12 citations · 29 across the 12 of their papers we have counts for
13 papers
Power counting in the spectral action matrix model
Eva-Maria Hekkelman, Teun D. H. van Nuland, Jesse Reimann
We derive power counting formulas for ribbon graph amplitudes that were recently independently discovered in two contexts, namely as a generalization of the Kontsevich model, and a…
Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions
Eva-Maria Hekkelman, Edward McDonald, Teun D. H. van Nuland
We push the definition of multiple operator integrals (MOIs) into the realm of unbounded operators, using the pseudodifferential calculus from the works of Connes and Moscovici, Hi…
Differentiation, Taylor series, and all order spectral shift functions, for relatively bounded perturbations
Arup Chattopadhyay, Teun D. H. van Nuland, Chandan Pradhan
Given self-adjoint, symmetric and relatively -bounded, and satisfying mild conditions, we show that the Gateaux derivative $$\frac{d^n}{dt^n}…
The basic resolvents of position and momentum operators form a total set in the resolvent algebra
Detlev Buchholz, Teun D. H. van Nuland
Let Q and P be the position and momentum operators of a particle in one dimension. It is shown that all compact operators can be approximated in norm by linear combinations of the…
Classical dynamics of infinite particle systems in an operator algebraic framework
T. D. H. van Nuland, C. J. F. van de Ven
We construct C*-dynamical systems for the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, a…
Noncompact uniform universal approximation
Teun D. H. van Nuland
The universal approximation theorem is generalised to uniform convergence on the (noncompact) input space . All continuous functions that vanish at infinity can be un…
Local invariants of conformally deformed non-commutative tori II: multiple operator integrals
Teun D. H. van Nuland, Fedor Sukochev, Dmitriy Zanin
We explicitly compute the local invariants (heat kernel coefficients) of a conformally deformed non-commutative -torus using multiple operator integrals. We derive a recursive f…
C*-algebraic results in the search for quantum gauge fields
Teun D. H. van Nuland
This thesis consists of two parts, both situated in operator theory, and both motivated by the quest for rigorous quantizations of gauge theories. The first part is based on [Skrip…
Strict deformation quantization of abelian lattice gauge fields
T. D. H. van Nuland
This paper shows how to construct classical and quantum field C*-algebras modeling a -gauge theory in any dimension using a novel approach to lattice gauge theory, while si…
One-loop corrections to the spectral action
Teun D. H. van Nuland, Walter D. van Suijlekom
We analyze the perturbative quantization of the spectral action in noncommutative geometry and establish its one-loop renormalizability in a generalized sense, while staying within…
Cyclic cocycles in the spectral action
Teun D. H. van Nuland, Walter D. van Suijlekom
We show that the spectral action, when perturbed by a gauge potential, can be written as a series of Chern--Simons actions and Yang--Mills actions of all orders. In the odd orders,…
Spectral shift for relative Schatten class perturbations
Teun D. H. van Nuland, Anna Skripka
We affirmatively settle the question on existence of a real-valued higher order spectral shift function for a pair of self-adjoint operators and such that is bounded an…
Quantization and the Resolvent Algebra
Teun D. H. van Nuland
We introduce a novel commutative C*-algebra of functions on a symplectic vector space admitting a complex structure, along with a strict deformation quan…