%0 Journal Article
%J Phys. Lett. B 297 (1992) 82-88
%D 1992
%T Topological \\\"observables\\\" in semiclassical field theories
%A Margherita Nolasco
%A Cesare Reina
%X We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\\\\cal M}$. The standard examples are of course Yang-Mills theory and non-linear $\\\\sigma$-models. The relevant space here is a family of measure spaces $\\\\tilde {\\\\cal N} \\\\ra {\\\\cal M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to ${\\\\cal M}$ in the space of smooth fields. Over $\\\\tilde {\\\\cal N}$ there is a probability measure $d\\\\mu$ given by the twisted product of the (normalized) volume element on ${\\\\cal M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\\\\phi$ in the background of an instanton $\\\\phi \\\\in {\\\\cal M}$. The space of \\\"observables\\\", i.e. measurable functions on ($\\\\tilde {\\\\cal N}, \\\\, d\\\\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on ${\\\\cal M}$. 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.
%B Phys. Lett. B 297 (1992) 82-88
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/3541
%1 1160
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-24T09:45:37Z\\nNo. of bitstreams: 1\\n9209096v1.pdf: 142343 bytes, checksum: 14465c321b35b3996ff40101c331960b (MD5)
%R 10.1016/0370-2693(92)91073-I