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Mathematical Physics in Mathematics and Physics: Quantum and Operator Algebraic Aspects
 
Edited by: Roberto Longo :  University of Rome II, Rome, Italy
A co-publication of the AMS and Fields Institute
Mathematical Physics in Mathematics and Physics
Hardcover ISBN:  978-0-8218-2814-4
Product Code:  FIC/30
List Price: $162.00
MAA Member Price: $145.80
AMS Member Price: $129.60
eBook ISBN:  978-1-4704-3054-2
Product Code:  FIC/30.E
List Price: $153.00
MAA Member Price: $137.70
AMS Member Price: $122.40
Hardcover ISBN:  978-0-8218-2814-4
eBook: ISBN:  978-1-4704-3054-2
Product Code:  FIC/30.B
List Price: $315.00 $238.50
MAA Member Price: $283.50 $214.65
AMS Member Price: $252.00 $190.80
Add to cart
Mathematical Physics in Mathematics and Physics
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Mathematical Physics in Mathematics and Physics: Quantum and Operator Algebraic Aspects
Edited by: Roberto Longo :  University of Rome II, Rome, Italy
A co-publication of the AMS and Fields Institute
Hardcover ISBN:  978-0-8218-2814-4
Product Code:  FIC/30
List Price: $162.00
MAA Member Price: $145.80
AMS Member Price: $129.60
eBook ISBN:  978-1-4704-3054-2
Product Code:  FIC/30.E
List Price: $153.00
MAA Member Price: $137.70
AMS Member Price: $122.40
Hardcover ISBN:  978-0-8218-2814-4
eBook ISBN:  978-1-4704-3054-2
Product Code:  FIC/30.B
List Price: $315.00 $238.50
MAA Member Price: $283.50 $214.65
AMS Member Price: $252.00 $190.80
Add to cart
  • Book Details
     
     
    Fields Institute Communications
    Volume: 30; 2001; 451 pp
    MSC: 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 Doplicher-Haag-Roberts 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 Tomita-Takesaki modular theory, Jones theory of subfactors, and Doplicher-Roberts 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.

    Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
    Readership

    Graduate students and research mathematicians interested in quantum theory and functional analysis.
  • Table of Contents
     
     
    • Chapters
    • Hellmut Baumgärtel and Fernando Lledó — An application of the DR-duality 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 PCT-theorem in the theory of local observables
    • Detlev Buchholz, Jens Mund and Stephen Summers — Transplantation of local nets and geometric modular action on Robertson-Walker space-times
    • 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 Lie-algebras 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 Jona-Lasinio, Carlo Presilla and Cristina Toninelli — Environment induced localization and superselection rules in a gas of pyramidal molecules
    • Daniel Kastler — Connes-Moscovici-Kreimer 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 Doplicher-Roberts 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 Stone-Weierstrass problem of $C^*$-algebras
    • Robert Schrader — Perron-Frobenius theory for positive maps on trace ideals
    • Bert Schroer — Space- and time-like 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Fields Institute Communications
Volume: 30; 2001; 451 pp
MSC: 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 Doplicher-Haag-Roberts 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 Tomita-Takesaki modular theory, Jones theory of subfactors, and Doplicher-Roberts 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.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Readership

Graduate students and research mathematicians interested in quantum theory and functional analysis.
  • Chapters
  • Hellmut Baumgärtel and Fernando Lledó — An application of the DR-duality 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 PCT-theorem in the theory of local observables
  • Detlev Buchholz, Jens Mund and Stephen Summers — Transplantation of local nets and geometric modular action on Robertson-Walker space-times
  • 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 Lie-algebras 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 Jona-Lasinio, Carlo Presilla and Cristina Toninelli — Environment induced localization and superselection rules in a gas of pyramidal molecules
  • Daniel Kastler — Connes-Moscovici-Kreimer 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 Doplicher-Roberts 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 Stone-Weierstrass problem of $C^*$-algebras
  • Robert Schrader — Perron-Frobenius theory for positive maps on trace ideals
  • Bert Schroer — Space- and time-like 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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