https://doi.org/10.1140/epjc/s10052-020-7784-2
Regular Article - Theoretical Physics
Heat kernel coefficients on the sphere in any dimension
Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH, UK
* e-mail: y.kluth@sussex.ac.uk
Received:
22
November
2019
Accepted:
25
February
2020
Published online:
26
March
2020
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.
© The Author(s), 2020
