Eur. Phys. J. C (2019) 79: 837
https://doi.org/10.1140/epjc/s10052-019-7322-2

Regular Article - Theoretical Physics

Extracting topological information from momentum space propagators

¹ Centro de Estudios Científicos (CECs), Casilla, 1469, Valdivia, Chile
² Department of Physics, KU Leuven Campus Kortrijk–Kulak, Etienne Sabbelaan 53 Bus 7657, 8500, Kortrijk, Belgium
³ Ghent University, Department of Physics and Astronomy, Krijgslaan 281-S9, 9000, Ghent, Belgium
⁴ Universidad Austral de Chile (UACh), Campus Isla Teja, Ed. Emilio Pugin, Valdivia, Chile
⁵ Instituto de Física, Universidade Federal Fluminense, Av. Litoranea s/n, 24210-346, Niterói, RJ, Brasil
⁶ Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000, Prague 8, Czech Republic
⁷ Institute of Physics of the ASCR, ELI Beamlines Project, Na Slovance 2, 18221, Prague, Czech Republic
⁸ Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Universitá di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Naples, Italy
⁹ INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Naples, Italy

^* e-mail: pais@ipnp.troja.mff.cuni.cz

Received: 24 July 2019
Accepted: 18 September 2019
Published online: 10 October 2019

Abstract

A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.