Letters in Mathematical Physics

, Volume 81, Issue 1, pp 41–59 | Cite as

Semi-Classical Quantum Fields Theories and Frobenius Manifolds

  • Jae-Suk Park


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.

Mathematics Subject Classification (2000)

81T70 58H15 


Quantum fields theory BV quantization special coordinates Frobenius manifold 


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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Department of MathematicsYonsei UniversitySeoulSouth Korea

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