Theorizing the Law/Politics Distinction: Neutral Principles, Affirmative Action, and the Enduring Insight of Paul Mishkin

Early in his career Mishkin saw that the law could be apprehended from two distinct and in part incompatible perspectives: from the internal perspective of a faithful practitioner and from the external perspective of the general public. If the social legitimacy of the law as a public institution resides in the latter, the legal legitimacy of the law as a principled unfolding of professional reason inheres in the former. Mishkin came to believe that although the law required both forms of legitimacy, there was nevertheless serious tension between them, and he dedicated his scholarly career to attempting to theorize this persistent but necessary tension, which he conceived almost as a form of antinomy. In this article we pay tribute to Mishkin\u27s quest for understanding. We argue that the tension identified by Mishkin is significant and unavoidable, but that it is also exaggerated because it presupposes an unduly stringent separation between professional reason and popular values. In our view the law/politics distinction is both real and suffused throughout with ambiguity and uncertainty. The existence of the law/politics distinction creates the possibility of the rule of law, but the ragged and blurred boundaries of that distinction vivify the law by infusing it with the commitments and ideals of those whom the law purports to govern

Soliton surfaces associated with sigma models; differential and algebraic aspect

In this paper, we consider both differential and algebraic properties of surfaces associated with sigma models. It is shown that surfaces defined by the generalized Weierstrass formula for immersion for solutions of the CP^{N-1} sigma model with finite action, defined in the Riemann sphere, are themselves solutions of the Euler-Lagrange equations for sigma models. On the other hand, we show that the Euler-Lagrange equations for surfaces immersed in the Lie algebra su(N), with conformal coordinates, that are extremals of the area functional subject to a fixed polynomial identity are exactly the Euler-Lagrange equations for sigma models. In addition to these differential constraints, the algebraic constraints, in the form of eigenvalues of the immersion functions, are treated systematically. The spectrum of the immersion functions, for different dimensions of the model, as well as its symmetry properties and its transformation under the action of the ladder operators are discussed. Another approach to the dynamics is given, i.e. description in terms of the unitary matrix which diagonalizes both the immersion functions and the projectors constituting the model.Comment: 22 pages, 3 figure

Hadronic Spectral Functions in Nuclear Matter

We study the in-medium properties of mesons $(\pi,\eta,\rho)$ and baryon resonances in cold nuclear matter within a coupled-channel analysis. The meson self energies are generated by particle-hole excitations. Thus multi-peak spectra are obtained for the mesonic spectral functions. In turn this leads to medium-modifications of the baryon resonances. Special care is taken to respect the analyticity of the spectral functions and to take into account effects from short-range correlations both for positive and negative parity states. Our model produces sensible results for pion and $\Delta$ dynamics in nuclear matter. We find a strong interplay of the $\rho$ meson and the $D_{13}(1520)$, which moves spectral strength of the $\rho$ spectrum to smaller invariant masses and leads to a broadening of the baryon resonance. The optical potential for the $\eta$ meson resulting from our model is rather attractive whereas the in-medium properties modifications of the $S_{11}(1535)$ are found to be quite small.Comment: 71 pages, 31 figures, accepted for Publication in Nuclear Physics A; minor modifications of the manuscript, several typos correcte

Infinite families of superintegrable systems separable in subgroup coordinates

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure

Corrections to Sirlin's Theorem in O(p6)O(p^6) Chiral Perturbation Theory

We present the results of the first two-loop calculation of a form factor in full $SU(3) \times SU(3)$ Chiral Perturbation Theory. We choose a specific linear combination of $\pi^+, K^+, K^0$ and $K\pi$ form factors (the one appearing in Sirlin's theorem) which does not get contributions from order $p^6$ operators with unknown constants. For the charge radii, the correction to the previous one-loop result turns out to be significant, but still there is no agreement with the present data due to large experimental uncertainties in the kaon charge radii.Comment: 6 pages, Latex, 2 LaTeX figure