57 research outputs found

    Geometry in spectral triples: Immersions and fermionic fuzzy geometries

    Get PDF
    We investigate the metric nature of spectral triples in two ways. Given an oriented Riemannian embedding i:X-\u3eY of codimension 1 we construct a family of unbounded KK-cycles i!(epsilon), each of which represents the shriek class of i in KK-theory. These unbounded KK-cycles are further equipped with connections, allowing for the explicit computation of the products of i! with the spectral triple of Y at the unbounded level. In the limit epsilon to 0 the product of these unbounded KK-cycles with the canonical spectral triple for Y admits an asymptotic expansion. The divergent part of this expansion is known and universal, the constant term in the expansion gives the canonical spectral triple for X. Furthermore, the curvature of these unbounded KK-cycles converges to the square of the mean curvature of X in Y as epsilon goes to 0. We define a random matrix ensemble for the Dirac operator on the (0,1) fuzzy geometry incorporating both the geometric and fermionic aspects of the spectral action. This yields a unitarily invariant, single-matrix multi-trace model. We generalize Coulomb-gas techniques for finding the spectral density of single-trace models to multi-trace models and apply these to our model of a fermionic fuzzy geometry. The resulting Fredholm integral equation for the spectral density is analyzed numerically and the effect of various parameters on the spectral density is investigated

    Gauge Theory of Elementary Particle Physics

    Get PDF
    The aim of this book is to provide student and researcher with a practical introduction to some of the principal ideas in gauge theories and their applications to elementary particle physics. Elementary particle physics has made remarkable progress. We have a comprehensive theory of particle interactions. One can argue that it gives a complete and correct description of all non-gravitational physics. This theory is based on the principle of gauge symmetry. Strong, weak, and electromagnetic interactions are all gauge interactions. A knowledge of gauge theory is essential for anyone interested in modern high energy physics. Regardless of the ultimate correctness of every detail of this theory, it is the framework within which new theoretical and experimental advances will be interpreted in the foreseeable future

    A probabilistic study of linear elliptic-parabolic equations of second order

    Get PDF

    Lie Algebras In Particle Physics

    Get PDF
    In this book, the author convinces that Sir Arthur Stanley Eddington had things a little bit wrong, as least as far as physics is concerned. He explores the theory of groups and Lie algebras and their representations to use group representations as labor-saving tools

    Generalised Sorkin-Johnston and Brum-Fredenhagen States for Quantum Fields on Curved Spacetimes

    Get PDF
    The presented work contains a new construction of a class of distinguished quasifree states for the scalar field and Proca field on globally hyperbolic spacetimes. Our idea is based on the axiomatic construction of the Sorkin-Johnston (SJ) state \cite{Sorkin:2017fcp}; we call these states \emph{generalised SJ states}. We give a concrete application of this framework with the construction of the `thermal' SJ state. By slightly modifying the construction of generalised SJ states, we also introduce a new class of Hadamard states, which we call \emph{generalised SJ states with softened boundaries}. We show when these states satisfy the Hadamard condition and compute the Wick polynomials. Finally we construct the SJ and Brum-Fredenhagen (BF) states for the Proca field on ultrastatic slabs with compact spatial sections. We show that the SJ state construction fails for the Proca field, yet the BF state is well defined and, moreover, satisfies the Hadamard condition

    Limit-point/limit-circle classification for Hain-Lust type equations

    Get PDF
    Hain-Lust equations appear in magnetohydrodynamics. They are Sturm-Liouville equations with coefficients depending rationally on the eigenvalue parameter. In this paper such equations are connected with a 2 x 2 system of differential equations, where the dependence on the eigenvalue parameter is linear. By means of this connection Weyl's fundamental limit-point/limit-circle classification is extended to a general setting of Hain-Lust-type equations

    Abstracts on Radio Direction Finding (1899 - 1995)

    Get PDF
    The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion

    Rosenblatt distribution subordinated to Gaussian fields with long-range dependence

    Get PDF
    The Karhunen-Lo`eve expansion and the Fredholm determinant formula are used, to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of Gaussian stationary random fields on R d displaying long-range dependence. This distribution reduces to the usual Rosenblatt distribution when d = 1. Several properties of this new distribution are obtained. Specifically, its series representation, in terms of independent chi-squared random variables, is established. Its L´evy-Khintchine representation, and membership to the Thorin subclass of self-decomposable distributions are obtained as well. The existence and boundedness of its probability density then follow as a direct consequence
    corecore