We give a geometrical set-up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces M. The standard examples are of course Yang-Mills theory and non-linear σ-models. The relevant space here is a family of measure spaces N ̃→M, with standard fibre a distribution space, given by a suitable extension of the normal bundle to M in the space of the smooth fields. Over N ̃ there is a probability measure dμ given by the twisted product of the (normalized) volume element on M and the family of gaussian measures with covariance given by the tree propagator Cφ in the background of an instanton φεlunateM. The space of "observables", i.e., measurable functions on ( N ̃, dμ), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on 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. © 1992.

Topological "observables" in semiclassical field theories / Nolasco, M.; Reina, Cesare. - In: PHYSICS LETTERS. SECTION B. - ISSN 0370-2693. - 297:1-2(1992), pp. 82-88. [10.1016/0370-2693(92)91073-I]

Topological "observables" in semiclassical field theories

Reina, Cesare
1992-01-01

Abstract

We give a geometrical set-up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces M. The standard examples are of course Yang-Mills theory and non-linear σ-models. The relevant space here is a family of measure spaces N ̃→M, with standard fibre a distribution space, given by a suitable extension of the normal bundle to M in the space of the smooth fields. Over N ̃ there is a probability measure dμ given by the twisted product of the (normalized) volume element on M and the family of gaussian measures with covariance given by the tree propagator Cφ in the background of an instanton φεlunateM. The space of "observables", i.e., measurable functions on ( N ̃, dμ), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on 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. © 1992.
1992
297
1-2
82
88
https://arxiv.org/abs/hep-th/9209096
Nolasco, M.; Reina, Cesare
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/59685
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