Cyclic cocycles from graded KMS functionals

TL;DR: In this article, the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spec- tral geometries from an operational formalism of states and categories of observables in a covariant theory is presented.

TL;DR: In this paper, a simple supersymmetric chiral field theory of a free Fermi and Bose field defined on $\R$ is analyzed, and it is shown that a meaningful C*-version of this model can be based on the tensor product of a CAR-algebra and a novel version of a CCR- algebra, the resolvent algebra.

TL;DR: In this article, a panoramic view of the current research program on the use of categorical methods in the setting of A.Connes' non-commutative geometry: morphisms/categories of spectral triples, categorification of Gel'fand duality.

TL;DR: In this paper, the Chern character in the equivariant entire cyclic cohomology was constructed and a general index theorem for the G-invariant Dirae operator was proved.

TL;DR: In this paper, the authors present an algebraic description of the chemical potential for a general compact gauge groupG, as a first step in the classification of thermodynamical equilibrium states of a given temperature.

TL;DR: In this paper, the authors used constructive field theory to generalize index theory to an infinite-dimensional setting and proved the first index theorem for a Dirac operator that couples infinitely many degrees of freedom.