In this paper we show that the Breitenlohner-Maison prescription for treating the presence of chiral symmetry in Dimensional Regularization fits remarkably well with the framework of noncommutative geometry. In fact, it corresponds to taking the cup product of spectral triples, with a specific spectral triple Xz whose dimension spectrum is a single complex number z. We give a realization of Xz ...

Spectral shaping of an all-fiber torsional acousto-optic (AO) tunable filter is studied. The technique is based on the axial modulation of AO coupling strength along a highly birefringent optical fiber, which is achieved by tailoring the outer diameter of the fiber along its propagation axis. Two kinds of filter spectral shaping schemes-Gaussian apodization and matched filtering with triple res...

We explain how a simple twisting of the notion of spectral triple allows to incorporate type III examples, such as those arising from the transverse geometry of codi-mension one foliations. We show that the classical cyclic cohomology valued Chern character of finitely summable spectral triples extends to the twisted case and lands in ordinary (un-twisted) cyclic cohomology. The index pairing w...

Given a free action of compact Lie group G on unital C?-algebra A and spectral triple the corresponding fixed point algebra AG, we present systematic in-depth construction that is build upon geometry AG G. We compare our with selection established examples.

The quantum version of the Bernstein–Gelfand–Gelfand resolution is used to construct a Dolbeault–Dirac operator on anti-holomorphic forms Heckenberger–Kolb calculus for B $${}_2$$ -irreducible flag manifold. spectrum and multiplicities eigenvalues are computed. It shown that this construction yields an equivariant, even, 0 $${}^+$$ -summable spectral triple.

A general formula and a computational scheme for estimating the power spectrum of the displacement correlation function of suspended test masses such as those used in interferometric gravitational wave detectors are presented. Unlike previous mode-summation approaches, the fluctuation-dissipation theorem has been applied directly to the displacement correlation. The resulting formula expresses ...

The two point angular correlation function is an excellent measure of structure in the universe. To extract from it the three dimensional power spectrum, one must invert Limber’s Equation. Here we perform this inversion using a Bayesian prior constraining the smoothness of the power spectrum. Among other virtues, this technique allows for the possibility that the estimates of the angular correl...

In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the “closed fibers at infinity”. Manin described the dual graph of any such closed fiber in terms of an infinite tangle of bounded geodesics in a hyperbolic handlebody endowed with a Schottky uniformization. In this paper we consider arithmetic surfaces over t...

We generalize the notion of spectral triple with reality structure to triples multitwisted real structure, class which is closed under tensor product composition. In particular, we introduce a first-order condition (characterizing Dirac operators as an analogue differential operator). This provides unified description known examples, include rescaled conformal factor from commutant algebra and ...