We discuss Faddeev-Popov quantization at the nonperturbative level and show that Gribov's prescription of cutting off the functional integral at the Gribov horizon does not change the Schwinger-Dyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov's prescription is not exact, and we therefore turn to the method of stochastic quantization in its time-independent formulation, and recall the proof that it is correct at the nonperturbative level. The nonperturbative Landau gauge is derived as a limiting case, and it is found that it yields the Faddeev-Popov method in the Landau gauge with a cutoff at the Gribov horizon, plus a novel term that corrects for overcounting of Gribov copies inside the Gribov horizon. Nonperturbative but truncated coupled Schwinger-Dyson equations for the gluon and ghost propagators $D(k)$ and $G(k)$ in the Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by $D(k)\ensuremath{\sim}{1/(k}^{2}{)}^{{1+a}_{D}}$ and $G(k)\ensuremath{\sim}{1/(k}^{2}{)}^{{1+a}_{G}},$ are obtained in space-time dimensions $d=2,$ 3, 4. Two possible solutions are obtained with the values, in $d=4$ dimensions, ${a}_{G}=1,$ ${a}_{D}=\ensuremath{-}2,$ or ${a}_{G}=(93\ensuremath{-}\sqrt{1201})/98\ensuremath{\approx}0.595353,$ ${a}_{D}=\ensuremath{-}{2a}_{G}.$

Nonperturbative Landau gauge and infrared critical exponents in QCD

A critical review on signatures of quark-gluon plasma (QGP) formation is given and the current (1998) experimental status is discussed. After giving an introduction to the properties of QCD matter in both, equilibrium and non-equilibrium theories, we focus on observables which may yield experimental evidence for QGP formation. For each individual observable the discussion is divided into three sections: first the connection between the respective observable and QGP formation in terms of the underlying theoretical concepts is given, then the relevant experimental results are reviewed and finally the current status concerning the interpretation of both, theory and experiment, is discussed. A comprehensive summary including an outlook towards RHIC is given in the final section.

https://iopscience.iop.org/article/10.1088/0954-3899/25/3/013/pdf

Signatures of quark-gluon plasma formation in high energy heavy-ion collisions: a critical review

The QCD running coupling

Behind the observed pattern of lepton flavor mixing is a partial or approximate mu-tau flavor symmetry --- a milestone on our road to the true origin of neutrino masses and flavor structures. In this review article we first describe the features of mu-tau permutation and reflection symmetries, and then explore their various consequences on model building and neutrino phenomenology. We pay particular attention to soft mu-tau symmetry breaking, which is crucial for our deeper understanding of the fine effects of flavor mixing and CP violation.

T.D. Lee

Papers

A Soluble Gauge Model with Gribov-Type Copies

Hidden symmetry of the CKM and neutrino-mapping matrices

A Convergent Iterative Solution of the Quantum Double-Well Potential

Jarlskog invariant of the neutrino mapping matrix

Convergent iterative solutions for a Sombrero-shaped potential in any space dimension and arbitrary angular momentum