90 citations · 731 across the 37 of their papers we have counts for
14 papers · 1 filter
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…
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…
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…
Inner Fluctuations in Noncommutative Geometry without the first order condition
Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom
We extend inner fluctuations to spectral triples that do not fulfill the first-order condition. This involves the addition of a quadratic term to the usual linear terms. We find a…
Gauge networks in noncommutative geometry
Matilde Marcolli, Walter D. van Suijlekom
We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo…
Moduli Spaces of Instantons on Toric Noncommutative Manifolds
Simon Brain, Giovanni Landi, Walter D. van Suijlekom
We study analytic aspects of U(n) gauge theory over a toric noncommutative manifold . We analyse moduli spaces of solutions to the self-dual Yang-Mills equations on U(2) vecto…
Renormalization of the asymptotically expanded Yang-Mills spectral action
Walter D. van Suijlekom
We study renormalizability aspects of the spectral action for the Yang-Mills system on a flat 4-dimensional background manifold, focusing on its asymptotic expansion. Interpreting…
Electrodynamics from Noncommutative Geometry
Koen van den Dungen, Walter D. van Suijlekom
Within the framework of Connes' noncommutative geometry, the notion of an almost commutative manifold can be used to describe field theories on compact Riemannian spin manifolds. T…
The noncommutative geometry of Yang-Mills fields
Jord Boeijink, Walter D. van Suijlekom
We generalize to topologically non-trivial gauge configurations the description of the Einstein-Yang-Mills system in terms of a noncommutative manifold, as was done previously by C…
The ADHM Construction of Instantons on Noncommutative Spaces
Simon Brain, Walter D. van Suijlekom
We present an account of the ADHM construction of instantons on Euclidean space-time from the point of view of noncommutative geometry. We recall the main ingredient…
The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras
Walter D. van Suijlekom
We study the structure of renormalization Hopf algebras of gauge theories. We identify certain Hopf subalgebras in them, whose character groups are semidirect products of invertibl…