Giampiero Esposito, Giuseppe Marmo, George Sudarshan
From Classical to Quantum Mechanics
An Introduction to the Formalism, Foundations
and Applications
January 2004 | Hardback | 608 pages 83 exercises
36 figures | ISBN: 0-521-83324-8
This textbook provides a pedagogical introduction
to the formalism, foundations and applications
of quantum mechanics. Part I covers the basic
material which is necessary to understand
the transition from classical to wave mechanics.
Topics include classical dynamics, with emphasis
on canonical transformations and the Hamilton-Jacobi
equation, the Cauchy problem for the wave
equation, Helmholtz equation and eikonal
approximation, introduction to spin, perturbation
theory and scattering theory. The Weyl quantisation
is presented in Part II, along with the postulates
of quantum mechanics. Part III is devoted
to topics such as statistical mechanics and
black-body radiation, Lagrangian and phase-space
formulations of quantum mechanics, and the
Dirac equation. This book is intended for
use as a textbook for beginning graduate
and advanced undergraduate courses. It is
self-contained and includes problems to aid
the reader’s understanding.
Janos Kollar, Karen E. Smith, Alessio Corti
Rational and Nearly Rational Varieties
January 2004 | Hardback | 241 pages | ISBN:
0-521-83207-1
The most basic algebraic varieties are the
projective spaces, and
rational varieties are their closest relatives.
In many
applications where algebraic varieties appear
in mathematics and
the sciences, we see rational ones emerging
as the most
interesting examples. The authors have given
an elementary
treatment of rationality questions using
a mix of classical and
modern methods. Arising from a summer school
course taught by
Janos Kollar, this book develops the modern
theory of rational
and nearly rational varieties at a level
that will particularly
suit graduate students. There are numerous
examples and
exercises, all of which are accompanied by
fully worked out
solutions, that will make this book ideal
as the basis of a
graduate course. It will act as a valuable
reference for
researchers whilst helping graduate students
to reach the point
where they can begin to tackle contemporary
research problems.
Edited by T. W. Mueller
Groups
Topological, Combinatorial and Arithmetic
Aspects
January 2004 | Paperback | 603 pages | ISBN:
0-521-54287-1
In 1999 a number of eminent mathematicians
were invited to
Bielefeld to present lectures at a conference
on topological,
combinatorial and arithmetic aspects of (infinite)
groups. The
present volume consists of survey and research
articles invited
from participants in this conference. Topics
covered include
topological finiteness properties of groups,
Kac-Moody groups,
the theory of Euler characteristics, the
connection between
groups, formal languages and automata, the
Magnus-Nielsen method
for one-relator groups, atomic and just infinite
groups, topology
in permutation groups, probabilistic group
theory, the theory of
subgroup growth, hyperbolic lattices in dimension
three,
generalised triangle groups and reduction
theory. All
contributions are written in a relaxed and
attractive style,
accessible not only to specialists, but also
to good graduate and
post-graduate students, who will find inspiration
for a number of
basic research projects at various levels
of technical difficulty.
Contributors
H. Abels, P. Abramenko, H. Behr, R. Bieri,
R. Geoghegan, K. U.
Bux, P. Cameron, I. Chiswell, D. J. Collins,
R. I. Grigorchuk, J.
S. Wilson, H. Helling, A. Mann, T. W. Muller,
V. Nekrashevych, S.
Sidki, J.
Miles Reid, Edited by Alexei Skorobogatov
Number Theory and Algebraic Geometry
January 2004 | Paperback | 306 pages | ISBN:
0-521-54518-8
Sir Peter Swinnerton-Dyer’s mathematical
career encompasses
more than 60 years’ work of amazing creativity.
This volume
provides contemporary insight into several
subjects in which Sir
Peter's influence has been notable, and is
dedicated to his 75th
birthday. The opening section reviews some
of his many remarkable
contributions to mathematics and other fields.
The remaining
contributions come from leading researchers
in analytic and
arithmetic number theory, and algebraic geometry.
The topics
treated include: rational points on algebraic
varieties, the
Hasse principle, Shafarevich-Tate groups
of elliptic curves and
motives, Zagier’s conjectures, descent and
zero-cycles,
Diophantine approximation, and Abelian and
Fano varieties.
Contributors
J. B. Birch, Jean-Louis Colliot-Thelene,
G. K. Sankaran, Miles
Reid, Alexei Skorobogatov, Carmen Laura Basile,
Enrico Bombieri,
Paula B. Cohen, Andrew Bremner, D. Harari,
Neil Dummigan, William
Stein, Mark Watkins, Tom Fisher, D. R. Heath-Brown,
Andrey Levin,
William G. McCallum, Pavlos Tzermias, Koari
Suzuki, Per Salberger