Conformal anomaly from gauge fields without gauge fixing
We show how the Weyl anomaly generated by gauge fields, can be computed from manifestly gauge invariant and diffeomorphism invariant exact renormalization group equations, without having to fix the gauge at any stage. Regularisation is provided by covariant higher derivatives and by embedding the Maxwell field into a spontaneously broken $U(1|1)$ supergauge theory. We first provide a realisation that leaves behind two versions of the original $U(1)$ gauge field, and then construct a manifestly $U(1|1)$ supergauge invariant flow equation which leaves behind only the original Maxwell field in the spontaneously broken regime.
The conformal anomaly and a new exact RG
For scalar field theory, a new generalization of the Exact RG to curved space is proposed, in which the conformal anomaly is explicitly present. Vacuum terms require regularization beyond that present in the canonical formulation of the Exact RG, which can be accomplished by adding certain free fields, each at a non-critical fixed-point. Taking the Legendre transform, the sole effect of the regulator fields is to remove a divergent vacuum term and they do not explicitly appear in the effective average action. As an illustration, both the integrated conformal anomaly and Polyakov action are recovered for the Gaussian theory in d=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=2$$\end{document}.
Resonant Auger decay study of C1s -> pi* core-excited OCS
The present work aims at characterizing short-lived C1s((-1)) pi*((1)) core-excited states of the OCS molecule based on the analysis of the vibrational fine structure and lineshape profiles of the high-resolution resonant Auger decay spectra recorded at the excitation energies along the C1s -> pi* resonance in the binding energy region 15-19eV. Very different behavior in terms of lineshape and resonant enhancement is observed for the (A) over tilde, (B) over tilde and (C) over tilde final states. This is explained by (1) the variation in the C-O bond lengths for the states involved in the electronic relaxation and (2) different contributions in terms of Mulliken population to the molecular orbitals determining the electronic character of the corresponding states. Since the final-state geometries are known from a number of previous experiments and ab initio calculations, the geometry of the C1s((-1)) pi*((1)) intermediate states can be predicted in analogy with e.g. the N-2, CO2 and N2O molecules. (C) 2009 Elsevier B.V. All rights reserved. (Less)