Mathematical Physics in Mathematics and Physics: Quantum and Operator Algebraic Aspects(Fields Institute Communications)

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.

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