Fields Institute Communications 2001; 451 pp; hardcover Volume: 30 ISBN10: 0821828142 ISBN13: 9780821828144 List Price: US$145 Member Price: US$116 Order Code: FIC/30
 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 subjectas 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. Titles in this series are copublished 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  H. Baumgärtel and F. Lledó  An application of the DRduality 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 PCTtheorem in the theory of local observables
 D. Buchholz, J. Mund, and S. J. Summers  Transplantation of local nets and geometric modular action on RobertsonWalker spacetimes
 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 Liealgebras 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. JanaLasinio, C. Presilla, and C. Toninelli  Environment induced localization and superselection rules in a gas of pyramidal molecules
 D. Kastler  ConnesMoscoviciKreimer 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 DoplicherRoberts 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 StoneWeierstrass problem of \(C^*\)algebras
 R. Schrader  PerronFrobenius theory for positive maps on trace ideals
 B. Schroer  Space and timelike 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
