Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scalar theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.Comment: 47 pages, 11 figures, final versio

History of clinical transplantation

How transplantation came to be a clinical discipline can be pieced together by perusing two volumes of reminiscences collected by Paul I. Terasaki in 1991-1992 from many of the persons who were directly involved. One volume was devoted to the discovery of the major histocompatibility complex (MHC), with particular reference to the human leukocyte antigens (HLAs) that are widely used today for tissue matching.1 The other focused on milestones in the development of clinical transplantation.2 All the contributions described in both volumes can be traced back in one way or other to the demonstration in the mid-1940s by Peter Brian Medawar that the rejection of allografts is an immunological phenomenon.3,4 © 2008 Springer New York

Atrial fibrillation: Prevalence after minimally invasive direct and standard coronary artery bypass

Background. This study identified and compared the prevalence of new-onset atrial fibrillation (AFIB) following standard coronary artery bypass grafting (SCABG) with cardiopulmonary bypass (CPB) and minimally invasive direct vision coronary artery bypass grafting (MIDCAB) without CPB. A further comparison was made between AFIB prevalence in SCABG and MIDCAB subjects with two or fewer bypasses. Methods. This is a retrospective, comparative survey. Patients with new-onset AFIB who underwent SCABG or MIDCAB alone were identified electronically using a triangulated method (International Classification of Diseases, 9th revision, Clinical Modification [ICD-9 CM] code; clinical database word search; and pharmacy database drug search). Results. The total sample (n = 814; 94 MIDCAB, 720 SCABG) exhibited a trend toward lower AFIB prevalence in MIDCAB (23.4%) versus SCABG (33.1%) subjects (p = 0.059). AFIB prevalence in the SCABG subset with two or less vessel bypasses (n = 98; n = 18 single vessel, n = 80 double vessels) and MIDCAB subjects (n = 94; n = 90 single vessels, n = 4 double vessels) was almost identical (SCABG subset 24.5% versus MIDCAB 23.4%, p = 0.860). Slightly more than half (56.9%) of new-onset AFIB subjects were identified by ICD-9 CM codes, with the remainder by word search (37.7%) or procainamide query (5.4%). Conclusions. In this sample, the number of vessels bypassed seemed to have a greater influence on AFIB prevalence than the application of CPB or the surgical approach. Retrospective identification of AFIB cases by ICD-9 CM code grossly underestimated AFIB prevalence. © 2001 by The Society of Thoracic Surgeons