Browsing Mathematics, Department of by Author "Warner, Garth"
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Bosonic Quantum Field Theory
Warner, Garth (20080331)The purpose of these notes is to provide a systematic account of that part of Quantum Field Theory in which symplectic methods play a major role. 
C*Algebras
Warner, Garth (20101115)This book is addressed to those readers who are already familiar with the elements of the theory but wish to go further. While some aspects, e.g. tensor products, are summarized without proof, others are dealt with in all ... 
Categorical Homotopy Theory
Warner, Garth (201201)This book is an account of certain developments in categorical homotopy theory that have taken place since the year 2000. Some aspects have been given the complete treatment (i.e., proofs in all detail), while others are ... 
Fibrations and Sheaves
Warner, Garth (20121213)The purpose of this book is to give a systematic treatment of fibration theory and sheaf theory, the emphasis being on the foundational essentials. 
Homotopical Topos Theory
Warner, Garth (201205)The purpose of this book is twofold: (1) To give a systematic introduction to topos theory from a purely categorical point of view, thus ignoring all logical and algebraic issues. (2) To give an account of the homotopy ... 
Lagrangian Mechanics
Warner, Garth (20090112)My original set of lectures on Mechanics was divided into three parts: Lagrangian Mechanics, Hamiltonian Mechanics, Equivariant Mechanics. The present text is an order of magnitude expansion of the first part and is ... 
Mathematical Aspects of General Relativity
Warner, Garth (20060908)These notes can serve as a mathematical supplement to the standard graduate level texts on general relativity and are suitable for selfstudy. The exposition is detailed and includes accounts of several topics of current ... 
Positivity
Warner, Garth (20091223)These notes provide a systematic account of certain aspects of the statistical structure of quantum theory. Here the all prevailing notion is that of a completely positive map and Stinespring's famous characterization ... 
Reconstruction Theory
Warner, Garth (201101)Suppose that G is a compact group. Denote by \underline{Rep} G the category whose objects are the continuous finite dimensional unitary representations of G and whose morphisms are the intertwining operatorsthen ... 
Topics in Topology and Homotopy Theory
Warner, Garth (Hopf Topology Archive, 200501)This book is addressed to those readers who have been through Rotman (or its equivalent), possess a wellthumbed copy of Spanier, and have a good background in algebra and general topology. Granted these prerequisites, ...