Gerard ’t Hooft Spinoza Institute Utrecht, the Netherlands Utrecht University.

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Presentation transcript:

Gerard ’t Hooft Spinoza Institute Utrecht, the Netherlands Utrecht University

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

What kinds of forces were holding them together?

ProtonLambda Antiproton Pi-plusPi-zero The hadronic particles …

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

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

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

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

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

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

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

Perturbative Confinement now generates a potential V between charges obeying

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

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:

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

Q -Q D

Legendre Transformations: 1

The dual transformation

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

Further References: 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 / Erice: hep-th / Montpellier Proceedings (2002) The End