1,721,047 research outputs found
A free particle in noncommutative space-time
No full textBy examining some known wave equations it is shown that the dynamics of a free quantum particle in a slightly noncommutative space-time is equivalent to that of a charged particle moving in a self-generated (weak) electromagnetic field
Gauge transformations of spectral triples with twisted real structures
No full textTwisted real structures are well-motivated as a way to implement the conformal transformation of a Dirac operator for a real spectral triple without needing to twist the noncommutative one-forms. We study the coupling of spectral triples with twisted real structures to gauge fields, adopting Morita equivalence via modules and bimodules as a guiding principle and paying special attention to modifications to the inner fluctuations of the Dirac operator. In particular, we analyze the twisted first-order condition as a possible alternative to abandoning the first-order condition in order to go beyond the standard model and elaborate upon the special case of gauge transformations accordingly. Applying the formalism to a toy model, we argue that under certain physically motivated assumptions, the spectral triple based on the left–right symmetric algebra should reduce to that of the standard model of fundamental particles and interactions, as in the untwisted case.
Abstract algebra, Noncommutative geometry, Operator theory, C*-algebra, Beyond the Standard Model, Standard Model, Gauge theory, Hilbert spac
Spin geometry of the rational noncommutative torus
Full text linkWe discuss the structure of topologically non-trivial almost-commutative manifold for spectral triples realized on the algebra of smooth functions on the noncommutative torus with rational parameter. This is done by showing isomorphisms with a spectral triple on the algebra of sections of certain bundle of algebras, and with a spectral triple on a certain invariant subalgebra of the product algebra. The isomorphisms intertwine also the grading and real structure. This holds for all four inequivalent spin structures, which are explicitly constructed in terms of double coverings of the noncommutative torus (with arbitrary real parameter). These results are extended also to a class of curved (non flat)spectral triples, obtained as a perturbation of the standard one by eight central elements
The Bestvina-Edwards theorem and the Hilbert-Smith conjecture
No full textWe prove a number of results surrounding the Borsuk-Ulam-type conjecture of Baum, Dabrowski, and Hajac (BDH, for short), which states that given a free action of a compact group G on a compact space X, there are no G-equivariant maps X * G -> X (with * denoting the topological join). Mainly, we prove the BDH conjecture for locally trivial principal G-bundles. The proof relies on the nonexistence of G-equivariant maps G*(n+1) -> G*n, which in turn is a strengthening of an unpublished result of Bestvina and Edwards. Moreover, we show that the BDH conjecture partially settles a conjecture of Ageev which implies the weak version of the Hilbert-Smith conjecture stating that no infinite compact zero-dimensional group can act freely on a manifold so that the orbit space is finite-dimensional
Time-dependent propagator with point interaction
No full textWe compute the time-dependent Schrodinger propagator with a point interaction in dimension n less-than-or-equal-to 3 including the new cases of n = 2 and the most general interaction supported by a point for n = 1. We also give the small-time asymptotics for n less-than-or-equal-to 3. The case n = 2 has the peculiarity of involving logarithmic terms in the expansion
Twisted Reality and the Second-Order Condition
No full textAn interesting feature of the finite-dimensional real spectral triple (A, H, D, J) of the Standard Model is that it satisfies a "second-order" condition: conjugation by J maps the Clifford algebra Cl-D (A) into its commutant, which in fact is isomorphic to the Clifford algebra itself (H is a self-Morita equivalence Cl-D (A)-bimodule). This resembles a property of the canonical spectral triple of a closed oriented Riemannian manifold: there is a dense subspace of H which is a self-Morita equivalence Cl-D (A)-bimodule. In this paper we argue that on manifolds, in order for the self-Morita equivalence to be implemented by a reality operator J, one has to introduce a "twist" and weaken one of the axioms of real spectral triples. We then investigate how the above mentioned conditions behave under products of spectral triples
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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