Series: Lecture Notes in Mathematics, Vol. 2189
1st ed. 2017, Approx. 100 p.
Softcover
ISBN 978-3-319-63205-6
* Gives an accessible introduction to current research
* Provides a common point of view on several interconnected, but
originally independently developed areas of mathematics
* Open problems suggest directions for future research
* Provides a survey of current research topics in functional analysis and its applications to quantum physics
* Offers a unique blend of uses of quantum symmetries (in quantum
groups, non-commutative probability and quantum physics)
* Covers a variety of different facets of the modern concept of quantum symmetries
Providing an introduction to current research topics in functional analysis and its
applications to quantum physics, this book presents three lectures surveying recent
progress and open problems.
A special focus is given to the role of symmetry in non-commutative probability, in
the theory of quantum groups, and in quantum physics. The first lecture presents the
close connection between distributional symmetries and independence properties. The
second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum
symmetries are much richer than their classical symmetry groups, and describes the
associated quantum symmetry groups. The last lecture shows how functional analytic and
geometric ideas can be used to detect and to quantify entanglement in high dimensions.
The book will allow graduate students and young researchers to gain a better
understanding of free probability, the theory of compact quantum groups, and
applications of the theory of Banach spaces to quantum information. The latter
applications will also be of interest to theoretical and mathematical physicists working in
quantum theory.
Series: Progress in Mathematical Physics, Vol. 72
1st ed. 2017, Approx. 300 p. Book + eBook.
Hardcover + eBook
ISBN 978-3-319-57408-0
* Provides a detailed description of the theoretical background of BEH mechanism
* Describes the experimental discovery of the H Boson
* New volume of the Poincare series
This volume provides a detailed description of the seminal theoretical construction in
1964, independently by Robert Brout and Francois Englert, and by Peter W. Higgs, of
a mechanism for short-range fundamental interactions, now called the Brout-Englert-
Higgs (BEH) mechanism. It accounts for the non-zero mass of elementary particles and
predicts the existence of a new particle - an elementary massive scalar boson. In addition
to this the book describes the experimental discovery of this fundamental missing
element in the Standard Model of particle physics. The H Boson, also called the Higgs
Boson, was produced and detected in the Large Hadron Collider (LHC) of CERN near
Geneva by two large experimental collaborations, ATLAS and CMS, which announced its
discovery on the 4th of July 2012. This new volume of the Poincare Seminar Series, The
H Boson, corresponds to the nineteenth seminar, held on November 29, 2014, at Institut
Henri Poincare in Paris.
Series: Springer INdAM Series, Vol. 21
250 p. 10 illus.
Hardcover
ISBN 978-3-319-62913-1
* Presents contributions from leading experts and emerging
researchers in the field of complex and symplectic geometry
* Provides up-to-date overviews on current topics in the field
* Provides an excellent introduction to the field, aimed at a wide readership
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was
held in Cortona in June 2016. Several leading specialists, including young researchers, in
the field of complex and symplectic geometry, present the state of the art of their research
on topics such as the cohomology of complex manifolds; analytic techniques in Kahler
and non-Kahler geometry; almost-complex and symplectic structures; special structures
on complex manifolds; and deformations of complex objects. The work is intended for
researchers in these areas.
Series, Functions of Several Variables, and Applications
Series: Undergraduate Texts in Mathematics
V, 447 p. 40 illus.
Hardcover
ISBN 978-1-4939-7367-5
* Corresponds to a second course in real analysis to follow the authors'
book Real Analysis: Foundations and Functions of One Variable
* Motivates ideas and results in analysis by exploring concepts and applications
* Showcases a comprehensive collection of exercises, allowing
students to develop proficiency over a broad range of problems
This book develops the theory of multivariable analysis, building on the single variable
foundations established in the companion volume, Real Analysis: Foundations and
Functions of One Variable. Together, these volumes form the first English edition of the
popular Hungarian original, Valos Analizis I & II, based on courses taught by the authors
at Eotvos Lorand University, Hungary, for more than 30 years. Numerous exercises are
included throughout, offering ample opportunities to master topics by progressing from
routine to difficult problems. Hints or solutions to many of the more challenging exercises
make this book ideal for independent study, or further reading.
Intended as a sequel to a course in single variable analysis, this book builds upon and
expands these ideas into higher dimensions. The modular organization makes this
text adaptable for either a semester or year-long introductory course. Topics include:
differentiation and integration of functions of several variables; infinite numerical series;
sequences and series of functions; and, applications to other areas of mathematics. Many
historical notes are given and there is an emphasis on conceptual understanding and
context, be it within mathematics itself or more broadly in applications, such as physics.
By developing the studentfs intuition throughout, many definitions and results become
motivated by insights from their context.
Series: Probability and Its Applications
1st ed. 2017, Approx. 635 p.
Hardcover
ISBN 978-3-319-62309-2
* Gives a rigorous yet understandable presentation of the theory of stochastic processes
* Presents the theory of distributions of functionals of diffusions
including local times, rarely found in literature
* Devotes serious attention to the Brownian local time
* Includes many examples and exercises
This book provides a rigorous yet accessible introduction to the theory of stochastic
processes. A significant part of the book is devoted to the classic theory of stochastic
processes. In turn, it also presents proofs of well-known results, sometimes together with
new approaches. Moreover, the book explores topics not previously covered elsewhere,
such as distributions of functionals of diffusions stopped at different random times, the
Brownian local time, diffusions with jumps, and an invariance principle for random walks
and local times.
Supported by carefully selected material, the book showcases a wealth of examples that
demonstrate how to solve concrete problems by applying theoretical results. It addresses
a broad range of applications, focusing on concrete computational techniques rather than
on abstract theory. The content presented here is largely self-contained, making it suitable
for researchers and graduate students alike.