Felix Finster, Universitat Regensburg, Germany
The Principle of the Fermionic Projector
Expected publication date is March 9, 2006
Description
The "principle of the fermionic projector" provides a
new mathematical framework for the formulation of physical
theories and is a promising approach for physics beyond the
standard model. This book begins with a brief review of
relativity, relativistic quantum mechanics, and classical gauge
theories, emphasizing the basic physical concepts and
mathematical foundations. The external field problem and Klein's
paradox are discussed and then resolved by introducing the
fermionic projector, a global object in space-time that
generalizes the notion of the Dirac sea. At the mathematical core
of the book is a precise definition of the fermionic projector
and the use of methods of hyperbolic differential equations for
detailed analysis. The fermionic projector makes it possible to
formulate a new type of variational principle in space-time. The
mathematical tools are developed for the analysis of the
corresponding Euler-Lagrange equations. A particular variational
principle is proposed that gives rise to an effective interaction
which shows many similarities to the interactions of the standard
model.
The main chapters of the book are easily accessible for beginning
graduate students in mathematics or physics. Several appendices
provide supplementary material, which will be useful to the
experienced researcher.
Contents
The principle of the Fermionic projector-A new mathematical model
of space-time
Preliminaries
The Fermionic projector in the continuum
The principle of the Fermionic projector
The continuum limit
The Euler-Lagrange equations in the vacuum
The dynamical gauge group
Spontaneous block formation
The effective gauge group
Connection to the Fock space formalism
Some formulas of the light-cone expansion
Normalization of chiral fermions
The regularized causal perturbation theory
Linear independence of the basic fractions
The commutator [P,Q]
Perturbation calculation for the spectral decomposition of P(x,y)
P(y,x)
Bibliography
Index
Notation index
Details:
Series: AMS/IP Studies in Advanced Mathematics, Volume: 35
Publication Year: 2006
ISBN: 0-8218-3974-8
Paging: 302 pp.
Binding: Hardcover
Alec L. Matheson, Lamar University, Beaumont, TX, Michael I. Stessin, State University of New York (SUNY), Albany, NY, and Richard M. Timoney, Trinity College, Dublin, Ireland
Recent Advances in Operator-Related Function Theory
Expected publication date is February 12, 2006
Description
The articles in this book are based on talks at a conference
devoted to interrelations between function theory and the theory
of operators. The main theme of the book is the role of
Alexandrov-Clark measures. Two of the articles provide the
introduction to the theory of Alexandrov-Clark measures and to
its applications in the spectral theory of linear operators. The
remaining articles deal with recent results in specific
directions related to the theme of the book.
Readership
Research mathematicians interested in operator theory and
function theory.
Contents
A. Poltoratski and D. Sarason -- Aleksandrov-Clark measures
A. Matheson and M. Stessin -- Applications of spectral measures
J. Agler and J. E. McCarthy -- Parametrizing distinguished
varieties
J. T. Anderson and J. Wermer -- Approximation by CR functions on
the unit sphere in \mathbb{C}^2
S. M. Buckley and D. Vukotic -- Superposition operators and the
order and type of entire functions
K. Dyakonov and D. Khavinson -- Smooth functions in star-invariant
subspaces
S. R. Garcia -- Conjugation and Clark operators
D. Girela -- A class of conformal mappings with applications to
function spaces
H. Koo and W. Smith -- Composition operators between Bergman
spaces of functions of several variables
M. J. Martin and D. Vukotic -- Isometries of some classical
function spaces among the composition operators
A. Montes-Rodriguez and S. A. Shkarin -- New results on a
classical operator
J. Pau -- Size conditions to be in a finitely generated ideal of
H^\infty
W. T. Ross -- The classical Dirichlet space
E. Saksman and C. Sundberg -- Comparing topologies on the space
of composition operators
W. Smith -- Brennan's conjecture for weighted composition
operators
Details:
Series: Contemporary Mathematics, Volume: 393
Publication Year: 2006
ISBN: 0-8218-3925-X
Paging: 214 pp.
Binding: Softcover
Ido Efrat
Valuations, Orderings, and Milnor K-Theory
Expected publication date is April 9, 2006
Description
This monograph is a comprehensive exposition of the modern theory
of valued and ordered fields. It presents the classical aspects
of such fields: their arithmetic, topology, and Galois theory.
Deeper cohomological aspects are studied in its last part in an
elementary manner. This is done by means of the newly developed
theory of generalized Milnor K-rings. The book emphasizes the
close connections and interplay between valuations and orderings,
and to a large extent, studies them in a unified manner.
The presentation is almost entirely self-contained. In
particular, the text develops the needed machinery of ordered
abelian groups. This is then used throughout the text to replace
the more classical techniques of commutative algebra. Likewise,
the book provides an introduction to the Milnor K-theory.
The reader is introduced to the valuation-theoretic techniques as
used in modern Galois theory, especially in applications to
birational anabelian geometry, where one needs to detect
valuations from their "cohomological footprints". These
powerful techniques are presented here for the first time in a
unified and elementary way.
Readership
Graduate students and research mathematicians interested in
valuations and orderings on fields (algebra and number theory).
Contents
Part I. Abelian Groups
Preliminaries on abelian groups
Ordered abelian groups
Part II. Valuations and orderings
Valuations
Examples of valuations
Coarsenings of valuations
Orderings
The tree of localities
Topologies
Complete fields
Approximation theorems
Canonical valuations
Valuations of mixed characteristics
Part III. Galois Theory
Infinite Galois theory
Valuations in field extensions
Decomposition groups
Ramification theory
The fundamental equality
Hensel's lemma
Real closures
Coarsening in algebraic extensions
Intersections of decomposition groups
Sections
Part IV. K-rings
\kappa-structures
Milnor K-rings of fields
Milnor K-rings and orderings
K-rings and valuations
K-rings of wild valued fields
Decomposition of K-rings
Realization of \kappa-structures
Bibliography
Glossary of notation
Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 124
Publication Year: 2006
ISBN: 0-8218-4041-X
Paging: 288 pp.
Binding: Hardcover
Edited by: Rostislav Grigorchuk, Michael Mihalik, Mark Sapir, and Zoran Sunik
Topological and Asymptotic Aspects of Group Theory
Expected publication date is March 29, 2006
Description
The articles in this volume are based on the talks given at two
special sessions at the AMS Sectional meetings held in 2004. The
articles cover various topological and asymptotic aspects of
group theory such as hyperbolic and relatively hyperbolic groups,
asymptotic cones, Thompson's group, Nielsen fixed point theory,
homology, groups acting on trees, groups generated by finite
automata, iterated monodromy groups, random walks on finitely
generated groups, heat kernels, and currents on free groups.
Readership
Graduate students and research mathematicians interested in
geometric group theory.
Contents
G. N. Arzhantseva -- A dichotomy for finitely generated subgroups
of word hyperbolic groups
L. Bartholdi and Z. Sunik -- Some solvable automaton groups
A. V. Borovik and A. G. Myasnikov -- Quotient tests and random
walks in computational group theory
K. S. Brown -- The homology of Richard Thompson's group F
K.-U. Bux and R. Perez -- On the growth of iterated monodromy
groups
A. N. Dranishnikov -- On Bestvina-Mess formula
K. Dykema -- Symmetric random walks on certain amalgamated free
product groups
D. Farley -- Homology of tree braid groups
R. Geoghegan and F. Guzman -- Associativity and Thompson's group
V. S. Guba -- Traveller salesman property and Richard Thompson's
group F
S. V. Ivanov -- On groups with periodic products of commutators
I. Kapovich -- Currents on free groups
A. Karlsson and M. Neuhauser -- Heat kernels, theta identities,
and zeta functions on cyclic groups
M. R. Kelly -- The Nielsen fixed point structure for homotopy
idempotents on surfaces
T. Napier and M. Ramachandran -- Thompson's group F is not Kahler
A. Yu. Ol'shanskii and M. V. Sapir -- Groups with non-simply
connected asymptotic cones
D. V. Osin -- Relative Dehn functions of amalgamated products and
HNN-extensions
A. M. Brunner and S. N. Sidki -- Endomorphisms of the finitary
group of isometries of the binary tree
Details:
Series: Contemporary Mathematics, Volume: 394
Publication Year: 2006
ISBN: 0-8218-3756-7
Paging: 234 pp.
Binding: Softcover
Edited by: Gary R. Jensen and Steven G. Krantz
150 Years of Mathematics at Washington University in St. Louis
Expected publication date is March 15, 2006
Description
Articles in this book cover a wide range of important topics in
mathematics, and are based on talks given at the conference
commemorating the 150th anniversary of Washington University in
St. Louis. The volume is prefaced by a brief history of the
Washington University Department of Mathematics, a roster of
those who received the PhD degree from the department, and a list
of the Washington University Department of Mathematics faculty
since the founding of the university.
Readership
Research mathematicians interested in various areas of
mathematics.
Contents
S. G. Krantz -- An anecdotal history of the Washington University
Mathematics Department
G. R. Jensen and S. G. Krantz -- Dissertation list
G. R. Jensen and S. G. Krantz -- History of the Mathematics
faculty
R. L. Bryant -- Geometry of manifolds with special holonomy:
"100 years of holonomy"
R. R. Coifman -- Geometric harmonic analysis in high dimensions:
Challenges and opportunities
J. P. D'Angelo -- An analogue of Hilbert's seventeenth problem in
one complex dimension
J. J. Kohn -- Hypoelliptic second order equations that lose
derivatives
H. B. Lawson, Jr. -- Stokes' theorem and minimal surfaces
J. D. McNeal -- L^2 estimates on twisted Cauchy-Riemann complexes
Y. Meyer -- From wavelets to atoms
R. Schoen -- The mathematics of general relativity: Problems and
progress
R. R. Coifman, A. Bonami, R. Bryant, and J. P. D'Angelo -- Panel
discussion
Details:
Series: Contemporary Mathematics, Volume: 395
Publication Year: 2006
ISBN: 0-8218-3603-X
Paging: 145 pp.
Binding: Softcover