Nuclearity and Thermal States in Conformal Field Theory

We introduce a new type of spectral density condition, that we call L^2-nuclearity. One formulation concerns lowest weight unitary representations of SL(2,R) and turns out to be equivalent to the existence of characters. A second formulation concerns inclusions of local observable von Neumann algebras in Quantum Field Theory. We show the two formulations to agree in chiral Conformal QFT and, starting from the trace class condition for the semigroup generated by the conformal Hamiltonian L_0, we infer and naturally estimate the Buchholz-Wichmann nuclearity condition and the (distal) split property. As a corollary, if L_0 is log-elliptic, the Buchholz-Junglas set up is realized and so there exists a beta-KMS state for the translation dynamics on the net of C*-algebras for every inverse temperature beta>0. We include further discussions on higher dimensional spacetimes. In particular, we verify that L^2-nuclearity is satisfied for the scalar, massless Klein-Gordon field.Comment: 37 pages, minor correction

Modular Structure and Duality in Conformal Quantum Field Theory

Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge region and the vacuum vector concides with the evolution given by the rescaled pure Lorentz transformations preserving the wedge. A similar geometric description is valid for the algebras associated with double cones. Moreover essential duality holds on the Minkowski space $M$, and Haag duality for double cones holds provided the net of local algebras is extended to a pre-cosheaf on the superworld $\tilde M$, i.e. the universal covering of the Dirac-Weyl compactification of $M$. As a consequence a PCT symmetry exists for any algebraic conformal field theory in even space-time dimension. Analogous results hold for a Poincar\'e covariant theory provided the modular groups corresponding to wedge algebras have the expected geometrical meaning and the split property is satisfied. In particular the Poincar\'e representation is unique in this case.Comment: 23 pages, plain TeX, TVM26-12-199

The Conformal Spin and Statistics Theorem

We prove the equality between the statistics phase and the conformal univalence for a superselection sector with finite index in Conformal Quantum Field Theory on $S^1$. A relevant point is the description of the PCT symmetry and the construction of the global conjugate charge.Comment: plain tex, 22 page

Jorge A. Swieca's contributions to quantum field theory in the 60s and 70s and their relevance in present research

After revisiting some high points of particle physics and QFT of the two decades from 1960 to 1980, I comment on the work by Jorge Andre Swieca. I explain how it fits into the quantum field theory during these two decades and draw attention to its relevance to the ongoing particle physics research. A particular aim of this article is to direct thr readers mindfulness to the relevance of what at the time of Swieca was called "the Schwinger Higgs screening mechanism". which, together with recent ideas which generalize the concept of gauge theories, has all the ingredients to revolutionize the issue of gauge theories and the standard model.Comment: 49 pages, expansion and actualization of text, improvement of formulations and addition of many references to be published in EPJH - Historical Perspectives on Contemporary Physic