Soliton fermionic number from the heat kernel expansion

• Published in: The European physical journal. C, Particles and fields Vol. 79; no. 6; pp. 1 - 11
• Main Authors: Alonso-Izquierdo, A., Fresneda, Rodrigo, Guilarte, J. Mateos, Vassilevich, D.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2019; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Astronomy; Astrophysics and Cosmology; Elementary Particles; Fermions; Hadrons; Heavy Ions; Kernels; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Solitary waves; String Theory
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-019-7041-8

We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized
η
function that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multi flavor extension of the Goldstone–Wilczek model. We also propose an improved expansion of the heat kernel that allows the tackling of the convergence issues and permits an automated computation of the coefficients.