2004 XII, 213 p. Softcover
3-540-40382-5
Concise textbook intended as a primer on
path integral formalism
both in classical and quantum field theories,
although emphasis
is on the latter. It is ideally suited as
an intensive one-semester
course, delivering the basics needed by readers
to follow
developments in field theory. Path Integrals
in Field Theory
paves the way for both more rigorous studies
in fundamental
mathematical issues as well as for applications
in hadron,
particle and nuclear physics, thus addressing
students in
mathematical and theoretical physics alike.
Assuming some
background in relativistic quantum theory
(but none in field
theory), it complements the authors monograph
Fields, Symmetries,
and Quarks (Springer, 1999).
Keywords: path integrals, quantum field theorie
Contents: Path Integral in Quantum Mechanics.-
Perturbation
Theory.- Generating Functionals.- Path Integrals
for Scalar
Fields.- Evaluation of Path Integrals.- Green's
Functions.-
Divergences in n-Point Functions.- Green's
Functions for Fermions.-
Interacting Fields.- S-Matrix And Green's
Functions.- Path
Integrals for Gauge Fields.- Examples for
Gauge Field Theories.-
Units and Metric.- Classical Fields.
Series: Advanced Texts in Physics.
2nd ed. 2004 XVI, 240 p. Softcover
3-540-40604-2
Recommended Retail Price: EUR 39.95 *
"In an increasingly crowded field of
financial engineering
titles, Seydel's Tools for Computational
Finance stands out as
filling an unmet need. It is an intermediate
level text with an
extremely practical focus. ... This is the
kind of book you can
read quickly, gaining a broad understanding
of practical
techniques of financial engineering. On the
other hand, you can
go through it slowly, working through all
the examples and
exercises in order to gain indepth practical
knowledge you can
use on the job."
For the second edition the author has enlarged
the chapter on
Monte Carlo Simulation, has added more figures,
more exercises,
more references, more material in the appendices
and has written
a new section on jump processes.
Keywords: Black-Scholes-Equation, Black/Scholes,
Computational
Finance, Derivative pricing, Exotic options,
Exotische Optionen,
Mathematical Finance, Mathematische Finanz,
Numerik, Preisen von
Optionen
Contents:
Modelling Tools for Financial Options.- Generating
Random Numbers
with Specified Distributions.- Integration
of Stochastic
Differential Equations.- Finite Difference
and Standard Options.-
Finite-Element Methods.- Pricing of Exotic
Options.- Appendices.
Series: Universitext.
2003 VI, 236 p. Softcover
3-540-40723-5
Separation of scales plays a fundamental
role in the
understanding of the dynamical behaviour
of complex systems in
physics and other natural sciences. A prominent
example is the
Born-Oppenheimer approximation in molecular
dynamics. This book
focuses on a recent approach to adiabatic
perturbation theory,
which emphasizes the role of effective equations
of motion and
the separation of the adiabatic limit from
the semiclassical
limit.
A detailed introduction gives an overview
of the subject and
makes the later chapters accessible also
to readers less familiar
with the material. Although the general mathematical
theory based
on pseudodifferential calculus is presented
in detail, there is
an emphasis on concrete and relevant examples
from physics.
Applications range from molecular dynamics
to the dynamics of
electrons in a crystal and from the quantum
mechanics of
partially confined systems to Dirac particles
and nonrelativistic
QED.
Keywords: Quantum mechanics, adiabatic limit,
semiclassical
limit, Pseudodifferential Operators
Contents:
Introduction.- First-order adiabatic theory.-
Space-adiabatic
perturbation theory.- Applications and extensions.-
Quantum
dynamics in periodic media.- Adiabatic decoupling
without
spectral gap.- Pseudodifferential operators.-
Operator-valued
Weyl calculus for tau-equivariant symbols.-
Related approaches.-
List of symbols.- References.- Index.
Series: Lecture Notes in Mathematics. Vol..
1821
2nd ed. 2004 Approx. 430 p. Hardcover
3-540-00832-2
The first edition of "Compact Complex
Surfaces" was
published in 1984 and has become one of the
most important books
on the subject. In this second enlarged edition
the major
developments of the last 20 years have been
incorporated. The
Enriques-Kodaira classification is carried
out in the spirit of
Mori theory and many new developments have
been added, including
new analytic tools as well as new algebraic
methods such as the
theorems of Bogomolov and Reider and their
applications. A new
section is devoted to the stunning results
achieved by the
introduction of Donaldson and Seiberg-Witten
invariants.
Keywords: Compact Complex Surfaces, Enriques-Kodaira
Classification, Kahler Surfaces, Mori Theory,
Donaldson and
Seiberg-Witten Invariants
Contents:
Introduction.- I. Preliminaries.- II. Curves
on Surfaces.- III.
Mappings of Surfaces.- IV. Some General Properties
of Surfaces. V.
Examples.- VI. The Enriques Kodaira Classification.-
VII.
Surfaces of General Type.- VIII. K3-Surfaces
and Enriques
Surfaces. IX. Topological and Differentiable
Structure of
Surfaces.- Bibliography.- Notation.- Index.
Series: Ergebnisse der Mathematik und ihrer
Grenzgebiete. 3.
Folge / A Series of Modern Surveys in Mathematics.
Vol.. 4
2004 Approx. 249 p. Softcover
3-540-40650-6
This book offers a mathematical introduction
to non-life
insurance and, at the same time, to a multitude
of applied
stochastic processes. It gives detailed discussions
of the
fundamental models for claim sizes, claim
arrivals, the total
claim amount, and their probabilistic properties.
Throughout the
book the language of stochastic processes
is used for describing
the dynamics of an insurance portfolio in
claim size space and
time. In addition to the standard actuarial
notions, the reader
learns about the basic models of modern non-life
insurance
mathematics: the Poisson, compound Poisson
and renewal processes
in collective risk theory and heterogeneity
and Buhlmann models
in experience rating. The reader gets to
know how the underlying
probabilistic structures allow one to determine
premiums in a
portfolio or in an individual policy. Special
emphasis is given
to the phenomena which are caused by large
claims in these models.
What makes this book special are more than
100 figures and tables
illustrating and visualizing the theory.
Every section ends with
extensive exercises. They are an integral
part of this course
since they support the access to the theory.
The book can serve either as a text for an
undergraduate/graduate
course on non-life insurance mathematics
or applied stochastic
processes. Its content is in agreement with
the European "Group
Consultatif" standards. An extensive
bibliography, annotated
by various comments sections with references
to more advanced
relevant literature, make the book broadly
and easiliy accessible.
Keywords: Non-life insurance mathematics,
applied stoachastic
process, risk theory, experience rating,
MSC (2000): 91B30, 60G35,
60K10
Series: Universitext.
2004 Approx. 572 p. 65 illus. Hardcover
3-540-40386-8
This two-volume work by V.A. Zorich on Mathematical
Analysis
constitutes a thorough first course in real
analysis, leading
from the most elementary facts about real
numbers to such
advanced topics as differential forms on
manifolds, asymptotic
methods, Fourier, Laplace, and Legendre transforms,
and elliptic
functions. With masterful exposition, the
author provides a
smooth, gradual transition from each topic
to the next, so that
the slope never feels too steep for the reader.
Making use of
Cartan's concept of a filter base, the author
disperses the fog
of epsilons and deltas that have always made
the crucial subject
of limits a barrier for the nonmathematical
specialist. As a
result, the major theorems of differentiation
and integration
reveal their essential unity in a nearly
painless manner. The
clarity of the exposition is matched by a
wealth of instructive
exercises and fresh applications to areas
seldom touched on in
real analysis books, many of which are taken
from physics and
technology.
Keywords: real numbers, differential calculus,
integral calculus,
Fourier transform, Stokes' theorem
2004 Approx. 706 p. 41 illus. Hardcover
3-540-40633-6
This two-volume work by V.A.Zorich on Mathematical
Analysis
constitutes a thorough first course in real
analysis, leading
from the most elementary facts about real
numbers to such
advanced topics as differential forms on
manifolds, asymptotic
methods, Fourier, Laplace, and Legendre transforms,
and elliptic
functions. With masterful exposition, the
author provides a
smooth, gradual transition from each topic
to the next, so that
the slope never feels too steep for the reader.
Making use of
Cartan's concept of a filter base, the author
disperses the fog
of epsilons and deltas that have always made
the crucial subject
of limits a barrier for the nonmathematical
specialist. As a
result, the major theorems of differentiation
and integration
reveal their essential unity in a nearly
painless manner. The
clarity of the exposition is matched by a
wealth of instructive
exercises and fresh applications to areas
seldom touched on in
real analysis books, many of which are taken
from physics and
technology.
Keywords: differential calculus, Fourier
transform, integral
calculus, real numbers, Stokes' theorem