Yoichiro Nambu

QCD and the string model

Abstract Infinitisimal variations of the path-dependent phase factor P exp(i∫σAμdzμ) in gauge theory are studied. They are shown to satisfy differential equations which are equivalent to those for a quantized string if the gauge fields meet certain constraints.

String-like configurations in the Weinberg-Salam theory☆

The Weinberg-Salam theory of electromagnetic and weak interactions admits classical configurations in which a pair of magnetic monopoles is bound by a flux string of the Z0 field. They give rise to Regge trajectories of excitations with a mass scale in the TeV range.

Dispersion relations for nucleon-nucleon scattering

Abstract Dispersion relations for nucleon-nucleon scattering are presented. The general case of nonforward scattering is treated, although the majority of the discussion is confined to the limiting cases of forward scattering and the non-relativistic approximation. It is shown that in the relativistic case the dispersion relations for nucleon-nucleon scattering necessarily involve the nucleon-antinucleon amplitude. Some qualitative conclusions are drawn about the differences between the nucleon-nucleon and nucleon-antinucleon interactions. The concept of a potential in quantum field theory is discussed briefly.

Relativistic Wave Equations for Particles with Internal Structure and Mass Spectrum

Relativistic wave equations may be expected to play two roles, which we will call kinematical and dynamical. In the kinematical sense, a wave equation singles out a particle of definite mass and spin, usually together with its anti-particle counterpart, and specifies how the components of the wave function transform as we change its state of motion or our reference system. This law of transformation must be in accordance with the Poincare group,**) and therefore a wave equation should characterize an irreducible unitary representation of that group appropriate to quantum mechanical description of a particle!) In the dynamical sense, however, a wave equation ought to serve more purposes. It should be able to describe not only an isolated free particle, but also a particle in interaction, at least with classical fields such as the electromagnetic and gravitational fields, and ideally with all other dynamical fields and associated particles. A wave equation then becomes an equation

PARAMETRIC REPRESENTATIONS OF GENERAL GREEN'S FUNCTIONS

SummaryParametric representations for the Green’s function of field theory are derived in perturbation theory. These representations are valid for each term in the perturbation series that corresponds to a Feynman diagram, and reflect its analytic property and threshold characteristics. As an example, the three-body (vertex) function is shown to satisfy a dispersion relation when two of the three momenta are fixed, with the correct location of the singularities expected from the thresholds of the competing real processes.RiassuntoSi derivano, nella teoria delle perturbazioni, delle rappresentazioni parametriche per la funzione di Green della teoria dei campi. Tali rappresentazioni sono valide per ogni termine della serie perturbativa corrispondente a un diagramma di Feynman e rispecchiano la sua proprietà analitica e le sue caratteristiche di soglia. Come esempio si dimostra che quando siano fissati due dei tre impulsi la funzione di tre corpi (di vertice) soddisfa una relazione di dispersione con la corretta localizzazione delle singolarità previste in base alle soglie dei prooessi reali in competizione.

Hamilton—Jacobi formalism for strings

Abstract It is shown that a Hamilton—Jacobi-type formalism can be set up to deal with the classical dynamics of relativistic strings and other one-dimensional extended systems. A special feature is that the formalism involves two evolution parameters which are treated on an equal footing. The corresponding Hamilton—Jacobi functions turn out to be vector potentials or Clebsch potentials, and in this sense we find a link between the string model and gauge field theory.

S Matrix in semiclassical approximation

Abstract It is shown that the tree approximation currently utilized in connection with phenomenological chiral Lagrangians corresponds to a semiclassical approximation applied to the S-matrix in quantum field theory. Some invariance properties of the S-matrix are derived in this framework.

Fermion-Boson relations in BCS-type theories

Supersymmetry is a mathematical idea in search of physical relevance, but so far the search has not been successful in the area where it originated: particle physics. The present report is an outcome of my attempt to understand the physical meaning of supersymmetry and to find examples of it in more familiar low energy physics. Iachello and collaborators [1] have observed that there is a kind of supersymmetry in nuclear physics. For certain nuclei in the mass number region of platinum, the low energy spectra of even-even nuclear species and neighboring even-odd species can be described by the same empirical formula based on group theory. I have been aware, on the other hand, that in theories of the BCS-type, there always is a simple relation between the mass (energy gap) of the basic fermion and those of the bosons (collective modes) [2]. To use the language of particle physics, the dynamically induced masses of the pion, quark and o meson stand in the ratio 0:1:2 (subject to higher order corrections). In terms of the effective o model (or Higgs or Ginsburg-Landau) Lagrangian, this implies that the self-coupling and the Yukawa constants are related by X = f 2 . Generic relations of this nature emerge in any BCS-Heisenberg-type four-fermion short-range interaction theory [3,11]. It is gratifying that such relations have been experimentally established in superconductors and superfluid helium 3, as I will discuss later. My speculation, then, is that the Iachello relation in nuclear physics may also be a manifestation of the BCS mechanism which is known to account for the nuclear pairing phenomenon. An immediate question that arises is whether the BCS or Ginsburg-Landau theory has a supersymmetry of which these relations are a consequence. I do not know the answer yet. Before coming to nuclear physics, however, I will first discuss the other examples to show the origin of the relations.

Anomalous thresholds in dispersion theory - I

SummaryThe form factor of a particle in the so-called anomalous case (loosely bound system) is studied from the viewpoint of: 1) description in terms of a Schrödinger-type wave function; 2) perturbation theory; and 3) dispersion theory. A prescription is given on how to calculate the absorptive part of a dispersion relation in the correct Riemann sheet.RiassuntoSi studia il fattore di forma di una particella nel cosidetto caso anomalo (sistema debolmente legato) dal punto di vista di: 1) la descrizione in termini di una funzione d’onda del tipo di Schrödinger; 2) la teoria della perturbazione e 3) la teoria della dispersione. Si da una prescrizione sul modo di calcolare la parte assorbitiva di una relazione di dispersione nel piano riemanniano appropriato.

The Aharonov–Bohm problem revisited

Abstract Explicit solutions are constructed, and their properties investigated, for a nonrelativistic charged particle in two dimensions in the presence of an arbitrary number of nonquantized magnetic vortices in free space as well as in a uniform magnetic field. After eliminating the gauge potential, the vortices are represented as branch points in one of the complex coordinates. Multivortex solutions in free space can be obtained only if the vortices are treated as dynamical objects. But all the solutions suffer from some unphysical properties. The formulas may be generalized to describe a system of anyons.