Murray Gell-Mann

The following sections are included:

• Murray Gell-Mann

• CONTENTS

The following sections are included:

• The Garden of Live Flowers

• Strangeness

• Quantum Electrodynamics at Small Distances

• Behavior of Neutral Particles under Charge Conjugation

• Sixth Annual Rochester Conference (Rochester, 1956)

• Theory of the Fermi Interaction

• The Eightfold Way: A Theory of Strong Interaction Symmetry

• Symmetries of Baryons and Mesons

• Prediction of the Ω⁻ Particle

• Elementary Particles of Conventional Field Theory as Regge Poles

• A Schematic Model of Baryons and Mesons

• Current Topics in Particle Physics

• Behavior of Current Divergences under SU₃ × SU₃

• Light Cone Current Algebra

• Light-Cone Current Algebra, π⁰ Decay, and e⁺e⁻ Annihilation

• Quarks

• Current Algebra: Quarks and What Else?

• Advantages of the Color Octet Gluon Picture

• Complex Spinors and Unified Theories

• Particle Theory: From S-Matrix to Quarks

• Remarks Given at the Celebration of Victor Weisskopf's 80th Birthday

• Quantum Mechanics in the Light of Quantum Cosmology

• Dick Feynman — The Guy in the Office Down the Hall

• Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

• Progress in Elementary Particle Theory, 1950–1964

• Nature Conformable to Herself

• Quarks, Color, and QCD

• Effective Complexity

• Asymptotically Scale-Invariant Occupancy of Phase Space Makes the Entropy S_q Extensive

• Quasiclassical Coarse Graining and Thermodynamic Entropy

• Progress in Elementary Particle Theory, 1946–1973

This section consists of an introduction by the author and the following reprint articles are included:

• Isotopic Spin and New Unstable Particles

• On the Classification of Particles

L'exposé ne prétend pas être une mise au point historique de la naissance du concept d'étrangeté. C'est simplement un récit de souvenirs personnels sur les idées et l'atmosphère de la période 1951 – 1953. Les raisons qui ont guidé l'auteur pour introduire “l'étrangeté” sont développées et il dit comment il a eu à convaincre et surmonter les oppositions.

This paper is not a history of the discovery of the strangeness, but rather a contribution to such a history, consisting of personal reminiscences. The atmosphere and ideas of the period 1951 – 1953 are described. The author explains the reasons that led him to introduce the concept of the strangeness and how he had to convince people and to overcome oppositions.

The renormalized propagation functions D_FC and S_FC for photons and electrons, respectively, are investigated for momenta much greater than the mass of the electron. It is found that in this region the individual terms of the perturbation series to all orders in the coupling constant take on very simple asymptotic forms. An attempt to sum the entire series is only partially successful. It is found that the series satisfy certain functional equations by virtue of the renormalizability of the theory. If photon self-energy parts are omitted from the series, so that D_FC=D_F, then S_FC has the asymptotic form A[p²/m²]ⁿ[iγ·p]⁻¹, where A = A(e₁²) and n = n(e₁²). When all diagrams are included, less specific results are found. One conclusion is that the shape of the charge distribution surrounding a test charge in the vacuum does not, at small distances, depend on the coupling constant except through a scale factor. The behavior of the propagation functions for large momenta is related to the magnitude of the renormalization constants in the theory. Thus it is shown that the unrenormalized coupling constant e₀²/4πħc, which appears in perturbation theory as a power series in the renormalized coupling constant e₁²/4πħc with divergent coefficients, may behave in either of two ways:

(a) It may really be infinite as perturbation theory indicates;

(b) It may be a finite number independent of e₁²/4πħc.

Some properties are discussed of the θ⁰, a heavy boson that is known to decay by the process θ⁰→π⁺+π⁻. According to certain schemes proposed for the interpretation of hyperons and K particles, the θ⁰ possesses an antiparticle distinct from itself. Some theoretical implications of this situation are discussed with special reference to clrarge conjugation invariance. The application of such invariance in familiar instances is surveyed in Sec. I. It is then shown in Sec. II that, within the framework of the tentative schemes under consideration, the θ⁰ must be considered as a “particle mixture” exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all θ⁰'s undergo the familiar decay into two pions. Some experimental consequences of this picture are mentioned.

The following reprint articles are included:

• Field Theory on the Mass Shell

• The Nature of the Weak Interaction

The representation of Fermi particles by two-component Pauli spinors satisfying a second order differential equation and the suggestion that in β decay these spinors act without gradient couplings leads to an essentially unique weak four-fermion coupling. It is equivalent to equal amounts of vector and axial vector coupling with two-component neutrinos and conservation of leptons. (The relative sign is not determined theoretically.) It is taken to be “universal”; the lifetime of the μ agrees to within the experimental errors of 2%. The vector part of the coupling is, by analogy with electric charge, assumed to be not renormalized by virtual mesons. This requires, for example, that pions are also “charged” in the sense that there is a direct interaction in which, say, a π⁰ goes to π⁻ and an electron goes to a neutrino. The weak decays of strange particles will result qualitatively if the universality is extended to include a coupling involving a Λ or Σ fermion. Parity is then not conserved even for those decays like K → 2π or 3π which involve no neutrinos. The theory is at variance with the measured angular correlation of electron and neutrino in He⁶, and with the fact that fewer than 10⁻⁴ pion decay into electron and neutrino.

The following sections are included:

• The “Leptons” as a Model for Unitary Symmetry

• Mathematical Description of the Baryons

• Pseudoscalar Mesons

• Vector Mesons

• Weak Interactions

• Properties of the New Mesons

• Violations of Unitary Symmetry

• Acknowledgments

• REFERENCES

The system of strongly interacting particles is discussed, with electromagnetism, weak interactions, and gravitation considered as perturbations. The electric current j_α, the weak current J_α, and the gravitational tensor θ_αβ are all well-defined operators, with finite matrix elements obeying dispersion relations. To the extent that the dispersion relations for matrix elements of these operators between the vacuum and other states are highly convergent and dominated by contributions from intermediate one-meson states, we have relations like the Goldberger-Treiman formula and universality principles like that of Sakurai according to which the ρ meson is coupled approximately to the isotopic spin. Homogeneous linear dispersion relations, even without subtractions, do not suffice to fix the scale of these matrix elements; in particular, for the nonconserved currents, the renormalization factors cannot be calculated, and the universality of strength of the weak interactions is undefined. More information than just the dispersion relations must be supplied, for example, by field-theoretic models; we consider, in fact, the equal-time commutation relations of the various parts of j₄ and J₄. These nonlinear relations define an algebraic system (or a group) that underlies the structure of baryons and mesons. It is suggested that the group is in fact U(3)×U(3), exemplified by the symmetrical Sakata model. The Hamiltonian density θ₄₄ is not completely invariant under the group; the noninvariant part transforms according to a particular representation of the group; it is possible that this information also is given correctly by the symmetrical Sakata model. Various exact relations among form factors follow from the algebraic structure. In addition, it may be worthwhile to consider the approximate situation in which the strangeness-changing vector currents are conserved and the Hamiltonian is invariant under U(3); we refer to this limiting case as “unitary symmetry.” In the limit, the baryons and mesons form degenerate supermultiplets, which break up into isotopic multiplets when the symmetry-breaking term in the Hamiltonian is “turned on.” The mesons are expected to form unitary singlets and octets; each octet breaks up into a triplet, a singlet, and a pair of strange doublets. The known pseudoscalar and vector mesons fit this pattern if there exists also an isotopic singlet pseudoscalar meson χ⁰. If we consider unitary symmetry in the abstract rather than in connection with a field theory, then we find, as an attractive alternative to the Sakata model, the scheme of Ne'eman and Gell-Mann, which we call the “eightfold way”; the baryons N, Λ, Σ, and Ξ form an octet, like the vector and pseudoscalar meson octets, in the limit of unitary symmetry. Although the violations of unitary symmetry must be quite large, there is some hope of relating certain violations to others. As an example of the methods advocated, we present a rough calculation of the rate of K⁺ → μ⁺+ρ in terms of that of π⁺ → μ⁺ + ν.

If we take the unitary symmetry model with baryon and meson octets, with first order violation giving rise to mass differences, we obtain some rules for supermultiplets. The broken symmetry picture is hard to interpret on any fundamental theoretical basis, but I hope that such a justification may be forthcoming on the basis of analytic continuation of resonant states in isotopic spin and strangeness. Instead of constructing just the inverse Regge function E (J), we can consider surfaces E (J, I, Y, etc.). Certainly the dynamical equations are as smooth in I and Y as they are in J…

Note from Publisher: This article contains the abstract only.

Composite states in nonrelativistic scattering theory lie on Regge trajectories¹ corresponding to poles in the angular momentum plane that move with varying energy. Simple approximations^2-5 indicate that composite particles in relativistic field theory have the same behavior. According to the Regge pole hypothesis^6-9, particles like the nucleon, that have customarily been treated as elementary in field theory, also lie on Regge trajectories. Is that in accord with describing such particles by ordinary perturbation theory?…

If we assume that the strong interactions of baryons and mesons are correctly described in terms of the broken “eightfold way”^1-3), we are tempted to look for some fundamental explanation of the situation. A highly promised approach is the purely dynamical “boot trap” model for all the strongly interacting particles within which one may try to derive isotopic spin and strangeness conservation and broken eightfold symmetry from self-consistency alone ⁴⁾. Of course, with only strong interactions, the orientation of the asymmetry in the unitary space cannot be specified; one hopes that in some way the selection of specific components of the F-spin by electromagnetism and the weak interactions determines the choice of isotopic spin and hyper-charge directions…

It's a great pleasure and a great honor to be here and to address such a distinguished audience and so many old friends, but I'm not at all clear about what the subject should be. It was implied that I had chosen the task of summarizing the Conference in advance; that is hardly the case. I've had lots of advice from many people about what to do. Some people have said, “I hope that you can tell us everything that's going to be important so we don't have to go to the sessions.” Others have insisted that it would be absurd to try to summarize the Conference in advance and what I should do is to give some general philosophical statements about the progress of high energy physics and the meaning of high energy physics. Other people have told me that I am far too young and far too involved in the subject to be able to give any general philosophical pronouncements and that I should concentrate on some discussion of what's going on in the field. I think the last is probably the most reasonable. I'll try to say something about my personal prejudices about the field. The theme, let us say, is what I am eager to hear about at the Conference in the next few days on the basis of all the rumors since the preceding Conference. Now, if I don't mention something that you have done that's not at all because I don't consider it important or because I'm not anxious to hear about it but only because there isn't time to talk about everything here. And if I mention very few names, it will be simply because I don't want to make the mistake of leaving out any. I may mention some for purposes of identification or to quote those people who modestly left themselves off the invitation list…

We investigate the behavior under SU₃×SU₃ of the hadron energy density and the closely related question of how the divergences of the axial-vector currents and the strangeness-changing vector currents transform under SU₃×SU₃. We assume that two terms in the energy density break SU₃×SU₃ symmetry; under SU₃ one transforms as a singlet, the other as the member of an octet. The simplest possible behavior of these terms under chiral transformations is proposed: They are assigned to a single (3,3*) + (3*,3) representation of SU₃×SU₃ and parity together with the current divergences. The commutators of charges and current divergences are derived in terms of a single constant c that describes the strength of the SU₃-breaking term relative to the chiral symmetry-breaking term. The constant c is found not to be small, as suggested earlier, but instead close to the value corresponding to an SU₂×SU₂ symmetry, realized mainly by massless pions rather than parity doubling. Some applications of the proposed commutation relations are given, mainly to the pseudoscalar mesons, and other applications are indicated.

The following sections are included:

• PREFACE

• INTRODUCTION

• DILATION OPERATOR AND BROKEN SCALE INVARIANCE

• LIGHT CONE COMMUTATORS AND DEEP INELASTIC ELECTRON SCATTERING

• GENERALIZED LIGHT CONE SCALING AND BROKEN SCALE INVARIANCE

• BILOCAL OPERATORS

• LIGHT CONE ALGEBRA ABSTRACTED FROM A QUARK PICTURE

• LIGHT CONE ALGEBRA AND DEEP INELASTIC SCATTERING

• CONCLUDING REMARKS

• ACKNOWLEDGEMENTS

• REFERENCES

The following sections are included:

• INTRODUCTION

• LIGHT-CONE ALGEBRA

• STATISTICS AND ALTERNATIVE SCHEMES

• DERIVATION OF THE π°→2γ AMPLITUDE IN THE PCAC APPROXIMATION

• ACKNOWLEDGMENTS

• REFERENCES

In these lectures I want to speak about at least two interpretations of the concept of quarks for hadrons and the possible relations between them.

First I want to talk about quarks as “constituent quarks”. These were used especially by G. Zweig (1964) who referred to them as aces. One has a sort of a simple model by which one gets elementary results about the low-lying bound and resonant states of mesons and baryons, and certain crude symmetry properties of these states, by saying that the hadrons act as if they were made up of subunits, the constituent quarks q. These quarks are arranged in an isotopic spin doublet u, d and an isotopic spin singlet s, which has the same charge as d and acts as if it had a slightly higher mass…

After receiving many requests for reprints of this article, describing the original ideas on the quark gluon gauge theory, which we later named QCD, we decided to place the article in the e–Print archive.

It is pointed out that there are several advantages in abstracting properties of hadrons and their currents from a Yang–Mills gauge model based on colored quarks and color octet gluons.

We were told by Frank Yang in his welcoming speech that supergravity is a phenomenon of theoretical physics. Why, at this time, is it not more than that? Self-coupled extended supergravity, especially for N = 8, seems very close to the overall unified theory for which all of us have yearned since the time of Einstein. There are no quanta of spin >2; there is just one graviton of spin 2; there are N gravitini of spin 3/2, just right for eating the N Goldstone fermions of spin 1/2 that are needed if N-fold supersymmetry is to be violated spontaneously; there are N(N−1)/2 spin 1 bosons, perfectly suited to be the gauge bosons for SO_N in the theory with self-coupling. There are N(N − 1)(N − 2)/6 spin 1/2 Majorana particles, and with the simplest assignments of charge and colour they include isotopic doublets of quarks and leptons. The theory is highly non–singular in perturbation theory, and the threatened divergence at the level of three loops has not even been demonstrated. The apparently arbitrary cancellation of huge contributions of opposite sign to the cosmological constant (from self-coupling on the one hand and from spontaneous violation of supersymmetry on the other) has been phrased in such an elegant way that it may be acceptable. (Of course, if we follow Hawking at al., we may not even need to cancel out the cosmological constant!)…

The following sections are included:

• The renormalization group and the possible failure of old-fashioned field theory

• Dispersion relations and the «S-matrix» program

• Hadron approximate symmetries and Yang-Mills theories for the electro-weak and strong interactions

• Quarks

Forty years ago, I arrived at M.I.T. as a graduate student. I was discouraged at having been rejected by Princeton and granted insufficient financial aid by Harvard. The only really friendly letter that I received from a graduate school in physics was one from M.I.T. welcoming me as a potential student and as a research assistant in theoretical physics to a certain Professor Weisskopf, of whom I had never heard, but who added a personal letter of invitation of his own. I have described elsewhere how that letter arrived as I was contemplating suicide, as befits someone rejected by the Ivy League. It occurred to me however, (and it is an interesting example of non-commutation of operators) that I could try M.I.T. first and kill myself later, while the reverse order of events was impossible…

We sketch a quantum-mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the “quasiclassical domain” of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is, in an appropriate sense, maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. We pose the problem of making these notions precise and quantitative. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An “observer” (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain, or rather a set of such domains among which it cannot discriminate because of its own very coarse graining. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its initial condition, and a study of the problem of quasiclassical domains.

The following sections are included:

• Summing over histories

• Shedding light on quantum mechanics

• Seeking rules for quantum gravity

• Quantum cosmology

• Turning things around

• References

The following sections are included:

• Introduction

• The Arrow of Time in Quantum Mechanics

• A Time-Neutral Formulation of Quantum Mechanics for Cosmology

• Classical Two-Time Boundary Problems
  • A Simple Statistical Model
  • Classical Dynamical Systems with Two-Time Statistical Boundary Conditions
  • Electromagnetic Radiation

• Hypothetical Quantum Cosmologies with Time Symmetries
  • CPT- and T-Symmetric Boundary Conditions
  • T Violation in the Weak Interactions

• The Limitations of Decoherence and Classicality
  • Decoherence
  • Impossibility of a Universe with ρ_f = ρ_i
  • Classicality

• Conclusions

• Acknowledgments

• References

I should like to begin by expressing regret for not having been able to be present for the last Fermilab meeting, at which I had been asked to give the final talk about what it was like to be a student of theoretical physics in the late forties, the end of the period covered by that meeting. I still hope to present that material somewhere. Between that conference and this one there were two others, one in Paris in the summer of 1982, where I gave a talk about my experiences with strangeness,¹ and one in 1983, in Sant Feliu de Guíxols in Catalunya, where I spoke on the subject “Particle Theory from S-Matrix to Quarks.”² That second conference was called a “trobada” in the Catalan language, a word that reminds us of the troubadours of the Middle Ages who flourished in Catalunya. It reminds us also that we have become much like those medieval minstrels. We spend a great deal of time now traveling from one orgy of reminiscence to another, each one held in the capital of some princely state. Here I am helping to close another “trobada.”…

Why are elegance and simplicity suitable criteria to apply in seeking to describe nature, especially at the fundamental level? Science has made notable progress in elucidating the basic laws that govern the behavior of all matter everywhere in the universe—the laws of the elementary particles and their interactions, which are responsible for all the forces of nature. And it is well known that a theory in elementary particle physics is more likely to be successful in describing and predicting observations if it is simple and elegant. Why should that be so? And what exactly do simplicity and elegance really mean in this connection?…

The story of my early speculations about quarks begins in March 1963, when I was on leave from Caltech at MIT and playing with various schemes for elementary objects that could underlie the hadrons. On a visit to Columbia, I was asked by Bob Serber why I didn&t postulate a triplet of what we would now call SU(3) of flavor, making use of my relation to explain baryon octets, decimets, and singlets. I explained to him that I had tried it. I showed him on a napkin (at the Columbia Faculty Club, I believe) that the electric charges would come out +⅔, −⅓, −⅓ for the fundamental objects. During my colloquium that afternoon, I mentioned the notion briefly, but meanwhile I was reflecting that if those objects could not emerge to be seen individually, then all observable hadrons could still have integral charge, and also the principle of “nuclear democracy” (better called “hadronic egalitarianism”) could still be preserved unchanged for observable hadrons. With that proviso, the scheme appealed to me…

It would take a great many different concepts—or quantities—to capture all of our notions of what is meant by complexity (or its opposite, simplicity). However, the notion that corresponds most closely to what we mean by complexity in ordinary conversation and in most scientific discourse is “effective complexity.” In nontechnical language, we can define the effective complexity (EC) of an entity as the length of a highly compressed description of its regularities [6, 7, 8]…

Phase space can be constructed for N equal and distinguishable subsystems that could be probabilistically either weakly correlated or strongly correlated. If they are locally correlated, we expect the Boltzmann–Gibbs entropy S_BG ≡ −k Σ_ip_i ln p_i to be extensive, i.e., S_BG(N) ∝ N for N → ∞. In particular, if they are independent, S_BG is strictly additive, i.e., S_BG(N) = NS_BG(1). ∀N. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy (with S₁ = S_BG) for some special value of q ≠ 1 to be the one which is extensive [i.e., S_q(N) ∝ N for N → ∞]. Another concept which is relevant is strict or asymptotic scale-freedom (or scale-invariance), defined as the situation for which all marginal probabilities of the N-system coincide or asymptotically approach (for N → ∞) the joint probabilities of the (N − 1)-system. If each subsystem is a binary one, scale-freedom is guaranteed by what we hereafter refer to as the Leibnitz rule, i.e., the sum of two successive joint probabilities of the N-system coincides or asymptotically approaches the corresponding joint probability of the (N − 1)-system. The kinds of interplay of these various concepts are illustrated in several examples. One of them justifies the title of this paper. We conjecture that these mechanisms are deeply related to the very frequent emergence, in natural and artificial complex systems, of scale-free structures and to their connections with nonextensive statistical mechanics. Summarizing, we have shown that, for asymptotically scale-invariant systems, it is S_q with q ≠ 1, and not S_BG, the entropy which matches standard, clausius-like, prescriptions of classical thermodynamics.

Our everyday descriptions of the universe are highly coarse grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modem quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no nontrivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact. Quantum theory allows for various coarse-grained descriptions, some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of “quasiclassical descriptions” defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a “quasiclassical realm” this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.

The following sections are included:

• PROGRESS TO 1951

• PROGRESS 1952-1962

• PROGRESS 1963-1967

• PROGRESS 1968-1973