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Hardcover ISBN:  9780821828144 
Product Code:  FIC/30 
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Hardcover ISBN:  9780821828144 
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Book DetailsFields Institute CommunicationsVolume: 30; 2001; 451 ppMSC: Primary 81; 46; Secondary 47;
The beauty and the mystery surrounding the interplay between mathematics and physics is captured by E. Wigner's famous expression, “The unreasonable effectiveness of mathematics”. We don't know why, but physical laws are described by mathematics, and good mathematics sooner or later finds applications in physics, often in a surprising way.
In this sense, mathematical physics is a very old subject—as Egyptian, Phoenician, or Greek history tells us. But mathematical physics is a very modern subject, as any working mathematician or physicist can witness. It is a challenging discipline that has to provide results of interest for both mathematics and physics. Ideas and motivations from both these sciences give it a vitality and freshness that is difficult to find anywhere else.
One of the big physical revolutions in the twentieth century, quantum physics, opened a new magnificent era for this interplay. With the appearance of noncommutative analysis, the role of classical calculus has been taken by commutation relations, a subject still growing in an astonishing way.
A good example where mathematical physics showed its power, beauty, and interdisciplinary character is the DoplicherHaagRoberts analysis of superselection sectors in the late 1960s. Not only did this theory explain the origin of statistics and classify it, but year after year, new connections have merged, for example with TomitaTakesaki modular theory, Jones theory of subfactors, and DoplicherRoberts abstract duality for compact groups.
This volume contains the proceedings of the conference, “Mathematical Physics in Mathematics and Physics”, dedicated to Sergio Doplicher and John E. Roberts held in Siena, Italy. The articles offer current research in various fields of mathematical physics, primarily concerning quantum aspects of operator algebras.ReadershipGraduate students and research mathematicians interested in quantum theory and functional analysis.

Table of Contents

Chapters

Hellmut Baumgärtel and Fernando Lledó  An application of the DRduality theory for compact groups to endomorphism categories of C*algebras with nontrivial center

Jens Böckenhauer and David Evans  Modular invariants and subfactors

H. Borchers and J. Yngvason  On the PCTtheorem in the theory of local observables

Detlev Buchholz, Jens Mund and Stephen Summers  Transplantation of local nets and geometric modular action on RobertsonWalker spacetimes

Sebastiano Carpi and Roberto Conti  Classification of subsystems, local symmetry generators and intrinsic definition of local observables

A. Connes and D. Kreimer  From local perturbation theory to Hopf and Liealgebras of Feynman graphs

Claudio D’Antoni and László Zsidó  The flat tube theorem for vector valued functions

Gianfausto Dell’Antonio  Point interactions

Michael Dütsch and Klaus Fredenhagen  Perturbative algebraic field theory, and deformation quantization

Francesco Guerra  Sum rules for the free energy in the mean field spin glass model

Daniele Guido and Tommaso Isola  Fractals in noncommutative geometry

Rudolf Haag  What I woud like to understand

Masaki Izumi  The Rohlin property for automorphisms of $C^*$algebras

Giovanni JonaLasinio, Carlo Presilla and Cristina Toninelli  Environment induced localization and superselection rules in a gas of pyramidal molecules

Daniel Kastler  ConnesMoscoviciKreimer Hopf algebras

Yoshikazu Katayama and Masamichi Takesaki  The structure of the automorhpism group of an approximately finite dimensional factor

Yasuyuki Kawahigashi  Braiding and extensions of endomrophisms of subfactors

N. Landsman  Bicategories of operator algebras and Poisson manifolds

Roberto Longo  Notes for a quantum index theorem introduction

Michael Müger  Conformal field theory and DoplicherRoberts reconstruction

Sorin Popa  On the distance between MASA’s in type II$_1$ factors

Robert Powers  Recent results concerning E$_o$semigroups of $\mathfrak {B}(\mathfrak {H})$

K.H. Rehren  Locality and modular invariance in 2D conformal QFT

Shôichiró Sakai  Tensor products of Banach spaces and the StoneWeierstrass problem of $C^*$algebras

Robert Schrader  PerronFrobenius theory for positive maps on trace ideals

Bert Schroer  Space and timelike superselection rules in conformal quantum field theory

Kornél Szlachányi  Finite quantum groupoids and inclusions of finite type

Rainer Verch  On generalizations of the spectrum condition

Feng Xu  Algebraic orbifold conformal field theories


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The beauty and the mystery surrounding the interplay between mathematics and physics is captured by E. Wigner's famous expression, “The unreasonable effectiveness of mathematics”. We don't know why, but physical laws are described by mathematics, and good mathematics sooner or later finds applications in physics, often in a surprising way.
In this sense, mathematical physics is a very old subject—as Egyptian, Phoenician, or Greek history tells us. But mathematical physics is a very modern subject, as any working mathematician or physicist can witness. It is a challenging discipline that has to provide results of interest for both mathematics and physics. Ideas and motivations from both these sciences give it a vitality and freshness that is difficult to find anywhere else.
One of the big physical revolutions in the twentieth century, quantum physics, opened a new magnificent era for this interplay. With the appearance of noncommutative analysis, the role of classical calculus has been taken by commutation relations, a subject still growing in an astonishing way.
A good example where mathematical physics showed its power, beauty, and interdisciplinary character is the DoplicherHaagRoberts analysis of superselection sectors in the late 1960s. Not only did this theory explain the origin of statistics and classify it, but year after year, new connections have merged, for example with TomitaTakesaki modular theory, Jones theory of subfactors, and DoplicherRoberts abstract duality for compact groups.
This volume contains the proceedings of the conference, “Mathematical Physics in Mathematics and Physics”, dedicated to Sergio Doplicher and John E. Roberts held in Siena, Italy. The articles offer current research in various fields of mathematical physics, primarily concerning quantum aspects of operator algebras.
Graduate students and research mathematicians interested in quantum theory and functional analysis.

Chapters

Hellmut Baumgärtel and Fernando Lledó  An application of the DRduality theory for compact groups to endomorphism categories of C*algebras with nontrivial center

Jens Böckenhauer and David Evans  Modular invariants and subfactors

H. Borchers and J. Yngvason  On the PCTtheorem in the theory of local observables

Detlev Buchholz, Jens Mund and Stephen Summers  Transplantation of local nets and geometric modular action on RobertsonWalker spacetimes

Sebastiano Carpi and Roberto Conti  Classification of subsystems, local symmetry generators and intrinsic definition of local observables

A. Connes and D. Kreimer  From local perturbation theory to Hopf and Liealgebras of Feynman graphs

Claudio D’Antoni and László Zsidó  The flat tube theorem for vector valued functions

Gianfausto Dell’Antonio  Point interactions

Michael Dütsch and Klaus Fredenhagen  Perturbative algebraic field theory, and deformation quantization

Francesco Guerra  Sum rules for the free energy in the mean field spin glass model

Daniele Guido and Tommaso Isola  Fractals in noncommutative geometry

Rudolf Haag  What I woud like to understand

Masaki Izumi  The Rohlin property for automorphisms of $C^*$algebras

Giovanni JonaLasinio, Carlo Presilla and Cristina Toninelli  Environment induced localization and superselection rules in a gas of pyramidal molecules

Daniel Kastler  ConnesMoscoviciKreimer Hopf algebras

Yoshikazu Katayama and Masamichi Takesaki  The structure of the automorhpism group of an approximately finite dimensional factor

Yasuyuki Kawahigashi  Braiding and extensions of endomrophisms of subfactors

N. Landsman  Bicategories of operator algebras and Poisson manifolds

Roberto Longo  Notes for a quantum index theorem introduction

Michael Müger  Conformal field theory and DoplicherRoberts reconstruction

Sorin Popa  On the distance between MASA’s in type II$_1$ factors

Robert Powers  Recent results concerning E$_o$semigroups of $\mathfrak {B}(\mathfrak {H})$

K.H. Rehren  Locality and modular invariance in 2D conformal QFT

Shôichiró Sakai  Tensor products of Banach spaces and the StoneWeierstrass problem of $C^*$algebras

Robert Schrader  PerronFrobenius theory for positive maps on trace ideals

Bert Schroer  Space and timelike superselection rules in conformal quantum field theory

Kornél Szlachányi  Finite quantum groupoids and inclusions of finite type

Rainer Verch  On generalizations of the spectrum condition

Feng Xu  Algebraic orbifold conformal field theories