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PATH
INTEGRALS IN QUANTUM MECHANICS,
STATISTICS, POLYMER PHYSICS, AND
FINANCIAL MARKETS
5th Edition
by Hagen Kleinert (Freie
Universitat Berlin, Germany)
1624pp
978-981-4273-56-5(pbk): US$48 / £32
US$33.60 /
£22.40
978-981-4273-55-8: US$168 / £126
US$117.60 /
£88.20
978-981-4273-57-2(ebook): US$218
US$152.60
Table
of Contents (2,741k)
Preface
(1,421k)
Chapter
1: Fundamentals (11,962k)
"Kleinert's
book presents the reader with a very
complete and very thorough
discussion of path integration … a
new extensive and, again, rather
complete chapter has been added on
the use of path integration
techniques in the analysis of
financial markets. This chapter
would do well in any high-level
course on stochastic financial
models and is a wonderful occasion
for candidate mathematical and
theoretical physicists to realize
what great potential there hides
still in the methodologies and
techniques that have been developed
… It profits from the clarity and
conciseness that is also a hallmark
of Kleinert's scientific papers …
this volume is highly recommendable
for any student considering majoring
in theoretical physics or chemistry,
and an absolute must for any
lecturer in this area … In fact, I
don't know of any excuse not to have
your own copy." --
Journal of Statistical Physics
This is the fifth,
expanded edition of the comprehensive
textbook published in 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 the hydrogen atom. The
solutions have been made possible by two
major advances. The first is a new
euclidean path integral formula which
increases the restricted range of
applicability of Feynman's time-sliced
formula to include singular attractive
1/r- and 1/r2-potentials. The second is
a new nonholonomic mapping principle
carrying physical laws in flat spacetime
to spacetimes with curvature and
torsion, which leads to time-sliced path
integrals that are manifestly invariant
under coordinate transformations.
In addition to the
time-sliced definition, the author gives
a perturbative, coordinate-independent
definition of path integrals, which
makes them invariant under coordinate
transformations. A consistent
implementation of this property leads to
an extension of the theory of
generalized functions by defining
uniquely 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
results. The convergence is uniform from
weak to strong couplings, opening a way
to precise evaluations of analytically
unsolvable path integrals in the
strong-coupling regime where they
describe critical phenomena.
Tunneling processes
are treated in detail, with applications
to the lifetimes of supercurrents, the
stability of metastable thermodynamic
phases, and the large-order behavior of
perturbation expansions. A variational
treatment extends the range of validity
to small barriers. A corresponding
extension of the large-order
perturbation theory now also applies to
small orders.
Special attention
is devoted to path integrals with
topological restrictions needed to
understand 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 integrals to financial markets is
discussed, and improvements of the
famous Black-Scholes formula for option
prices are developed which account for
the fact, recently experienced in the
world markets, that large fluctuations
occur much more frequently than in
Gaussian distributions.
Contents:
- Fundamentals
- Path Integrals - Elementary
Properties and Simple Solutions
- External Sources, Correlations, and
Perturbation Theory
- Semiclassical Time Evolution
Amplitude
- Variational Perturbation Theory
- Path Integrals with Topological
Constraints
- Many Particle Orbits - Statistics
and Second Quantization
- Path Integrals in Polar and
Spherical Coordinates
- Wave Functions
- Spaces with Curvature and Torsion
- Schrodinger Equation in General
Metric-Affine Spaces
- New Path Integral Formula for
Singular Potentials
- Path Integral of Coulomb System
- Solution of Further Path Integrals
by Duru-Kleinert Method
- Path Integrals in Polymer Physics
- Polymers and Particle Orbits in
Multiply Connected Spaces
- Tunneling
- Nonequilibrium Quantum Statistics
- Relativistic Particle Orbits
- Path Integrals and Financial Markets
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