Abstract
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., satisfies a system of second 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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This work was supported by KOSEF Interdisciplinary Research Grant No. R01-2006-000-10638-0.
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Park, JS. Semi-Classical Quantum Fields Theories and Frobenius Manifolds. Lett Math Phys 81, 41–59 (2007). https://doi.org/10.1007/s11005-007-0165-z
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DOI: https://doi.org/10.1007/s11005-007-0165-z