** Next:** About this document

For email orders of the book click
this URL.
Price $38 (approx 50 DM)!

#### This is the blurb as it appears on the cover of the book.

### H. Kleinert

## PATH INTEGRALS

###
in Quantum Mechanics, Statistics, Polymer Physics,

and Financial Markets

World Scientific Publishing Co., Singapore 2003.

This is the third, significantly expanded
edition of the comprehensive textbook
of 1990 on the theory and applications
of path integrals. It is the first book
to explicitly solve path integrals of
a wide variety of nontrivial
quantum-mechanical systems, in particular
of the hydrogen atom.
The solutions have become possible
by
two major advances.
The first is a * new euclidean path integral formula*
which increases the restricted
range of applicability of Feynman's famous
formula
to include singular attractive 1/r- and
1/r^2-potentials.
The second is a simple quantum equivalence principle
governing the transformation
of euclidean
path integrals
to spaces with curvature and torsion
which leads to time-sliced path integrals
which are manifestly invariant under coordinate transformations.
In addition to the time-sliced definition, we
give a perturbative
definition to path integrals
which makes them invariant under coordinate
transformations. A consitent implementation of this property leads
to an extension of the theory of generlaized functions
by defining uniquely integrals over products of distributions.

The powerful
Feynman-Kleinert
variational approach
is explained
and
developed systematically
into a
variational perturbation theory
which, in contrast to
ordinary
perturbation theory, produces convergent expansions.
The
convergence is uniform from
weak to strong couplings,
opening a way to precise
approximate evaluations of analytically unsolvable
path integrals.

Tunneling
processes are treated in detail.
The results are used
to determine the
lifetime of supercurrents,
the stability of metastable
thermodynamic phases, and
the large-order behavior of perturbation
expansions.
A new variational treatment
extends
the range of validity
of previous tunneling theories from large to small barriers.
A corresponding extension of large-order perturbation theory now also applies to
small orders.

Special attention is devoted to path integrals with topological restrictions.
These are relevant to the understanding of
the statistical properties of elementary particles
and the
entanglement phenomena in polymer physics and biophysics.
The Chern-Simons theory of particles with fractional statistics (* anyons*)
is introduced and applied to explain
the fractional quantum Hall effect.

The relevance of path integral to
financial markets is discussed, and
improvements of the
famous Black-Scholes formula for
option prices are developed which account for the
fact that large market fluctuation
occur much more frequently
than in
Gaussian distributions.

### ABOUT THE AUTHOR

Hagen Kleinert is Professor of Physics at the Freie Universität Berlin,
Germany.
As a visiting scientist, he has spent extended periods of time
at CERN,
the
European Organization for Nuclear Research in Geneva;
at the California Institute of Technology in Pasadena; at the
Universities of California in Berkeley, Santa Barbara,
and San Diego; at the Los Alamos National Laboratories
in New Mexico; and at Princeton University, New Jersey.
He has made numerous contributions to our understanding of
particle physics, mathematical physics, condensed matter physics,
chemical physics, and nuclear physics.
His
two-volume book
* Gauge Fields in Condensed Matter*,
published by World Scientific,
develops a new quantum
field-theory of
phase transitions on the basis of * disorder fields*. Such fields
have since
become
a powerful tool
to investigate the
statistical properties of
fluctuating
line-like
excitations in various many-body
systems such as superfluids, superconductors, and crystals.
His book *Critical Poperties of Phi^4-Theories*,
coauthored with V. Schulte-Frohlinde,
presents a thorough introduction to the field
of critical phenomena
and develops powerful resummation methods for the
divergent perturbation expansions
of quantum field theories, resulting in the most accurate
critical exponents so far.

**
To order the book from the publishing company
click this line!
**

** To List of Books and Articles **

----> Back to HOMEPAGE of this server

----> Go to MASTER INDEX of this server

Administration