43 research outputs found
Modular localization and Wigner particles
We propose a framework for the free field construction of algebras of local
observables which uses as an input the Bisognano-Wichmann relations and a
representation of the Poincare' group on the one-particle Hilbert space. The
abstract real Hilbert subspace version of the Tomita-Takesaki theory enables us
to bypass some limitations of the Wigner formalism by introducing an intrinsic
spacetime localization. Our approach works also for continuous spin
representations to which we associate a net of von Neumann algebras on
spacelike cones with the Reeh-Schlieder property. The positivity of the energy
in the representation turns out to be equivalent to the isotony of the net, in
the spirit of Borchers theorem. Our procedure extends to other spacetimes
homogeneous under a group of geometric transformations as in the case of
conformal symmetries and de Sitter spacetime.Comment: 22 pages, LaTeX. Some errors have been corrected. To appear on Rev.
Math. Phy
Geometric modular action for disjoint intervals and boundary conformal field theory
In suitable states, the modular group of local algebras associated with
unions of disjoint intervals in chiral conformal quantum field theory acts
geometrically. We translate this result into the setting of boundary conformal
QFT and interpret it as a relation between temperature and acceleration. We
also discuss aspects ("mixing" and "charge splitting") of geometric modular
action for unions of disjoint intervals in the vacuum state.Comment: Dedicated to John E. Roberts on the occasion of his 70th birthday; 24
pages, 3 figure