Authors:Lucio S. Cirio et al Abstract: Reviews in Mathematical Physics, Ahead of Print.
We elaborate on the quantization of toric varieties by combining techniques from toric geometry, isospectral deformations and noncommutative geometry in braided monoidal categories, and the construction of instantons thereon by combining methods from noncommutative algebraic geometry and a quantized twistor theory. We classify the real structures on a toric noncommutative deformation of the Klein quadric and use this to derive a new noncommutative four-sphere which is the unique deformation compatible with the noncommutative twistor correspondence. We extend the computation of equivariant instanton partition functions to noncommutative gauge theories with both adjoint and fundamental matter fields, finding agreement with the classical results in all instances. We construct moduli spaces of noncommutative vortices from the moduli of invariant instantons, and derive corresponding equivariant partition functions which also agree with those of the classical limit. PubDate: Wed, 10 Sep 2014 02:52:09 GMT

Authors:Jean-Marie Barbaroux et al Abstract: Reviews in Mathematical Physics, Volume 26, Issue 08, September 2014.
The hydrogen binding energy in the Pauli–Fierz model with the spin Zeeman term is determined up to the order α3, where α denotes the fine-structure constant. PubDate: Tue, 09 Sep 2014 04:16:26 GMT

Authors:Nicolas Franco Abstract: Reviews in Mathematical Physics, Ahead of Print.
We present the notion of temporal Lorentzian spectral triple which is an extension of the notion of pseudo-Riemannian spectral triple with a way to ensure that the signature of the metric is Lorentzian. A temporal Lorentzian spectral triple corresponds to a specific 3 + 1 decomposition of a possibly noncommutative Lorentzian space. This structure introduces a notion of global time in noncommutative geometry. As an example, we construct a temporal Lorentzian spectral triple over a Moyal–Minkowski spacetime. We show that, when time is commutative, the algebra can be extended to unbounded elements. Using such an extension, it is possible to define a Lorentzian distance formula between pure states with a well-defined noncommutative formulation. PubDate: Wed, 20 Aug 2014 10:30:21 GMT

Authors:Jussi Behrndt et al Abstract: Reviews in Mathematical Physics, Ahead of Print.
We investigate Schrödinger operators with δ- and δ'-interactions supported on hypersurfaces, which separate the Euclidean space into finitely many bounded and unbounded Lipschitz domains. It turns out that the combinatorial properties of the partition and the spectral properties of the corresponding operators are related. As the main result, we prove an operator inequality for the Schrödinger operators with δ- and δ'-interactions which is based on an optimal coloring and involves the chromatic number of the partition. This inequality implies various relations for the spectra of the Schrödinger operators and, in particular, it allows to transform known results for Schrödinger operators with δ-interactions to Schrödinger operators with δ′-interactions. PubDate: Thu, 31 Jul 2014 08:36:35 GMT