Leonard Susskind

Charge shielding and quark confinement in the massive schwinger model

The Schwinger model is quantum electrodynamics with massless fermions in two dimensions. It is known that the asymptotic states of the theory contain no states corresponding to free fermions (“quark trapping”) and that local charge conservation is spontaneously broken (“Higgs phenomenon”). We investigate to what extent these phenomena persist when the fermion is given a bare mass. We find quark trapping but no Higgs phenomenon. The second of these results is dependent on mass perturbation theory; the first is not.

Dual-symmetric theory of hadrons.—I

SummaryA theory of mesons is based on the experimentally observed linear level spacing of hadron excitations. The theory uses a model for the internal structure of mesons consisting of a system of harmonic vibrations. Roughly speaking, a meson is described by the degrees of freedom of a four-dimensional rubber band with a quark pair embedded in it. The theory satisfies relativistic invariance, crossing symmetry and a generalization of duality which we call dual-symmetry. In the approximation of retaining only tree graphs, the scattering amplitudes are given by then-point dual amplitudes recently proposed by Virasoro, Bardakci and Ruegg, Chan and Goebel and Sakita. In the special case,n=4, we reproduce Veneziano’s formula.RiassuntoSi basa una teoria mesonica sul distanziamento lineare dei livelli osservato sperimentalmente. La teoria usa un modello per la struttura interna dei mesoni consistente di un sistema di vibrazioni armoniche. Parlando in generale, si descrive un mesone con i gradi di libertà di una striscia di gomma a quattro dimensioni che porta incastonata una coppia di quark. La teoria soddisfa l’invariauza relativistica, la simmetria incrociata ed una generalizzazione della dualità che è chiamata simmetria duale. Facendo l’approssimazione di conservare solo tre grafici, si esprimono le ampiezze di scattering con le ampiezze duali conn punti proposte recentemente da Virasoro, Bardakci e Ruegg, da Chan e Goebel e da Sakita. Nel caso specialen=4 si riottiene la formula di Veneziano.РезюмеТеория мезона основывается на экспериментально наблюдаемом линейном интервале между уровнями для адронных возбуждений. Эта теория использует модель для внутренней структуры мезонов, состоящую из системы гармонических колебаний. Грубо говоря, мезон описывается степенями свободы для четырехмерного «резинового слоя» с внедренной в него парой кварков. Рассматриваемая теория удовлетворяет релятивистской инвариантности, кроссинг-симметрии и обобщению дуальности, которое мы называем дуальной симметрией. В приближении, сохраняющем лишь древовидные графики, вьшисываются амплитуды рассеяния черезn-точечные дуальные амплитуды, недавно предложенные Вирасоро, Вардакчи и Руеггом, Ченом и Гоебелом и Сакита. В частном случаеn=4 мы воспроизводим формулу Венециано.

The parton picture of elementary particles

Abstract The parton theory is developed along several lines. We begin by developing quantum mechanics in the infinite momentum frame. The Galilean analogy is worked out and the use of non-relativistic reasoning in relativistic contexts is illustrated. Applications of infinite momentum quantum mechanics include the computation of the radius of a relativistic bound state, space time visualization of the multiperipheral model, and the eikonal approach to high energy scattering. The classic phenomenological applications of the parton model are reviewed and explained. These include deep inelastic electroproduction, the shrinking photon effect and heavy lepton pair production. The string-model of hadrons is formulated in the infinite momentum frame as a parton model. We consider currents and the distribution of spins among the partons of the hadronic string. We suggest that it is profitable to view a hadron as a one-dimensional lattice of spins and isospins and show that many of the properties of the lattice can be related to the meson spectrum. Applications of the spin lattice idea are made to deep inelastic electron and neutrino scattering. Predictions are made for the behavior of the structure functions in these processes. Multiparticle production is examined in the string model. We derive the distribution of secondaries in longitudinal and transverse momentum, the charge per secondary as a function of rapidity and the correlations among secondaries at different rapidities. Speculations are made about a class of phenomena which go beyond the string model. These phenomena we call hard parton effects. They include the production of large transverse momenta among secondaries, logarithmically increasing total cross sections and power behaviors of wide angle exlusive cross sections. We conclude with some speculations about the breakdown of the parton model.

A quantitative approach to low-energy quantum chromodynamics

Abstract A general method for solving the low-energy spectrum of an infrared unstable field theory is presented. The method involves a strong coupling expansion of the lattice approximation to the theory. Ultimately the results must be continued to zero-coupling constant in accord with the asymptotic freedom of such theories. The method is applied to the pure gauge field (glueball) part of quantum chromodynamics. The spectrum of lowest-lying states consists of a scalar and tensor which are almost degenerate and an axial vector with mass ≈1.6 times the scalar mass. The same procedure applied to the Abelian gauge theory yields unstable results which may indicate the presence of a phase transition.

Non-planar dual symmetric loop graphs and the pomeron

Abstract Dual symmetric single loop graph amplitudes are constructed using the world sheet postulate and H. B. Nielsens Lagrangian method. The result agrees with the sewing procedure of Bardakci, Halpern and Shapiro for planar loops and the prescription of Gallardo, Galli and Susskind for non-planar graphs. Non-planar loops possess a Pomeranchuk-like trajectory with slope 1 2 α′(0) .

HARD AND SOFT PROCESSES IN HADRODYNAMICS.

Abstract We consider the consequences of a parton-parton interaction which is long range in rapidity and capable of transferring large momentum. The results of our analysis for hadron-hadron inclusive processes are presented.

REMOVAL OF THE DIVERGENCE OF A PLANAR DUAL-SYMMETRIC LOOP.

Abstract The nature of the divergence in the planar loop dual amplitude is examined. The divergent part is isolated and subtracted. The subtraction is Regge behaved and is essentially unique.

Recent Progress in Theories of Deep Inelastic Phenomena

We discuss in simple physical terms two recently proposed field theoretic mechanisms which may shed light on deep inelastic phenomena. Certain gauge theories of quarks can have the short distance and light cone properties of quark fields without their production in scattering experiments. Gauge theories can also be free at short distances and lead to asymptotic Bjorken scaling broken only by logarithms. These proposals suggest non‐abelian gauge theories of colored quarks as the field‐theoretic basis of strong interactions.