Information theory and statistical nuclear reactions. II. Many-channel case and Hauser-Feshbach formula: W. A. Friedman and P. A. Mello, Physics Department, University of Wisconsin-Madison, Madison, Wisconsin 53706

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 87 KB
• Volume: 160
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(85)90158-7

✦ Synopsis

containing possible obstructions to the renormalization of the transformation laws, and of noting the absence of obstructions when M has finite fundamental group and nonabelian semi-simple isometry group. The renormalization group equation for the metric coupling is A-'(a/&-')g,= -bg(g) P&T-k) = --ET-k,+ R,+tTR,,R,,,,,+ O(T*). R,,,,, is the curvature tensor and R,= R,, the Ricci tensor of the metric g,. The b-function B,,Cp) is a vector field on the infinite dimensional space of Riemannian metrics on M. Two results on global properties of /I are obtained. When M is a homogeneous space G/H, the b-function is shown to be a gradient on the finite dimensional space of Ginvariant metric couplings on M. And, when M is a two-dimensional compact manifold, the p-function is shown to be a gradient on the infinite dimensional space of metrics on M. The rest of the results are concerned with fixed points. The fixed points are shown to correspond to the metrics satisfying a generalized Einstein equation R, -ag,, = ~t,u, + D,D,, a = & 1 or 0 for u' some vector held on M. Known solutions to these equations are discussed and some of their general properties described. In particular, it is shown that infrared instability occurs in at most a tinite number of directions in the infinite dimensional space of metric couplings.