Double field theory algebroid and curved <i>L</i>_<i>∞</i>-algebras

Quantum Field Theory in Curved Spacetime

We review the mathematically rigorous formulation of the quantum theory of a linear field propagating in a globally hyperbolic spacetime. This formulation is accomplished via the algebraic approach, which, in essence, simultaneously admits all states in all possible (unitarily inequivalent) Hilbert space constructions. The physically nonsingular states are restricted by the requirement that the...

Quantum Field Theory in Curved Spacetime1

OUTLINE These lectures will deal with selected aspects of quantum field theory in curved spacetime [1]. The basic outline of this series of lectures will be as follows: • Lecture 1. Quantization of fields on a curved background, particle creation by gravitational fields, particle creation in an expanding universe; moving mirror radiation. • Lecture 2. The Hawking effect-particle creation by bla...

Quantum Field Theory on Curved Backgrounds

Homotopy Gerstenhaber Algebras and Topological Field Theory

We prove that the BRST complex of a topological conformal field theory is a homotopy Gerstenhaber algebra, as conjectured by Lian and Zuckerman in 1992. We also suggest a refinement of the original conjecture for topological vertex operator algebras. We illustrate the usefulness of our main tools, operads and “string vertices” by obtaining new results on Vassiliev invariants of knots and double...

Operator Algebras and Conformal Field Theory

We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III1 factor. The conformal net determined by the algebras of local observables is proven to satis...