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Models for CONFINEMENT

Explore the different models and phenomena related to absolute quark confinement in lattice QCD and as a topological phenomenon. Study the gluon chain model and compare renormalization procedures to better understand confinement. Investigate perturbative approaches and the concept of unitarity. This comprehensive study at Utrecht University sheds light on the forces holding hadronic particles together, with further references and insights.

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Models for CONFINEMENT

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  1. Utrecht University Models for CONFINEMENT Gerard ’t Hooft Spinoza Institute Utrecht, the Netherlands

  2. Contents First part: Absolute Quark Confinement in lattice QCD Second part: Absolute Quark Confinement as a topological Phenomenon Third part: The Gluon Chain Model (Greensite, Thorn) Try to do it better: compare Renormalization Procedure (infinite) Infrared Renormalization The renormalized Coulomb potential (in radiation gauge) Fourth part: Gauge invariant procedure Renormalized effective actions: an exercise in Legendre Transformations

  3. What kinds of forces were holding them together?

  4. The hadronic particles … Antiproton Proton Lambda Pi-plus Pi-zero

  5. Using the expansion In the expansion, only terms where the energy increases linearly with inter- quark distance survive ! Part 1: Lattice QCD (K. Wilson, London, 1974)

  6. S N Part 2: Magnetic Confinement In case of spontaneous "breakdown" of H.B. Nielsen and P. Olesen, 1970.

  7. _ + Color Magnetic Super Conductivity S N Electric Super Conductor Magnetic Super Conductor

  8. The Magnetic Monopole G. ’t H (1974), A.M. Polyakov (1974) • Mandelstam (1975), • G. ’t H (1976)

  9. Ansatz for the "Wave Function": Use variational principle, minimize Part 3:The gluon chain approach Anti- quark quark J. Greensite and C.B. Thorn hep-ph/0112326 [ ? ] then, improve Ansatz

  10. This can be done better The gluon chain model gives reasonable – looking "stringlike“ structures for the mesons … but confinement is not built in … The chainlike states will surely not form a complete set of states. UNITARITY ? Describe a "modified" perturbative approach, where unitarity is guaranteed Infinite infrared renormalization

  11. Compare UV renormalization Lowest order Combine this with the higher order terms

  12. now generates a potential Vbetween charges obeying Perturbative Confinement

  13. in space: Let V be a confining potential, typically: then

  14. should be treated exactly like a renormalization counter term. Compare our procedures in the renormalization group: the coefficients (here: ) must be adjusted in such a way that the higher order correction terms, together with the contributions from , should be as insignificant as possible. At lowest order, we should start with a Fock space of Eigen states of particles bound by the potential V . They are confined from the very beginning:

  15. Stationary case: Part 4: A Classically Confining Theory: U ( D ) can become any monotonically increasing function of D

  16. D Q -Q

  17. 1 Legendre Transformations:

  18. The dual transformation

  19. Quantum Chromodynamics is an extremely accurate theory. At short distances, the forces become weak, so that perturbative treatment there is possible. Calculating the QCD contributions to high-energy scattering processes has become routine. Interesting and important problems remain: - find a quark-gluon plasma - find more accurately converging calculation procedures ... Utrecht University

  20. Further References: Erice: hep-th / 9812204 Montpellier Proceedings (2002) Nucl. Phys. B 138 (1978) 1 Nucl. Phys. B 153 (1979) 141 Nucl. Phys. B 190 (1981) 455 Acta Phys. Austriaca Suppl. XXII (1980) 531 Physics Reports 142 (1986) #6, 357 hep-th / 9903189 The End

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