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Mathematical Physics in Mathematics and Physics: Quantum and Operator Algebraic Aspects
Edited by: Roberto Longo, University of Rome II, Italy
A co-publication of the AMS and Fields Institute.

Fields Institute Communications
2001; 451 pp; hardcover
Volume: 30
ISBN-10: 0-8218-2814-2
ISBN-13: 978-0-8218-2814-4
List Price: US$145
Member Price: US$116
Order Code: FIC/30
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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 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).


Graduate students and research mathematicians interested in quantum theory and functional analysis.

Table of Contents

  • H. Baumgärtel and F. Lledó -- An application of the DR-duality theory for compact groups to endomorphism categories of C*-algebras with nontrivial center
  • J. Böckenhauer and D. E. Evans -- Modular invariants and subfactors
  • H. J. Borchers and J. Yngvason -- On the PCT-theorem in the theory of local observables
  • D. Buchholz, J. Mund, and S. J. Summers -- Transplantation of local nets and geometric modular action on Robertson-Walker space-times
  • S. Carpi and R. 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
  • C. D'Antoni and L. Zsidó -- The flat tube theorem for vector valued functions
  • G. Dell'Antonio -- Point interactions
  • M. Dütsch and K. Fredenhagen -- Perturbative algebraic field theory, and deformation quantization
  • F. Guerra -- Sum rules for the free energy in the mean field spin glass model
  • D. Guido and T. Isola -- Fractals in noncommutative geometry
  • R. Haag -- What I woud like to understand
  • M. Izumi -- The Rohlin property for automorphisms of \(C^*\)-algebras
  • G. Jana-Lasinio, C. Presilla, and C. Toninelli -- Environment induced localization and superselection rules in a gas of pyramidal molecules
  • D. Kastler -- Connes-Moscovici-Kreimer Hopf algebras
  • Y. Katayama and M. Takesaki -- The structure of the automorhpism group of an approximately finite dimensional factor
  • Y. Kawahigashi -- Braiding and extensions of endomrophisms of subfactors
  • N. P. Landsman -- Bicategories of operator algebras and Poisson manifolds
  • R. Longo -- Notes for a quantum index theorem introduction
  • M. Müger -- Conformal field theory and Doplicher-Roberts reconstruction
  • S. Popa -- On the distance between MASA's in type II\(_1\) factors
  • R. T. Powers -- Recent results concerning E\(_o\)-semigroups of \(\mathfrak{B}(\mathfrak{H})\)
  • K.-H. Rehren -- Locality and modular invariance in 2D conformal QFT
  • S. Sakai -- Tensor products of Banach spaces and the Stone-Weierstrass problem of \(C^*\)-algebras
  • R. Schrader -- Perron-Frobenius theory for positive maps on trace ideals
  • B. Schroer -- Space- and time-like superselection rules in conformal quantum field theory
  • K. Szlachányi -- Finite quantum groupoids and inclusions of finite type
  • R. Verch -- On generalizations of the spectrum condition
  • F. Xu -- Algebraic orbifold conformal field theories
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