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A new topological invariant quantity, sensitive to the analytic structure ofboth fermionic and bosonic propagators, is proposed. The gauge invariance ofour construct is guaranteed for at least small gauge transformations. Ageneralization compatible with the presence of complex poles is introduced andapplied to the classification of propagators typically emerging fromnon-perturbative considerations. We present partial evidence that thetopological number can be used to detect chiral symmetry breaking ordeconfinement.

Extracting topological information from momentum space propagators