eTextbook: The Decomposition of Global Conformal Invariants (AM-182)

Book Jacket Image

List Price 1: $75.00

eTextbook Purchase: $60.00

You save $15.00

Are you a school looking to buy multiple copies of this book?

  • Free Book Promotion

    For a limited time, this book is eligible for free.

    Click here to redeem the Facebook Offer

    Author(s): Alexakis, Spyros

    ISBN 10: 0691153485. See all ISBN's

    ISBN 13: 9780691153483

    Edition:

    Publisher: Princeton University Press

    This is an eTextbook Learn More

    Description:

    This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Deser and Schwimmer asserted that the Riemannian scalar must be a linear combination of three obvious candidates, each of which clearly satisfies the required property: a local conformal invariant, a divergence of a Riemannian vector field, and the Chern-Gauss-Bonnet integrand. This book provides a proof of this conjecture.

    The result itself sheds light on the algebraic structure of conformal anomalies, which appear in many settings in theoretical physics. It also clarifies the geometric significance of the renormalized volume of asymptotically hyperbolic Einstein manifolds. The methods introduced here make an interesting connection between algebraic properties of local invariants--such as the classical Riemannian invariants and the more recently studied conformal invariants--and the study of global invariants, in this case conformally invariant integrals. Key tools used to establish this connection include the Fefferman-Graham ambient metric and the author's super divergence formula.

    All ISBN's for this title:

    ISBN 10: 0691153485, ISBN 13: 9780691153483, eISBN 10: 1400842727, eISBN 13: 9781400842728

    1. List price can refer to either the digital or print list price, whichever is available to Kno.
  • Cool Product Features

    Kno In Action

    Search

    Journal

    Flashcards

    Kno Me

    Smart Links