From Yang-Mills to Asymptotic Freedom to Quantum Chromodynamics

From Yang-Mills to Asymptotic Freedom to Quantum ChromodynamicsJiří Chýla, Institute of Physics, Prague

Včera v CERN

From Yang-Mills to Asymptotic Freedom to Quantum ChromodynamicsJiří Chýla, Institute of Physics, Prague

The story of the emergence of the concept of gauge invarianceand its importance for the formulation of physical laws showthat Dirac was right to expect that

Physical laws should have mathematical beauty

From Yang-Mills to Asymptotic Freedom to Quantum ChromodynamicsJiří Chýla, Institute of Physics, Prague

The story of the emergence of the concept of gauge invarianceand its importance for the formulation of physical laws showthat Dirac was right to expect that

Physical laws should have mathematical beautybut the converse is not true as

mathematical beauty does not necessarily imply physical relevance.

C.N. Yang: Interview in The Mathematical Intelligencer 15/4

N. Straumann: Early Histrory of Gauge TheoriesS. Weinberg: The Making of the Standard ModelH. Lipkin: Quark model and quark

phenomenologyO. Greenberg: From Wigner’s supermultiplet

theory to QCD G. ‘t Hooft: When was the asymptotic freedom

discovered? A.de Rujula: Fifty years of Yang-Mills theories:

a phenomeno- logical point of viewD. Gross: Oscar Klein and gauge theory

D. Gross: Twenty five years of asymptotic freedom

There are many excellent texts covering various aspects of the emergence and application of nonabelian gauge theories. Myrecommendations:

Premature burial

The renormalization procedure, developed by Dyson, Feynman, Schwinger and Tomanaga was spectacularly successful in QED. The physical meaning of renormalization was, however, not truly understood and the renormalization was considered by most physicists, including Dirac and Wigner a trick.

From Nambu’s book Quarks

The prevalent feeling was that renormalization simply swept the infinities under the rug, but that they were still there.

In middle 1950’s Landau and Pomeranchuk attempted to give the renormalization procedure in QED good physical meaning and mathematical sense. They put a finite “bare” electric charge e0=e(r0) on a sphere of radius r0 , placed it in the QED vacuum and calculated how it appears at a finite distance r>r0.

Sending the radius of bare electron to zero and keeping the bare charge e0 constant, the effective charge e2(r) vanishes for any fixed distance r! This is the famous problem of “zero charge”, which for Landau implied that QED is incomplete:We reach the conclusion that within

the limits of formal electrodymics a point interaction is equivalent to no interaction at all.

i.e. the QED vacuum screens the bare electric charge!

bare charge e0 must be a function of the radius r0!

Turning the argument around, they could have asked how would the bare charge e0=e(r0) or rather α(r0) have to depend on r0 to yield a finite effective electric coupling α(r) at distance r when r0 vanishes.

The second formula suggests that it would have to grow to infinity at finite distance rL defining the so called “Landau pole”.

In fact, the problem with the renormalization proce-dure in QED is not the fact that bare electric charge diverges, but that it does so at a finite (though very small) distance!

Landau pole in QED ...

Modern, inherently nonperturbative, approach to the renorma-lization, which lies at the heart of lattice gauge theory, is just to construct the dependence α0=α(r0) in such a way to yield finite values of physical quantities in the limit of vanishing r0.

One can only wonder whether Landau and Pomeranchuk asked themselves this natural question. Had they done it, they might be led to the concept of asymptotic freedom because it suffices to change the sign of β0 for the bare as well as effective charges to be well-defined, and actually vanish, at small distances

... is absent in QCD!

Dirac on renormalization of QED in 1974

Hence most physicists are very satisfied with the situation. They say: “Quantum electrodynamics is a good theory, and we do not have to worry about it any more.”

I must say that I am very dissatisfied with the situation, because this so-called “good theory” does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics.

Sensible mathematics involves neglecting a quantity when it turns out to be small – not neglecting it just because it is infinitely great and you do not want it!

Of course, the proper inference from this work is that the basic equations are not right....

There must be some drastic change introduced into them so that no infinities occur in the theory at all and so that we can carry out the solution of the equations sensibly, according to ordinary rules.

Dirac draw uncompromising conclusion:

Dirac criticism of the renormalization procedure

• was justified for QED, but • does not apply to Yang-Mills gauge theories.

For these theories Dirac was thus wrong!

' S

The beginning of all

In the present paper we wish to exlore the possibility of requiring all interactions to be invariant under independent rotations of the isotopic spin at all space-time points,..

pn starting point: isotopic dublet of nucleons:

We then propose that all physical processes (not involving electromagnetic field) be invariant under the isotopic gau-ge transformation

' S

Three electrically charged gauge bosons and their selfcoupling ensued automatically

this requirement lead them to the following Lagrangian density

The quanta of the b-field clearly have spin unity and iso-spin unity. We know their electric charge too because all the interactions that we propose must satisfy the law of conservation of the electric charge, which is exact.

gauge bosons

but question remained about the mass of the b-quantum

A conclusion about the mass of the b-quantum is of course very important in deciding whether the proposal of the existen-ce of the b-field is consistent with experimental information.

We next come to the question of the mass of the b-quantum,to which we do not have a satisfactory answer. One may argue that without a nucleon field the lagrangian would contain noquantity of the dimension of a mass and that therefore the massof the b-quantum in such a case is zero. The argument is how-ever subject to the criticism that, like all field theories, the b-fieldis beset with divergences and dimensional arguments are not sarisfactory.

YM considered seriously the possibility that their gauge bosons will eventually be massive:

mass of the gauge boson to be determined by its full propagator

b b

Under the spell of gauge principle

Since around 1960 Sakurai, Salam, Ward, Neeman and others started considering local gauge invariance as guiding principle in constructing theories of strong, weak as well as electromagnetic interactions. Abdus Salam & John Ward in On a Gauge Theory of Elementary particles Nuovo Cimento 11 (1960), 165

Our basic postulate is that it should be possible to generate strong, weak and electromagnetic inter-action terms by making local gauge transformations on the kinetic terms in the free Lagrangian for all particles. This is the statement of ideal, which in thispaper at least, is only very partially realized.

The straightforward generalization of the original Yang-Mills was proposed in 1961 by Salam and Ward who extended isospin symmetry to SU(3) version of the Sakata model

by gauging the fundamental triplet of baryons

1

p

n iH

they got the octet of selfinteracting gauge vector mesons

8-parameter traceless hermitian 3 3matrix

infinitesimal gaugetransformation

kinetic term invariant

Close to Eightfold way but different in basic multiplet and nodiscussion of baryons beyond the fundamental triplet p,n,

full YM

these break GI!

As an alternative to the Sakata model based on the relation

Y. Neeman and M. Gell-Mann proposed in early 1961 the

Eightfold Way

which starts with the product of three SU(3) triplets

_

3 3 3 15 6 3 3

_

3 3 3 10 8 8 1 and leads to different set of multiplets. At the beginning of 1961 it was still not quite clear which scenario was correct.

The stories of their discoveries are quite different as are theirprofessional careers and whole lives.

Eightfold way according to Y. Neeman

contains a full-fledged

Yang-Mills gauge theory of strong interactions

extending the original YM theory to SU(3) unitary symmetry.

Derivation of Strong interactions from a Gauge invariance

Y. Neeman, Nucl. Phys. 26 (1961), 222

But no interpretation of the fundamental triplet attempted.

Baryons are assigned to octets as are the pseudoscalar mesons. Octet of selfinteracting vector bosons is predicted, though no vector meson was known at the end of 1960.

Discovery of vector mesons

proceeding as quasi two-body process

followed by ρ in May, Φ in July and ω in August 1961

Who was afraid of gauge theory?

MGM’s preprint

is truly fantastic for the straightforwardness with which the idea is presented.

The vector mesons are introduced in a very natural way, by extension of the the gauge principle of Yang and Mills. Here we have a supermultiplet of eight mesons. In the limit of unitary symmetry we have completely gauge-invariant and minimal theory like electromagnetism.

Now the vector mesons themselves carry F spin and there-fore contribute to the current which is their source. The prob-lem of constructing a nonlinear theory of this kind has been completely solved in the case of isotopis spin by Yang and Mills and by Shaw. We have only to generalize their result (for three vector mesons) to the case of F spin and eight vector mesons.

and on another place

leptons played the role of quarks:

gauge transformations on all particles involved:

full Yang-Mills Lagrangian written out

“There are trilinear and quadrilinear interactions amongst the vector mesons, as usual ...”

But this preprint has never been published!!

noting that

unique coupling

In Section VIII we propose, as an alternative to the symmetrical Sakata model, another scheme with the same group, which we call ``eightfold way''. Here the baryons, as well as mesons, can form octets and singlets, and the baryons N, , and are supposed to constitute an approximately degenerate octet.

Nowhere does our work conflict with the program of the Chewet al. of dynamical calculation of the S-matrix from strong interactions using dispersion relations.

If there are no fundamental fields …. all baryons and mesons being bound or resonant states of one another, models like Sakata will fail; the symmetry properties we have abstracted can still be correct, however.

instead we read in “Symmetries of Baryons and Mesons”

Remarkably, this paper does not mention the gauge principle and does not refer to Yang-Mills paper at all!

S-matrix and bootstrap: Theory of everything?

I do not wish to assert (as does Landau) that conventional field theory is necessarily wrong, but only that it is sterile with respect to the strong interactions and that, like an old soldier, it is destined not to die but just to fade away… The notion, inherent in conventional Lagrangian field theory, that certain particles are fundamental while others are complex, is becoming less and less palatable …

From G. Chew: S-Matrix Theory, (W.A. Benjamin Inc, 1963).

I believe the conventional association of fields with strong interacting particles to be empty. It seems to me that no aspect of strong interactions has been clarified by the field concept. Whatever success theory has achieved in this area is based on the unitarity of the analytically continued S-matrix plus symmetry principles.

For application of YM theories to strong interactions the

identification of correct space to gauge

was crucial. This sounds trivial, but was not. It took 20 years to come to the conclusion that the fundamental object of nonabelian theory of strong interactions are

colored quarksand that forces acting between them follow from gauging the color degree of freedom.

Quark model according to Zweig

Both mesons and baryons are constructed from a set of three fundamental particles, called aces. Each ace carries baryon number 1/3 and is fractionally charged.

SU(3) is adopted as a higher symmetry for the strong inte- interactions. Extensive space-time and group theoretic structure is then predicted for both mesons and baryons …

An experimental search for the aces is suggested.

Zweig:

Quark model according to Gell-Mann

A formal mathematical model based on field theory can be built up for the quarks exactly as for p, n and Λ in the old Sakata model, for example with all strong interactions ascribed to a neutral vector meson field interacting symmetrically with the three particles. Within such a framework the electromagnetic currents is just

PL 8 (1964), 214

In order to obtain such relations that we conjecture to be true, we use the method of

abstraction from a Lagrangian field theory model.

In other words, we construct a mathematical theory of the strongly interacting particles, which

may or may not have anything to do with reality,

find suitable algebraic relations that hold in the model, postulate their validity and then

throw away the model.

We may compare this process to a method some-times employed in French cuisine: a piece of phea-sant meat is cooked between two slices of veal,

which are then discarded.

MGM’s view of the role of quarks (Physics 1 (1964), 63)

M. Gell-Mann at 1992 ICHEP:

Confinement: consequence or source of nuclear democracy?

I was reflecting that if those objects (i.e. quarks) could not emerge to be seen individually, then all observable hadrons could still have integral charge and also the principle of “nuclear democracy” could be preserved unchanged for observable hadrons. With this proviso, the scheme appealed to me.

Since I was always convinced that quarks would not emerge to be observed as single particles (“real quarks”), I never paid much attention to the Hahn-Nambu model in which their emergence was supposed to be made possible by giving them integral charges.

For MGM nuclear democracy was fundamental principle of strong interactions and confinement its consequence:

The concept of colored quarks

has been introduced in late 1964 primarily in order to explain the apparent problem of quark statistics implied by the success of SU(6) symmetric quark model. To reconcile this model with Pauli principle Greenberg proposed to interpret quarks as parafermions of rank 3. It soon became clear that this assumption is equivalent to assigning to each quark flavor another internal quantum number, which could take three different values and which, following Pais’ suggestion at 1965 Erice Summer School, has been called color.

Nambu had used it since early 1965 as a dynamical variable generating the force between quarks, assuming furthermore that the force between colored quarks is due to the exchange of octet of colored gauge bosons, which induce the effective four quark coupling of the type

While for most of theorists color was introduced to solve the quark statistics problem

In this way his model contained all essential elements of QCD, except that it was not Quantum Field Theory.

and lead to (potentially infinite) gap between colorlessand colored states.

If the mesons and baryons are made of mathematical quarks, then the quark model may perfectly well be compatible with bootstrap hypothesis, that hadrons are made up out of one another.

Gell-Mann on quarks (summer 1967)

The idea that mesons and baryons are made primarily of quarks is difficult to believe, since we know that, in the sense of dispersion theory, they are mostly, if not entirely, made up out of one another. The probability that a meson consists of a real quark pair rather than two mesons or a baryon and antibaryon must be quite small. Thus it seems to me that whether or not real quarks exist, the q or q we have been talking about are mathematical entities ......

Too much scaling may be misleading

Bjorken derived scaling behavior observed at SLAC from current algebra considerations assuming that the nucleon structure functions stay finite in the limit of infinite momentum transfer. But we now know that in QCD the above

assumption does not hold and, consequently, his paper is, indeed, empty!

Bardeen, Fritzsch, Gell–Mann in 1972 (hep-ph/0211388)

One is considering the abstraction of results that are true only formally, with canonical manipulation of operators, and that fail, by powers of logarithmic factors, in each order of renormalized perturbation theory, in all barely renormalizable models.The reason for the recent trend is, of course, the tendency of the deep inelastic electron scattering experiments at SLAC to encourage belief in Bjorken scaling, which fails to every order of renormalized perturbation theory in barely renormalizable models. There is also the availability of beautiful algebraic results, with Bjorken scaling as one of their predictions, ….

Why asymptotic freedom?

Because only asymptotically free QFT could explain surprisingly good scaling behavior of nucleon structure functions observed since 1967 in deep inelastic electron-nucleon scattering at SLAC and reconcile it with experimental fact of quark confinement.

Because for asymptotically free quantum field theories the renormalization procedure as formulated by Landau & Pomeranchuk can be consistently carried through. In this sense asymptotically free Quantum Field Theories do not contain ultraviolet divergencies. For these theories Dirac was thus wrong!

&

In 1972 quarks were still not taken seriously

Current Algebra: Quarks and What Else?

We assume here that quarks do not have real counterparts that are detectable in isolation in the laboratory – they are supposed to be permanently bound inside mesons and baryons .........It might be a convenience

In Summer 1972 Gell-Mann and Fritzsch presented their view at XVI ICHEP in Chicago in a contribution called

to abstract quark operators themselves, or other non–singlets with respect to color, …, but it is not a necessity. It may not even be much of a convenience

we probably don’t want to load ourselves with so much spurious information.

since we would .... be discussing a fictitious spectrum for each fictitious sector of Hilbert space, and

Their hope that

We might eventually abstract from the quark vector–gluon field theory model enough algebraic information about the color singlet operators in the model to describe all the degrees of freedom that are present.We would have a complete theory of the hadrons and their currents, and we need never mention any operators other than color singlets.

and thus

has not been born out by further theoretical developments and experimental results, in particular those on

• heavy quarkonia spectra and• jet phenomenawhich require that we treat quarks and gluons in the same way as leptons and basically forget about confinement.

Now the interesting question has been raised lately whether we should regard the gluons as well as the quarks as being non–singlets with respect to color (private communication of J. Wess to B. Zumino). For example, they could form a color octet of neutral vector fields obeying the Yang–Mills equations.

This paper is quoted as containing the suggestion that gluons could form the octet of Yang-Mills gauge bosons. In fact this option is mentioned in the following context

they, however, ignored this option:

In the next three Sections we shall usually treat the vector gluon, for convenience, as a color singlet.

D. Gross: QFT must be destroyed!

I decided, quite deliberately, to prove that local field theory could not explain the experimental fact of scaling and thus was not an appropriate framework for the description of the strong interactions. Thus, deep inelastic scattering would finally settle the issue as to the validity of quantum field theory. The plan of the attack was twofold. First, I would prove that “ultraviolet stability,” the vanishing of the efective coupling at short distances, later called asymptotic freedom, was necessary to explain scaling.

Second, I would show that there existed no asymptotically free field theories. The latter was to be expected. After all the paradigm of quantum field theory –QED- was infrared stable; in other words, the efective charge grew larger at short distances and no one had ever constructed a theory in which the opposite occurredTogether with Frank Wilczek they succeeded in the first step, but failed in the second because:

Nonabelian gauge theories have turned out to be (under certain circumstances) asymptotically free!

D. Gross: For me the discovery of asymptotic freedom was totally unexpected. …. Field theory was not wrong, instead scaling must be explained by an asymptotically free gauge theory of the strong interactions.

Asymptotic freedom had been discovered in these two papers

shortly followed by three papers containing complete formulation of QCD, together with elaboration of its application to DIS.

All these papers existed as preprints by the date of their submissions and thus months before the submission of the paper which is often, but incorrectly, credited with the formulation of QCD.

A fourth apparent advantage of the color octet gluon scheme has recently been demonstrated ……the behavior of light cone commutators comes closer to scaling behavior than in the color singlet vector gluon case. However, actual Bjorken scaling does not occur…..For us, the result that the color octet field theory model comes closer to asymptotic scaling than the color singlet model is interesting, but not necessarily conclusive, since we conjecture that there may be a modification at high frequencies that produces true asymptotic scaling.

31 years after their work Gross, Wilczek and Politzer were awarded the 2004 Nobel Prize.Their theory provides

the basic frameworkfor reconciling the apparently conflictingfacts that quarks do notexist as free particlesbut in some situationsappear to behave asalmost free.

The key manifestation of their “existence” are

jets

Frank Wilczek

Pamětní medaile UK

Karolinum 10. 6. 2003

People knowing without understanding

Studying the effects of vacuum polari-zation due to loops of charged vector bosons on the renormalized electric charge they found the expression

Perhaps the first who observed this behaviour of a coupling constant were V. S. Vanyashin and M. V. Terentev in 1965.

and noted that these loops give the opposite sign that those of fermion loops in standard QED!

But they attributed this result to the fact that the theory with charged vector bosons coupled to photons is not renormalizable.

G. ‘t Hooft: When was asymptotic freedom discovered? hep-th/9808154

I knew about the beautiful scaling behaviour of non-Abelian gauge theories. Suspecting that this feature should be known by now by the experts on the subject of scaling, I did not speak up louder. Veltman … warned me that no-one would take such an idea seriously as long as it could not be explained why quarks cannot be isolated one from another.

By 1972, I had calculated the scaling behavior, and I wrote it in the form

where Cj are Casimirs for VB, fermions and scalars

(5.3)

In June, 1972, a small meeting was organised by Korthal Atles in Marseille. I announced at that meeting my finding that the coefficient determining the running of the coupling strength,

for non-Abelian gauge theories is negative

and I wrote down (5.3) on the blackboard.

Symanzik was surprised and skeptical. “If this is true, it will be very important, and you should publish this result quickly, and if you won’t, somebody else will,” he said. I did not follow his advice.

‘t Hooft now likely regrets his decision.

D. Gross: Nowadays, when you listen to experimentalists talk about their results they point to their lego plots and say, “Here we see a quark here a gluon.”

Believing is seeing, seeing is believieng. We now believe in the physical reality of quarks and gluons…The way in which we see quarks and gluons through the the efects they have on our measuring instruments is not much different from the way we see electrons.

Seeing quarks and gluons

One typical DIS eventfrom H1 experiment

Nice H1 event with 3 clearly separate and different jets

Z přednášky F. Wilczeka Výsledky měření z různých experimentů

≈1/r→

Potvrzení asymptotické volnosti QCD

DataLEP

Z přednášky F. Wilczeka v Karolinu 2003

dva jety

tři jety

dilepton

dilepton+foton

Jets at LEP

ALEPH

μ+

μ-

jet

jet

jet

jet

jet

jet

jet

jet

jet

Triple gluon coupling (1990)measured by the angular distri-

bution of four jet events at LEP:

Experimental evidence for the basic feature of nonabelian gauge theories

taking into account that

as well as ZWW and WW vertices (1998) Thanks to LEP2 we nowsee the effects of triple gauge boson coupling.

Origins of the concept of Gauge Invariance

goes back to the attempt of Hermann Weyl in 1918 to generalize Riemannian geometry, discarding its assumption that it makes sense to compare magnitudes of vectors at distant points.

But Riemannian geometry described above there is contained a last element of geometry “at a distance” – with no good reason as far as I can see – it is due only to the accidental development of Riemannian geometry from Euclidean geometry. The metric allows the two magnitudes of two vec-tors to be compared not only at the same point, but at any arbitrary separated points.

He observes:

A true infinitesimal geometry should, however, recognize only a

principle for transfering the magnitude of a vector to an infinitesimally close point

and then, on transfer to an arbitrary distant point

the integrability of the magnitude of a vector is no more to be expected than the integrability of its directions.

makes his suggestion

On the removal of this inconsistency there appears a geometry that, surprisingly, when applied to the world,

explains not only gravitational phenomena, but also the electrical.

According to the resultant theory both spring from the same source, indeed in general one cannot separate gravitation from electromagnetism in a unique manner.

and concludes

In 1929, shortly after the formulation of QED by Dirac, Weyl reformulated his theory, this time

Though mathematically beautiful, Weyl’s theory, did not describe reality and Weyl had to abandon it.

Weyl equipped space-time manifold with conformal structure, i.e. with a class of conformally equivalent Lorentz metrics g.The gauge transformation concerned this metric

2'g e g

relating electromagnetism to quantized matter field. This time he got it right!

The Dirac field equations for ψ together with the Maxwell equations for the four potentials fp of the electromagnetic field have an invariance property ....the equations remaininvariant when one makes simultaneous substitutions

Weyl’s 1929 classic: Electron and gravitation

It seems to me that this new principle of gauge invariance, which follows not from speculation but from experiment, tells us that the electromagnetic field is a necessary accompany-ing phenomenon not of gravitation, but of material wave field represented by ψ. Since gauge invariance involves an arbit-rary function λ it has the character of “general relativity” and can naturally be understood in this context.

ie p p pf f

x

and

Steps into extra dimensions

Kaluza, Klein and later Pauli tried to formulate gravitationaland other forces (preludes to Theories of everything) in more-dimensional space-time. Particularly remarkable was the paper of Oscar Klein

On the Theory of Charged Fields

and discussed at length by David Gross in his article Oscar Klein and Gauge Theory

presented in 1938 at the Warsaw conference New Theories in Physics

Klein’s goal was to construct a theory of all forces based on the U(1) gauge theory of isospinors. He almost constructed an SU(2) gauge theory, but not exactly.

In his words:

The emergence of nonabelian gauge theories and the role of mathematics in the formulation of the concept of nonabelian gauge invariance is discussed at length in an interview of D.Z. Zhang with C.N. Yang in the Mathematical Intelligencer. Some excerpts:Q: How about ideas in mathematics becoming important for physics. We may recall Einstein was adviced to pay attention to tensor analysis. Is that similar to your getting help from Simmons?

Yang: As to the entry of mathematics into general theory of relativity and into gauge theory, the processes were quite different. In the former, Einstein could not formulate his ideas without Riemannian geometry, while in the latter, the equati-ons were written down, but an intrinsic overall understanding of them was later supplied by mathematics.

Q: Is it true what M.E. Mayer said in 1977: A reading of the Yang-Mills paper shows that the geometricmeaning of the gauge potentials must have been clear to the authors since they use the gauge invariant derivative and the curvature for the connection …

Yang: Totally false. What Mills and I were doing in 1954 was generalizing Maxwell’s theory. We knew of no geometrical meaning of Maxwell’s theory and were not looking in this direction. Connection is a geometrical concept which I only learned around 1970. Q: An interesting question is whether you understood in 1954

the tremendous importance of your original paper ……

Yang: No. In 1950 we felt our work was elegant. I realized its importance in the 1960s and its great importance to physics in the 1970s. Its relation to deep mathematics became clear to me only after 1974.

Pair of leaves: C.N. Yang and mathematicsAs the concept of Yang-Mills

theories has had a profound influence on mathematics it is interesting to know how Yang himself sees the relation between mathematics and physics.

Q: Is it important for a physicist to learn a lot of mathematics? Yang: No, if a physicist learns too much of mathematics, he or she is likely to be seduced by the value judgment of ma-thematics, and may loose his or her physical intuition. I have likened the relation between physics and mathematics to a pair of leaves. They share a small common part at the base, but mostly they are separate.Q: For a physicist, experimental results are more important to learn?

Yang: This is right.

The relation between mathematics and physics is addressed also by Straumann in his essay:

All major theoretical developments of the last 20 years, such as grand unification, supergravity and supersymmetric string theory are almost completely separated from experience. There is a great danger that theoreticians get lost in pure speculations. Like in the first unification proposal of Hermann Weyl they may create beautiful and highly relevant mathema-tics which does, however, not describe nature. Remember what Weyl wrote to C. Sellig in his late years: Einstein thinks that in this field the gap between ideas and experience is so large that only mathematical speculations ..... have the chance to succeeed, whereas my trust in pure speculations has declined ....

So, what does the Nature read?The lesson from the preceding is, at least for me, that there is no substitute for genuine dynamical laws.

The claim or hope of Fritzsch, Gell-Mann & Co. that

all results in deep inelastic electron and neutrino scatter-ing can be explained by assuming that leading singulari-ties of current products near the light cone are determined by the light cone algebra “abstracted from the free quark model”is simply wrong! The nature does not read in the book of free field theory, but it definitely prefers the textbook on Yang-Mills theories with all the subtleties which cannot be abstracted from free field theory, but which are responsible for both the confinment and asymptotic freedom.

END

Color as a dynamical variable Nambu’s model has been resurrected and cast into modern langu-age by Lipkin shortly after the discovery of asymptotic freedom.The color part of the interaction between pairs of quarks is assu-med to have form analogous to isospin-isospin interaction term implying the

following form of interaction energy

where C stands for quadratic Casimir operator

The total mass of a system of n colored quarks, each of large mass Mq equalsAssuming Mq=cv/2, we finally get

i.e. only color singlet states have zero(small) mass, whereas all color non-singlet ones have masses of the order of Mq and cannot thus be observed!

Red herring: integer charge colored quarksNambu is most often associated with the idea of colored integer charge quarks he proposed in April 1965 with Hahn.

To avoid fractional electric charges of quarks, Hahn and Nambumade the electric charge Q, the third component of isospin I3 and the hypercharge Y dependent on the quark color

u d s

red blue yellow

Plausible idea, but • mixes strong and electro- magnetic interactions • excluded by data