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17 papers · 1 filter
Feynman integrals and motives
Matilde Marcolli
This article gives an overview of recent results on the relation between quantum field theory and motives, with an emphasis on two different approaches: a "bottom-up" approach base…
Algebraic Structures in Euclidean and Minkowskian Two-Dimensional Conformal Field Theory
Liang Kong, Ingo Runkel
We review how modular categories, and commutative and non-commutative Frobenius algebras arise in rational conformal field theory. For Euclidean CFT we use an approach based on sew…
The Hilbert Transform of a Measure
Alexei Poltoratski, Barry Simon, Maxim Zinchenko
Let $\fre$ be a homogeneous subset of in the sense of Carleson. Let be a finite positive measure on and its Hilbert transform. We prove that if $\lim_{t\…
Trace Formulas and a Borg-type Theorem for CMV Operators with Matrix-valued Coefficients
Maxim Zinchenko
We prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Velázquez) associated with matrix-valued Verblunsky coef…
Discrete Approximation of Quantum Stochastic Models
Luc Bouten, Ramon van Handel
We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the…
Approximation and limit theorems for quantum stochastic models with unbounded coefficients
Luc Bouten, Ramon van Handel, Andrew Silberfarb
We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theo…