Dressing the Quark with QCD Condensates
A condensate of $\pvec = 0$ partons in the perturbative vacuum gives rise to a term $\propto\delta^4(p)$ in the free PQCD propagators. The leading condensate contribution to the quark propagator can be exactly summed since there is a factor $\delta^4(p)$ associated to each loop. We calculate the dressed quark propagator in the presence of either a gluon or a quark condensate, for a number of colors $N \to \infty$. The dressed quark propagator satisfies a Dyson-Schwinger type equation which can be exactly solved within our framework. In the case of a gluon condensate the dressed quark propagator has no pole, hence quarks cannot appear in asymptotic states, and moreover the DS equation has a solution which spontaneously breaks chiral symmetry. We also calculate the dressed quark-photon vertex and verify that the corresponding Ward-Takahashi identity is satisfied, and that the dressed self-energy correction to the photon propagator does not shift the physical photon pole.
The theory of quark confinement
Abstract. This is the second of the two last papers by V.N. Gribov concluding his 20 year long study of the problem of quark confinement in QCD. In this paper the analytic structure of quark and gluon Green functions is investigated in the framework of the theory of confinement based on the phenomenon of supercritical binding of light quarks. The problem of unitarity in a confining theory is discussed. The write-up remained unfinished and as such it is presented here. The author was planning to emphasise the link between the electroweak and strong interactions, and in particular the rôle of pions (Goldstone bosons) in confinement, to present an explicit solution for bound states, and to write down an analytic model for quark and gluon Green functions corresponding to confinement.
Positive Rights and State Constitutions: The Limits of Federal Rationality Review
INTRODUCTION ............................................................................................................................. 1132 I. STATE CONSTITUTIONAL WELFARE PRACTICE ............................................................. 1144 A. A Mandatory Obligation: The New York Example .................................................. 1144 B. A Typology of Current State Court Decisions .......................................................... 1145 IT. RECONSIDERING FEDERAL RATIONALITY REVIEW IN STATE CONSTITUTIONAL WELFARE CASES ................................................................................ 1153 A. Rationality Review and Positive Rights .................................................................. 1155 B. Rationality Review and Democratic Legitimacy .................................................... 1157 C. Rationality Review and Judicial Finality ............................................................. xi61 D. Rationality Review and Federalism ......................................................................... i166 E. Rationality Review Revisited .................................................................................... 1169 III. TOWARD A NEW STANDARD OF REVIEW ......................................................................... 1169 A. The Need for Judicial Review .................................................................................. 1170 B. Institutional Competence and Welfare Litigation ................................................... 1175 I. State Courts as Fact Gatherers ......................................................................... 1175 2. State Courts as Policymakers ......................................................................... " 179 3. State Courts as Rights Enforcers ..................................................................... 1182 C. A Jurisprudence of Consequences .............................................................................. 1183 D. Why Education and Not Welfare? ........................................................................... i86 E. Implications for Welfare Litigation ........................................................................... i9i IV. CONCLUSION ........................................................................................................................ 1194