algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
In perturbative quantum field theory a tadpole is a contribution to the S-matrix/scattering amplitude corresponding to a Feynman diagram which contains an edge that connects some vertex with itself.
Typically tadpoles are required to be absent. For instance the construction of time-ordered products in causal perturbation theory via the “star product” induced by the Feynman propagator (see there) implies that tadpoles are absent.
Discussion in context of causal perturbation theory/perturbative AQFT is in
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