90 citations · 731 across the 37 of their papers we have counts for
45 papers
K-theoretic invariants of four three-dimensional operator systems
Walter D. van Suijlekom
We compute -theoretic invariants for four three-dimensional operator systems to illustrate the general theory. We find that in some cases the invariants distinguish the operator…
K-theoretic invariants of the Toeplitz operator system and its dual, and of all graph operator systems
Walter D. van Suijlekom
We compute -theoretic invariants for several finite-dimensional operator systems. These include the Toeplitz operator system and its dual (the Fejér-Riesz operator system), as w…
Particle Creation in a Cosmological Background in Analogy to the Schwinger Effect
Walter D. van Suijlekom, Michael F. Wondrak, Heino Falcke
We consider a gravitational analogue of the Schwinger effect in a cosmological context. While the Schwinger effect is usually attributed to a static electric background, its deriva…
Convergence of spectral truncations for compact metric groups
Yvann Gaudillot-Estrada, Walter D. van Suijlekom
We consider Gromov-Hausdorff convergence of state spaces for spectral truncations of a compact metric group . We work in the context of order-unit spaces and consider orthogonal…
Reply to "Comment on 'Gravitational Pair Production and Black Hole Evaporation'"
Michael F. Wondrak, Walter D. van Suijlekom, Heino Falcke
In a recent letter, the authors presented a unified derivation of the electric Schwinger effect and a generalized Hawking effect with an additional radiation component. The approac…
Gravitational Pair Production and Black Hole Evaporation
Michael F. Wondrak, Walter D. van Suijlekom, Heino Falcke
We present a new avenue to black hole evaporation using a heat-kernel approach analogous as for the Schwinger effect. Applying this method to an uncharged massless scalar field in…
Gromov--Hausdorff Convergence of Spectral Truncations for Tori
Malte Leimbach, Walter D. van Suijlekom
We consider operator systems associated to spectral truncations of tori. We show that their state spaces, when equipped with the Connes distance function, converge in the Gromov--H…
Riemannian embeddings in codimension one as unbounded -cycles
Walter D. van Suijlekom, Luuk S. Verhoeven
Given a codimension one Riemannian embedding of Riemannian spin-manifolds we construct a family of unbounded -cycles from $C(…
Noncommutativity and Physics: A non-technical review
Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting…
Operator systems for tolerance relations on finite sets
Mick Gielen, Walter D. van Suijlekom
We study the duals of a certain class of finite-dimensional operator systems, namely the class of operator systems associated to tolerance relations on finite sets or equivalently…
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,…
A survey of spectral models of gravity coupled to matter
Ali H. Chamseddine, Walter D. van Suijlekom
This is a survey of the historical development of the Spectral Standard Model and beyond, starting with the ground breaking paper of Alain Connes in 1988 where he observed that the…
Entropy and the spectral action
Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom
We compute the information theoretic von Neumann entropy of the state associated to the fermionic second quantization of a spectral triple. We show that this entropy is given by th…
Reflection positivity in higher derivative scalar theories
Francesca Arici, Daniel Becker, Chris Ripken +2
Reflection positivity constitutes an integral prerequisite in the Osterwalder-Schrader reconstruction theorem which relates quantum field theories defined on Euclidean space to the…
Reduction of quantum systems and the local Gauss law
Ruben Stienstra, Walter D. van Suijlekom
We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated to the elements of the Lie algebra of a Lie group that implem…
Quantum lattice gauge fields and groupoid C*-algebras
Francesca Arici, Ruben Stienstra, Walter D. van Suijlekom
We present an operator-algebraic approach to the quantization and reduction of lattice field theories. Our approach uses groupoid C*-algebras to describe the observables and exploi…
Riemannian submersions and factorization of Dirac operators
Jens Kaad, Walter D. van Suijlekom
We establish the factorization of Dirac operators on Riemannian submersions of compact spin manifolds in unbounded KK-theory. More precisely, we show that the Dirac operator on…
Noncommutative geometry and the BV formalism: application to a matrix model
Roberta A. Iseppi, Walter D. van Suijlekom
We analyze a U(2)-matrix model derived from a finite spectral triple. By applying the BV formalism, we find a general solution to the classical master equation. To describe the BV…
Quantization commutes with singular reduction: cotangent bundles of compact Lie groups
Jord Boeijink, Klaas Landsman, Walter van Suijlekom
We analyse the `quantization commutes with reduction' problem (first studied in physics by Dirac, and known in the mathematical literature also as the Guillemin-Sternberg Conjectur…
Grand Unification in the Spectral Pati-Salam Model
Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom
We analyze the running at one-loop of the gauge couplings in the spectral Pati-Salam model that was derived in the framework of noncommutative geometry. There are a few different s…
Localizing gauge theories from noncommutative geometry
Walter D. van Suijlekom
We recall the emergence of a generalized gauge theory from a noncommutative Riemannian spin manifold, viz. a real spectral triple . This includes a gauge group determine…
Perturbation semigroup of matrix algebras
Niels Neumann, Walter D. van Suijlekom
In this article we analyze the structure of the semigroup of inner perturbations in noncommutative geometry. This perturbation semigroup is associated to a unital associative *-alg…
Supersymmetry and noncommutative geometry Part III: The noncommutative supersymmetric Standard Model
Wim Beenakker, Walter D. van Suijlekom, Thijs van den Broek
In a previous paper we developed a formalism to construct (potentially) supersymmetric theories in the context of noncommutative geometry. We apply this formalism to explore the ex…