Semi-Classical Quantum Fields Theories and Frobenius Manifolds

Details Semi-Classical Quantum Fields Theories and Frobenius Manifolds Semi-Classical Quantum Fields Theories and Frobenius Manifolds

2007-05-10

arxiv.org/abs/0705.1507v1

Lett.Math.Phys.81:41-59,2007

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1007/s11005-007-0165-z

We show that a semi-classical quantum field theory comes with a versal family with the property that the corresponding partition function generates all path integrals and satisfies a system of 2nd order differential equations determined by algebras of classical observables. This versal family gives rise to a notion of special coordinates that is analogous to that in string theories. We also show that for a large class of semi-classical theories, their moduli space has the structure of a Frobenius super-manifold.

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