values for pairs of particles, in general agree with the predictions of statistical theory at 0.81 Bev and disagree at 1.5 Bev. The data that are not consistent with statistical predictions suggest that a $\ensuremath{\pi}$-nucleon interaction may affect pion production in an important way, but the data are not sufficiently accurate for definite conclusions.

Note on the nucleon self-action in the classical scalar meson field theory

The nucleon self-force terms in the equations of motion in the classical scalar meson field theory are evaluated in the case of a uniform circular motion for both the symmetric and retarded fields. The self-force is discussed in the case of the two-body problem.

Classical Meson Theory. I

Meson field theory is introduced from an elementary point of view in analogy with familiar classical fields. Three formulations are considered: scalar, pseudoscalar, and vector. In the symmetric theory the isotopic spin of a nucleon is taken to be a classical vector in charge space.

SOME HINT TO THE FORM OF NUCLEAR POTENTIAL OBTAIEND FROM MESON FIELD THEORY

摘要 Abstract A nuclear potential based on meson field theory is obtained in analogy with the derivation of Breit interaetion between two electrons, as given by Ivanenko and Sokolov.In this treatment the meson field is not quantized. All the four type of the current meson field and their mixture can be treated in the same way. The result has been further reduced by expansion in the v/c of the nucleon, the zeroth-order potental being identical with the static potential previously obtained by Mller and Rosenfeld . The first-order poential will vanish if there is only one coupling constant for each type of meson field , in which case the expansion has been carried to the second order of v/c , retardation effects being also included. Many-body forces naturally appear. 作者及机构信息 严肃 1. 北京大学物理系 Authors and contacts Yan Su 参考文献 [1] 施引文献

Modified propagators in field theory (with application to the anomalous magnetic moment of the nucleon)

Many attempts have been made to improve upon the perturbation expansion in meson-field theories, one such attempt being the introduction of modified propagators S' F and ∆' F . It is shown in this paper that the introduction of these new propagators (or at least in the form that has been proposed) creates new infinities which cannot be removed by renormalization. These new infinities are due to new complex poles of the modified propagators. A tentative prescription is put forth to get over these new difficulties, but it is still intimately connected with the perturbation expansion. Unfortunately, the prescription does not give an unambiguous answer. A particular S' F is used in the calculation of the anomalous magnetic moment of the nucleon. The results obtained are no better than those of other workers. However, there are many reasons why this may be the case. It is also shown that the subseries which arises in this case leads, at best, to an asymptotic expansion in the coupling constant. The nature of the singularity at zero coupling is found.