Quantum Field Theory and Critical Phenomena

Abstract

There are nine and sixty ways of constructing tribal lays-(Rudyard Kipling, "Ballads and Barrack Room Ballads")Virtually all of the "lays" of renormalizable quantum field theory can be found in Quantum Field Theory and Critical Phenomena. This remarkable work contains the most exhaustive collection of techniques, descriptions of subtleties and pitfalls, and helpful hints on the subject to date. Although several books have been written on critical phenomena-perhaps more of them on renormalizable field theories-yet none reaches the breadth or depth of the present book.The birth of quantum field theory nearly 50 years ago out of the divergences of quantum electrodynamics, and the emergence of the theory of universal properties of critical phenomena some 20 years ago, are only the beginnings of a very fertile intellectual enterprise. The author has participated in a large number of developments himself, and this book is a wonderful monograph conveying these subjects. The book is so clearly written and complete that students with a basic knowledge of quantum field theory can understand it. When they finish reading the book, they will be experts on the subject.The 40 chapters in this book are equally divided in four ways: (1) general renormalizable field theory; (2) particle physics applications and subtleties; (3) all about critical phenomena; and (4) instantons, mostly (not entirely) applied to the Bore1 summability of large-order perturbation series. At the end of each chapter are numerous relevant appendices, as well as textbooklike exercises for the reader. And yet, the book is not a textbook; rather, it is an encyclopedia written as a textbook.In an age where scientific results are published piecemeal and distributed in several journals and short review articles, it is gratifying to find a monograph that harks back to older times, when the material could all be found between the covers of a single book. I am confident that this book will find a place as a valuable sourcebook.PRADEEP KUMAR

Experimental characterization of a quantum many-body system via higher-order correlations

“…G (N >2) con (z, z ) ≡ 0. Hence, all correlation functions factorise and one recovers Wick's theorem [14] stating that, for a Gaussian state,…”

“…con is zero for all N > 2, the higher-order correlation functions factorise and are given by the Wick decomposition [14,15] containing only terms of G (N ) with N ≤ 2. In this case, the quantum many-body states are Gaussian.…”

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

“…breaking in infinite volume [17,18,39]. It is due to the long-range correlations left in the system at finite volume.…”

The O(N) model on a squashedS3and the Klebanov-Polyakov correspondence

“…In flat space, the critical O(N ) vector model in three dimensions exhibits a renormalisation group flow from a free fixed point in the ultraviolet (UV) to an interacting fixed point in the infrared (IR), see for example [4,17,18]. This flow is induced by the quartic interaction which is a relevant operator with a coupling constant that has mass dimension one.…”