"Clear and coherent One of the most exciting aspects of the book is the author's account of how the consequences and implications of the breakthroughs in quantum mechanics challenged the mechanistic, deterministic philosophy fostered by classical science." The Science Teacher Written by a respected Harvard physicist who did his doctoral work in Munich among many of the founding fathers of quantum mechanics, this introductory account of the evolution of quantum physics also explores the subject's philosophical implications. Beginning with brief background sketches, the author offers...
"Clear and coherent One of the most exciting aspects of the book is the author's account of how the consequences and implications of the breakthroughs...
The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations.
If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known...
The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For insta...
The subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose light-like geodesics are periodic? A surprising fact is that such manifolds exist in abundance in (2 + 1)-dimensions (though in higher dimensions they are quite rare). This book is concerned with the deformation theory of M2,1 (which furnishes almost all the known examples of these objects). It also has a section describing conformal invariants of these objects, the most interesting being the determinant of a two dimensional...
The subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifo...
Equivariant cohomology on smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Bruning and V.W. Guillemin. The point of departure are two relatively short but very remarkable papers be Henry Cartan, published in 1950 in the Proceedings of the "Colloque de Topologie." These papers are reproduced here, together with a modern introduction to the subject, written by two of the leading experts in the field. This "introduction" comes as a textbook of its own, though, presenting the first full treatment of equivariant cohomology in the de Rahm setting....
Equivariant cohomology on smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Bruning and V.W. Guillemi...
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytope, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. For instance, the first chapter is largely devoted to the Delzant theorem, which says that there is a one-one correspondence between certain types of moment polytopes and certain types of...
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest...
Symplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathematical thought for the past 300 years - the relations between the wave and the corpuscular theories of light. The purpose of this book is to develop these themes, and present some of the advances, using the language of differential geometry as a unifying influence.
Symplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathemat...
This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu- larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn Rm (m 2n - 1) and R2 R2, and Marston Morse, for mappings who studied these singularities for Rn R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and...
This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu- l...
