## e-books in Geometry & Physics category

**Geometry and Topology in Electronic Structure Theory**

by

**Raffaele Resta**-

**University of Trieste**,

**2012**

From the table of contents: Introduction; Early discoveries; Berry-ology (geometry in nonrelativistic quantum mechanics); Manifestations of the Berry phase; Modern theory of polarization; Quantum metric and the theory of the insulating state.

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**5523**views)

**First Steps Towards a Symplectic Dynamics**

by

**Barney Bramham, Helmut Hofer**-

**arXiv**,

**2011**

Both dynamical systems and symplectic geometry have rich theories and the time seems ripe to develop the common core with integrated ideas from both fields. We discuss problems which show how dynamical systems and symplectic ideas come together.

(

**6718**views)

**Topology and Physics: A Historical Essay**

by

**C. Nash**-

**arXiv**,

**1997**

In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.

(

**8878**views)

**Geometry, Topology and Physics**

by

**Maximilian Kreuzer**-

**Technische Universitat Wien**,

**2010**

From the table of contents: Topology (Homotopy, Manifolds, Surfaces, Homology, Intersection numbers and the mapping class group); Differentiable manifolds; Riemannian geometry; Vector bundles; Lie algebras and representations; Complex manifolds.

(

**11955**views)

**Edinburgh Lectures on Geometry, Analysis and Physics**

by

**Michael Atiyah**-

**arXiv**,

**2010**

These notes are based on a set of six lectures that the author gave in Edinburgh and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and they may stimulate readers to investigate them.

(

**5314**views)

**Geometry in Physics**

by

**Alexander Altland**,

**2010**

Contents: Exterior Calculus (Exterior Algebra, Differential forms in Rn, Metric, Gauge theory); Manifolds (Basic structures, Tangent space); Lie groups (Lie group actions, Lie algebras, Lie algebra actions, From Lie algebras to Lie groups).

(

**7412**views)

**Geometry and Group Theory**

by

**Christopher Pope**-

**Texas A&M University**,

**2008**

Lecture notes on Geometry and Group Theory. In this course, we develop the basic notions of Manifolds and Geometry, with applications in physics, and also we develop the basic notions of the theory of Lie Groups, and their applications in physics.

(

**13127**views)

**Lectures on Calabi-Yau and Special Lagrangian Geometry**

by

**Dominic Joyce**-

**arXiv**,

**2002**

An introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture.

(

**7991**views)

**Lectures on complex geometry, Calabi-Yau manifolds and toric geometry**

by

**Vincent Bouchard**-

**arXiv**,

**2007**

These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds.

(

**5160**views)

**Introduction to Braided Geometry and q-Minkowski Space**

by

**Shahn Majid**-

**arXiv**,

**1994**

Systematic introduction to the geometry of linear braided spaces. These are versions of Rn in which the coordinates xi have braid-statistics described by an R-matrix. From this starting point we survey the author's braided-approach to q-deformation.

(

**4888**views)

**An Introduction to Noncommutative Spaces and their Geometry**

by

**Giovanni Landi**-

**arXiv**,

**1997**

These lectures notes are an introduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists.

(

**8034**views)

**Noncommutative Geometry, Quantum Fields and Motives**

by

**Alain Connes, Matilde Marcolli**-

**American Mathematical Society**,

**2007**

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.

(

**7541**views)

**Noncommutative Geometry**

by

**Alain Connes**-

**Academic Press**,

**1994**

The definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics. Ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics.

(

**8594**views)

**Geometry of Quantum Mechanics**

by

**Ingemar Bengtsson**-

**Stockholms universitet, Fysikum**,

**1998**

These are the lecture notes from a graduate course in the geometry of quantum mechanics. The idea was to introduce the mathematics in its own right, but not to introduce anything that is not directly relevant to the subject.

(

**9320**views)

**The Geometrization of Physics**

by

**Richard S. Palais**-

**University of California at Irvine**,

**1981**

The major goal of these notes is to develop an observation that not only can gauge fields of the Yang-Mills type be unified with the Einstein model of gravitation, but also that when this unification is made they are described by pure geometry.

(

**8290**views)

**Lectures on the Geometry of Quantization**

by

**Sean Bates, Alan Weinstein**-

**University of California at Berkeley**,

**1997**

An introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role which these ideas play in formalizing the transition between the mathematics of classical dynamics and that of quantum mechanics.

(

**7962**views)

**Differential Geometry in Physics**

by

**Gabriel Lugo**-

**University of North Carolina at Wilmington**,

**2006**

These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.

(

**13053**views)