@article {1992,
	title = {Topological "observables" in semiclassical field theories},
	journal = {Phys. Lett. B 297 (1992) 82-88},
	number = {arXiv.org;hep-th/9209096v1},
	year = {1992},
	publisher = {Elsevier},
	abstract = {<p>We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $\sigma$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}}\&nbsp;\rightarrow \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $d\mu$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\phi$ in the background of an instanton $\phi \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, d\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.</p>},
	doi = {10.1016/0370-2693(92)91073-I},
	url = {http://hdl.handle.net/1963/3541},
	author = {Margherita Nolasco and Cesare Reina}
}
