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Now showing items 1-10 of 10

#### Bosonic Quantum Field Theory

(2008-03-31)

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.

#### Topics in Topology and Homotopy Theory

(Hopf Topology Archive, 2005-01)

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, my intention is to provide at the core a state of the art treatment of the homotopical foundations of ...

#### Mathematical Aspects of General Relativity

(2006-09-08)

These notes can serve as a mathematical supplement to the standard graduate level texts on general relativity and are suitable for self-study. The exposition is detailed and includes accounts of several topics of current interest, e.g., Lovelock theory and Ashtekar's variables.

#### Fibrations and Sheaves

(2012-12-13)

The purpose of this book is to give a systematic treatment of fibration theory and sheaf theory, the emphasis being on the foundational essentials.

#### Categorical Homotopy Theory

(2012-01)

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 merely surveyed. Therefore a lot of ground is covered in a relatively compact manner, thus giving the ...

#### C*-Algebras

(2010-11-15)

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 detail. Numerous examples have been included and I have also appended an extensive list of references.

#### Reconstruction Theory

(2011-01)

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 operators--then \underline{Rep} G is a monoidal *-category with certain properties P_1,P_2, ... . Conversely, if \underline{C} ...

#### Lagrangian Mechanics

(2009-01-12)

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 differential geometric in character, the arena being the tangent bundle rather than the cotangent bundle. I ...

#### Positivity

(2009-12-23)

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 thereof. I have also included a systematic treatment of "quantum dynamical semigroups," culminating in ...

#### Homotopical Topos Theory

(2012-05)

The purpose of this book is two-fold: (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 theory of the simplicial objects in a Grothendieck topos.