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I don't think these diagrams could correspond to different contributions. Trimok already posted an explanation in the comments, but I think there is an even simpler way to see that the diagrams must be the same: If you write out the expression corresponding to them, the only difference will be the 'placement' of the counterterm factor. However, this is just ...


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Advanced Classical Field Theory (2009) by Giachetta, Mangiarotti, Sardanashvily remarks on p. 248: A non-compact world manifold admits a Dirac spinor structure if and only if it is parallelizable. For a compact world manifold $X$, its Euler characteristic and the second Stiefel-Whitney class $w_2$ must be zero, and its first Pontryagin number ...


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There is no better definition than what Wikipedia offers - in general, a topological excitation is a (field) state, i.e. a localized quantity since fields depend on spacetime, whose integral is a topological invariant. One prime example are Yang-Mills theories in 4D, where the integral $\int \mathrm{Tr}(F\wedge F)$, as essentially the second Chern class of ...



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