2019/10/31 by Yannick Kluth, Daniel F. Litim
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Dimension (graph theory) #Eigenvalues and eigenvectors #Function (biology) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Heat kernel #Kernel (algebra) #Quantum #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1140/epjc/s10052-020-7784-2
published as Eur. Phys. J. C 80, 269 (2020) · 33 pages, v2: results on spectral integrals and analytic continuation added; matches with published version
openalex created_date 2019/10/10 · openalex publication_date 2020/03/01 · arxiv created 2020/07/01 · arxiv updated 2020/07/02 · openalex updated_date 2026/08/05
Abstract We derive all heat kernel coefficients for Laplacians acting on scalars, vectors, and tensors on fully symmetric spaces, in any dimension. Final expressions are easy to evaluate and implement, and confirmed independently using spectral sums and the Euler–Maclaurin formula. We also obtain the Green’s function for Laplacians acting on transverse traceless tensors in any dimension, and new integral representations for heat kernels using known eigenvalue spectra of Laplacians. Applications to quantum gravity and the functional renormalisation group, and other, are indicated.