QCD. What else is needed for understanding the proton structure function?

1. QCD. What else is needed for understanding the proton structure function? Y. S. Kim University of Maryland Gatchina, Ruussia June 2014

2. QED. What else is needed to calculate the n-p mass difference? On April 29, at the 1965 spring meeting of the American Physical Society in Washington, Freeman J. Dyson of the Institute of Advanced Study (Princeton) presented an invited talk entitled Old and New Fashions in Field Theory and the content of his talk was published in the June issue of the Physic Today, on page 21-24.

3. The first of these two achievements is the explanation of the mass difference between neutron and proton by Roger Dashen, working at the time as a graduate student under the supervision of Steve Frautschi. The neutron-proton mass difference has for thirty years been believed to be electromagnetic in origin, and it offers a splendid experimental test of any theory which tries to cover the borderline between electromagnetic and strong interactions. However, no convincing theory of the mass-difference had appeared before1964. In this connection I exclude as unconvincing all theories, like the early theory of Feynman and Speisman, which use one arbitrary cut-off parameter to fit one experimental number. Dashen for the first time made an honest calculation without arbitrary parameters and got the right answer.

4. His method is a beautiful marriage between old-fashioned electrodynamics and modern bootstrap techniques. He writes down the equations expressing the fact that the neutron can be considered to be a bound state of a proton with a negative pi meson, and the proton a bound state of a neutron with a positive pi meson, according to the bootstrap method. Then into these equations he puts electromagnetic perturbations, the interaction of a photon with both nucleon and pi meson, according to the Feynman rules. The calculation of the resulting mass difference is neither long nor hard to understand, and in my opinion, it will become a classic in the history of physics. Dyson was talking about the paper by R. F. Dashen and S. C. Frautschi published in Phys. Rev. [135], B1190 and B1196 (1964). They use the S-matrix formalism for bound states.

5. Later in the same year, Steve Adler and Roger Dashen became full professors at the Institute for Advanced Study. Naturally, they were admired by their colleagues, and many young physicists studied Dashen's paper on the neutron-proton mass difference. I was one of those who studied the paper carefully during the summer of 1965. I then published a paper in the Physical Review [42], 1150 (1966). In their paper, Dashen and Frautschi use the S-matrix method to calculate a perturbed energy level. Of course, they use approximations because they are dealing with strong interactions. If we translate what they did into the language of the Schrodinger picture, they are using the following approximation for

6. First-order energy shift • Disaster! However, the background is more fundamental. For Lorentz-covariant problems, physicists had to go to the only covariant formalism available at the time. S-matrix and Feynman diagrams. • The question. Is QFT adequate for bound state problems? Wait until what Feynman says in 1970. For bound-state problems, use harmonic oscillators.

7. QED. What else is needed to calculate the Lamb shift? QED produces a delta function perturbation at the origin. Thus it gives a correction to the 2s state of the hydrogen atom, but its effect is zero for the 2p state. You need wave functions to calculate this energy shift. Where does this wave function come from? Not from QED. QED cannot produce localized hydrogen wave functions. .

8. QCD. What else is needed for understanding the parton distribution function? It is well known that that QCD can produce corrections (moments) to the distribution, but not the distribution itself. Where does this distribution come from?

9. Gell-Mann and Feynman in two different Lorentz frames. Quantum bound state of quarks, and a collection of partons

10. In 1970, at the APS meeting in Washington, Feynman stated the Regge trajectories consistent with the degeneracy of the 3-dimensional harmonic oscillator.

11. Proton: the oscillator bound state of three quarks, and collection of the infinite number of partons. Are we talking about the same thing? For a bound state of the quark, we can talk about a wave function. For partons, how can we get the initial distribution? There is only one answer. Lorentz boost the quark wave function.

12. Einstein and Bohr met very often. 2014: 50 years of the Quark model. 101 years of the Bohr atom.

13. Bohr was worrying about the electron orbit of the hydrogen atom. Einstein was worrying about how things look to a moving observer.Bohr and Einstein never worried about how the orbit looks to the moving observer.

14. There were and are still no hydrogen atoms moving with relativistic speed. Thus, we can stretch our imagination to draw this picture. This picture came from John Bell’s book (1988). Bell did not know this picture became out-dated in 1927. The orbit became a standing wave!

16. Hydrogen Atom becomes the Hadron (bound state of two quarks) in the Lorentz-covariant world.

17. Dirac and Feynman in Poland (1962) • Dirac: construct a beautiful mathematics. • Feynman: mathematical instrument that will produce numbers which can be compared with what we observe in the real world.

18. I had anaudience with Dirac in 1962. Like Nicodemus asking Jesus

19. I asked Dirac what I should do in Physics.Study Lorentz covariance. Americans should study more about this subject.

20. By “American physicists,” Dirac was talking about Feynman. He met F. in Poland 3 months earlier.

21. Five Books of Dirac • First Book. 1927 paper on time-energy uncertainty – c-number • Second Book. 1945 paper on harmonic oscillators. Gaussian time distribution. • Third Book. 1949 paper on light-cone coordinate system • Fourth Book: 1963 paper on two-oscill. system-– two mode squeezed states. • Fifth Book. Translate his poems into cartoons, and combine all four earlier books.

22. Why do we need the Fifth Book? • Dirac’s papers are like poems, but contain no figures. Translate those poems into cartoons. • Those papers lack continuity. Dirac does not make reference to his earlier papers. • Dirac does not make difference between time and time interval.

23. Bohr radius is a space-like separation. If we boost this, it picks up its time-like component.

24. Feynman’s Interpretation of Physics The adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing.

25. Feynman’s Philosophical Base • Feynman wrote 150 papers. • He wanted to pack them into one paper. • We can combine three of them into one paper.. 1969 paper on partons. 1971 paper on covariant oscillators 1972 book. Rest of the universe. Concept of entanglement. It then becomes the Fifth Book of Paul A, M Dirac

26. 1970 Feynman’s Crazy Talk

27. 1965. Feynman diagrams do not guarantee localization.

28. Feynman said! • For Scattering problems, use Feynman diagrams. • For bound-state problems, use harmonic oscillators. • However, there were no well-known Lorentz-covariant oscillators in 1970. • People said Feynman was absolutely crazy. • But, I became excited about what he said, and studied his physics systematically since then. I also became crazy.

29. Based on Feynman’s 1970 Talk

30. Covariant Bound States (Standing Waves) • Bound States: Hydrogen Atom or Harmonic Oscillators. • Feynman chooses osc. wave functions to understand the covariant world. • Hadron consisting of two quarks. Overall coordinate and space-time separation.

31. Feynman said

32. Feynman’s One Equation In his 1971 paper, Feynman wrote Down one partial differential equation to cover both comets and planets.

33. Feynman’s One Equation

35. Hadrons – Running wavesQuarks inside – Harmonic Oscillator

36. Feynman was successful in solving the mysteries of Regge poles, but totally failed in providing Lorentz-covariant solutions of his own equation for harmonic oscillators. From the Lorentzian point of view, his paper is total mess.

37. Feynman’s One Equation In order to handle the differential equation Feynman wrote down, we have to import things from both Wigner and Dirac.

38. Two famous brothers in law

39. Running waves and Standing Waves

40. Feynman said

41. Wigner’s Little Group • The space-time symmetry inside the hadron is smaller than the Lorentz group. It is isomorphic to O(3), three-dimensional rotation group.

42. After fixing up Feynman’s oscillators We can assert that Dirac’s Five Books are for the real world.

44. Parton PictureCoherence to Incoherence

45. Feynman’s Parton Picture

47. Paul Hussar’s Calculation of the parton distribution.

48. Two different aspects(quarks and partons) of nature coming from one thing!

49. Register ownership with authoritiesPhys. Rev. Letters