174 research outputs found
Spectral Torsion
We introduce a trilinear functional of differential one-forms for a finitely
summable regular spectral triple with a noncommutative residue. We demonstrate
that for a canonical spectral triple over a spin manifold it recovers the
torsion of the linear connection. We examine several spectral triples,
including Hodge-de\,Rham, Einstein-Yang-Mills, almost-commutative two-sheeted
space, conformally rescaled noncommutative tori, and quantum group,
showing that the third one has a nonvanishing torsion if nontrivially coupled
Spectral action and the electroweak -terms for the Standard Model without fermion doubling
We compute the leading terms of the spectral action for a noncommutative
geometry model that has no fermion doubling. The spectral triple describing it,
which is chiral and allows for CP-symmetry breaking, has the Dirac operator
that is not of the product type. Using Wick rotation we derive explicitly the
Lagrangian of the model from the spectral action for a flat metric,
demonstrating the appearance of the topological -terms for the
electroweak gauge fields.Comment: 26 page
Spectral Metric and Einstein Functionals for Hodge-Dirac operator
We examine the metric and Einstein bilinear functionals of differential forms
introduced in Adv.Math.,Vol.427,(2023)1091286, for Hodge-Dirac operator
on an oriented even-dimensional Riemannian manifold. We show that
they reproduce these functionals for the canonical Dirac operator on a spin
manifold up to a numerical factor. Furthermore, we demonstrate that the
associated spectral triple is spectrally closed, which implies that it is
torsion-free.Comment: Final versio
Riemannian Geometry of a Discretized Circle and Torus
We extend the results of Riemannian geometry over finite groups and provide a
full classification of all linear connections for the minimal noncommutative
differential calculus over a finite cyclic group. We solve the torsion-free and
metric compatibility condition in general and show that there are several
classes of solutions, out of which only special ones are compatible with a
metric that gives a Hilbert -module structure on the space of the
one-forms. We compute curvature and scalar curvature for these metrics and find
their continuous limits
Pseudo-Riemannian Structures in Pati-Salam models
We discuss the role of the pseudo-Riemannian structure of the finite spectral
triple for the family of Pati-Salam models. We argue that its existence is a
very restrictive condition that separates leptons from quarks, and restricts
the whole family of Pati-Salam models into the class of generalized Left-Right
Symmetric Models
Effect of microstructure on properties of MgB 2 synthesized by SHS method
Abstract MgB 2 samples were obtained by self-propagating high-temperature synthesis (SHS). Microstructure, phase and chemical analysis of the samples were studied by XRD and cross-sectional TEM-SAD. MgB 2 samples contained very small uniformly distributed MgO particles. Temperature dependence of the upper critical field and of the critical current densities were determined from ac magnetic susceptibility measurements. Normal metallic state was characterised by measurements of valence band structure by ultraviolet photoelectron spectroscopy (ARUPS). We concluded that MgB 2 is a hard II type superconductor and that SHS method is suitable to fabricate material with strong pinning centers of MgO
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